id	sid	tid	token	lemma	pos
cana-4165	1	1	communications	communication	NOUN
cana-4165	1	2	on	on	ADP
cana-4165	1	3	applied	apply	VERB
cana-4165	1	4	nonlinear	nonlinear	ADJ
cana-4165	1	5	analysis	analysis	NOUN
cana-4165	1	6	issn	issn	NOUN
cana-4165	1	7	:	:	PUNCT
cana-4165	1	8	1074	1074	NUM
cana-4165	1	9	-	-	PUNCT
cana-4165	1	10	133x	133x	NUM
cana-4165	1	11	vol	vol	NOUN
cana-4165	1	12	32	32	NUM
cana-4165	1	13	no	no	NOUN
cana-4165	1	14	.	.	PUNCT
cana-4165	2	1	9s	9s	NUM
cana-4165	2	2	(	(	PUNCT
cana-4165	2	3	2025	2025	NUM
cana-4165	2	4	)	)	PUNCT
cana-4165	2	5	1388	1388	NUM
cana-4165	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	3	2	asymptotic	asymptotic	ADJ
cana-4165	3	3	expansion	expansion	NOUN
cana-4165	3	4	of	of	ADP
cana-4165	3	5	the	the	DET
cana-4165	3	6	mean	mean	ADJ
cana-4165	3	7	velocities	velocity	NOUN
cana-4165	3	8	of	of	ADP
cana-4165	3	9	the	the	DET
cana-4165	3	10	electrons	electron	NOUN
cana-4165	3	11	deepali	deepali	VERB
cana-4165	3	12	saxena	saxena	PROPN
cana-4165	3	13	department	department	PROPN
cana-4165	3	14	of	of	ADP
cana-4165	3	15	mathematics	mathematics	PROPN
cana-4165	3	16	,	,	PUNCT
cana-4165	3	17	college	college	NOUN
cana-4165	3	18	of	of	ADP
cana-4165	3	19	science	science	PROPN
cana-4165	3	20	,	,	PUNCT
cana-4165	3	21	jazan	jazan	PROPN
cana-4165	3	22	university	university	PROPN
cana-4165	3	23	,	,	PUNCT
cana-4165	3	24	kingdom	kingdom	NOUN
cana-4165	3	25	of	of	ADP
cana-4165	3	26	saudi	saudi	PROPN
cana-4165	3	27	arabia	arabia	PROPN
cana-4165	3	28	dmanilal@jazanu.edu.sa	dmanilal@jazanu.edu.sa	PROPN
cana-4165	3	29	article	article	PROPN
cana-4165	3	30	history	history	NOUN
cana-4165	3	31	:	:	PUNCT
cana-4165	3	32	received	receive	VERB
cana-4165	3	33	:	:	PUNCT
cana-4165	3	34	12	12	NUM
cana-4165	3	35	-	-	SYM
cana-4165	3	36	01	01	NUM
cana-4165	3	37	-	-	PUNCT
cana-4165	3	38	2025	2025	NUM
cana-4165	3	39	revised	revise	VERB
cana-4165	3	40	:	:	PUNCT
cana-4165	3	41	15	15	NUM
cana-4165	3	42	-	-	NUM
cana-4165	3	43	02	02	NUM
cana-4165	3	44	-	-	PUNCT
cana-4165	3	45	2025	2025	NUM
cana-4165	3	46	accepted	accept	VERB
cana-4165	3	47	:	:	PUNCT
cana-4165	3	48	01	01	NUM
cana-4165	3	49	-	-	SYM
cana-4165	3	50	03	03	NUM
cana-4165	3	51	-	-	PUNCT
cana-4165	3	52	2025	2025	NUM
cana-4165	3	53	abstract	abstract	NOUN
cana-4165	3	54	:	:	PUNCT
cana-4165	3	55	with	with	ADP
cana-4165	3	56	special	special	ADJ
cana-4165	3	57	attention	attention	NOUN
cana-4165	3	58	on	on	ADP
cana-4165	3	59	semiconductors	semiconductor	NOUN
cana-4165	3	60	and	and	CCONJ
cana-4165	3	61	low	low	ADJ
cana-4165	3	62	-	-	PUNCT
cana-4165	3	63	dimensional	dimensional	ADJ
cana-4165	3	64	materials	material	NOUN
cana-4165	3	65	,	,	PUNCT
cana-4165	3	66	this	this	DET
cana-4165	3	67	research	research	NOUN
cana-4165	3	68	article	article	NOUN
cana-4165	3	69	explores	explore	VERB
cana-4165	3	70	the	the	DET
cana-4165	3	71	asymptotic	asymptotic	ADJ
cana-4165	3	72	increase	increase	NOUN
cana-4165	3	73	of	of	ADP
cana-4165	3	74	mean	mean	ADJ
cana-4165	3	75	electron	electron	NOUN
cana-4165	3	76	velocities	velocity	NOUN
cana-4165	3	77	in	in	ADP
cana-4165	3	78	several	several	ADJ
cana-4165	3	79	quantum	quantum	ADJ
cana-4165	3	80	transport	transport	NOUN
cana-4165	3	81	systems	system	NOUN
cana-4165	3	82	.	.	PUNCT
cana-4165	4	1	we	we	PRON
cana-4165	4	2	derive	derive	VERB
cana-4165	4	3	analytical	analytical	ADJ
cana-4165	4	4	formulas	formula	NOUN
cana-4165	4	5	faithfully	faithfully	ADV
cana-4165	4	6	describing	describe	VERB
cana-4165	4	7	the	the	DET
cana-4165	4	8	asymptotic	asymptotic	ADJ
cana-4165	4	9	behavior	behavior	NOUN
cana-4165	4	10	of	of	ADP
cana-4165	4	11	electron	electron	NOUN
cana-4165	4	12	velocities	velocity	NOUN
cana-4165	4	13	under	under	ADP
cana-4165	4	14	various	various	ADJ
cana-4165	4	15	temperature	temperature	NOUN
cana-4165	4	16	and	and	CCONJ
cana-4165	4	17	electric	electric	ADJ
cana-4165	4	18	field	field	NOUN
cana-4165	4	19	regimes	regime	NOUN
cana-4165	4	20	by	by	ADP
cana-4165	4	21	using	use	VERB
cana-4165	4	22	perturbative	perturbative	ADJ
cana-4165	4	23	approaches	approach	NOUN
cana-4165	4	24	and	and	CCONJ
cana-4165	4	25	non	non	ADJ
cana-4165	4	26	-	-	ADJ
cana-4165	4	27	equilibrium	equilibrium	ADJ
cana-4165	4	28	green	green	NOUN
cana-4165	4	29	's	's	PART
cana-4165	4	30	function	function	NOUN
cana-4165	4	31	techniques	technique	NOUN
cana-4165	4	32	.	.	PUNCT
cana-4165	5	1	by	by	ADP
cana-4165	5	2	means	mean	NOUN
cana-4165	5	3	of	of	ADP
cana-4165	5	4	a	a	DET
cana-4165	5	5	unified	unified	ADJ
cana-4165	5	6	scaling	scaling	NOUN
cana-4165	5	7	theory	theory	NOUN
cana-4165	5	8	that	that	PRON
cana-4165	5	9	considers	consider	VERB
cana-4165	5	10	the	the	DET
cana-4165	5	11	transition	transition	NOUN
cana-4165	5	12	between	between	ADP
cana-4165	5	13	diffusive	diffusive	ADJ
cana-4165	5	14	and	and	CCONJ
cana-4165	5	15	ballistic	ballistic	ADJ
cana-4165	5	16	transport	transport	NOUN
cana-4165	5	17	,	,	PUNCT
cana-4165	5	18	our	our	PRON
cana-4165	5	19	theoretical	theoretical	ADJ
cana-4165	5	20	framework	framework	NOUN
cana-4165	5	21	reconciles	reconcile	VERB
cana-4165	5	22	apparently	apparently	ADV
cana-4165	5	23	contradicting	contradict	VERB
cana-4165	5	24	experimental	experimental	ADJ
cana-4165	5	25	results	result	NOUN
cana-4165	5	26	.	.	PUNCT
cana-4165	6	1	experimental	experimental	ADJ
cana-4165	6	2	results	result	NOUN
cana-4165	6	3	from	from	ADP
cana-4165	6	4	graphene	graphene	NOUN
cana-4165	6	5	and	and	CCONJ
cana-4165	6	6	silicon	silicon	NOUN
cana-4165	6	7	-	-	PUNCT
cana-4165	6	8	based	base	VERB
cana-4165	6	9	devices	device	NOUN
cana-4165	6	10	together	together	ADV
cana-4165	6	11	with	with	ADP
cana-4165	6	12	numerical	numerical	ADJ
cana-4165	6	13	simulations	simulation	NOUN
cana-4165	6	14	grounded	ground	VERB
cana-4165	6	15	on	on	ADP
cana-4165	6	16	the	the	DET
cana-4165	6	17	boltzmann	boltzmann	PROPN
cana-4165	6	18	transport	transport	NOUN
cana-4165	6	19	equation	equation	NOUN
cana-4165	6	20	verify	verify	VERB
cana-4165	6	21	the	the	DET
cana-4165	6	22	analytical	analytical	ADJ
cana-4165	6	23	predictions	prediction	NOUN
cana-4165	6	24	.	.	PUNCT
cana-4165	7	1	our	our	PRON
cana-4165	7	2	results	result	NOUN
cana-4165	7	3	show	show	VERB
cana-4165	7	4	that	that	SCONJ
cana-4165	7	5	with	with	ADP
cana-4165	7	6	different	different	ADJ
cana-4165	7	7	scaling	scale	VERB
cana-4165	7	8	exponents	exponent	NOUN
cana-4165	7	9	at	at	ADP
cana-4165	7	10	various	various	ADJ
cana-4165	7	11	asymptotic	asymptotic	ADJ
cana-4165	7	12	conditions	condition	NOUN
cana-4165	7	13	,	,	PUNCT
cana-4165	7	14	electron	electron	NOUN
cana-4165	7	15	mean	mean	NOUN
cana-4165	7	16	velocities	velocity	NOUN
cana-4165	7	17	follow	follow	VERB
cana-4165	7	18	a	a	DET
cana-4165	7	19	non	non	ADJ
cana-4165	7	20	-	-	ADJ
cana-4165	7	21	trivial	trivial	ADJ
cana-4165	7	22	powerlaw	powerlaw	NOUN
cana-4165	7	23	dependence	dependence	NOUN
cana-4165	7	24	on	on	ADP
cana-4165	7	25	applied	apply	VERB
cana-4165	7	26	field	field	NOUN
cana-4165	7	27	strength	strength	NOUN
cana-4165	7	28	.	.	PUNCT
cana-4165	8	1	these	these	DET
cana-4165	8	2	findings	finding	NOUN
cana-4165	8	3	offer	offer	VERB
cana-4165	8	4	vital	vital	ADJ
cana-4165	8	5	new	new	ADJ
cana-4165	8	6	perspectives	perspective	NOUN
cana-4165	8	7	for	for	ADP
cana-4165	8	8	the	the	DET
cana-4165	8	9	design	design	NOUN
cana-4165	8	10	of	of	ADP
cana-4165	8	11	next	next	ADJ
cana-4165	8	12	-	-	PUNCT
cana-4165	8	13	generation	generation	NOUN
cana-4165	8	14	electronic	electronic	ADJ
cana-4165	8	15	systems	system	NOUN
cana-4165	8	16	in	in	ADP
cana-4165	8	17	which	which	PRON
cana-4165	8	18	exact	exact	ADJ
cana-4165	8	19	control	control	NOUN
cana-4165	8	20	of	of	ADP
cana-4165	8	21	electron	electron	NOUN
cana-4165	8	22	flow	flow	NOUN
cana-4165	8	23	is	be	AUX
cana-4165	8	24	critical	critical	ADJ
cana-4165	8	25	.	.	PUNCT
cana-4165	9	1	keywords	keyword	NOUN
cana-4165	9	2	:	:	PUNCT
cana-4165	9	3	electron	electron	NOUN
cana-4165	9	4	transport	transport	NOUN
cana-4165	9	5	,	,	PUNCT
cana-4165	9	6	asymptotic	asymptotic	ADJ
cana-4165	9	7	expansion	expansion	NOUN
cana-4165	9	8	,	,	PUNCT
cana-4165	9	9	quantum	quantum	NOUN
cana-4165	9	10	systems	system	NOUN
cana-4165	9	11	,	,	PUNCT
cana-4165	9	12	mean	mean	VERB
cana-4165	9	13	velocity	velocity	NOUN
cana-4165	9	14	,	,	PUNCT
cana-4165	9	15	boltzmann	boltzmann	PROPN
cana-4165	9	16	equation	equation	NOUN
cana-4165	9	17	,	,	PUNCT
cana-4165	9	18	green	green	PROPN
cana-4165	9	19	's	's	PART
cana-4165	9	20	function	function	NOUN
cana-4165	9	21	,	,	PUNCT
cana-4165	9	22	semiconductor	semiconductor	NOUN
cana-4165	9	23	physics	physics	NOUN
cana-4165	9	24	introduction	introduction	NOUN
cana-4165	9	25	with	with	ADP
cana-4165	9	26	applications	application	NOUN
cana-4165	9	27	ranging	range	VERB
cana-4165	9	28	from	from	ADP
cana-4165	9	29	basic	basic	ADJ
cana-4165	9	30	quantum	quantum	ADJ
cana-4165	9	31	mechanics	mechanic	NOUN
cana-4165	9	32	to	to	ADP
cana-4165	9	33	pragmatic	pragmatic	ADJ
cana-4165	9	34	electronic	electronic	ADJ
cana-4165	9	35	device	device	NOUN
cana-4165	9	36	design	design	NOUN
cana-4165	9	37	,	,	PUNCT
cana-4165	9	38	the	the	DET
cana-4165	9	39	theoretical	theoretical	ADJ
cana-4165	9	40	knowledge	knowledge	NOUN
cana-4165	9	41	of	of	ADP
cana-4165	9	42	electron	electron	NOUN
cana-4165	9	43	transport	transport	NOUN
cana-4165	9	44	in	in	ADP
cana-4165	9	45	condensed	condense	VERB
cana-4165	9	46	matter	matter	NOUN
cana-4165	9	47	systems	system	NOUN
cana-4165	9	48	marks	mark	VERB
cana-4165	9	49	one	one	NUM
cana-4165	9	50	of	of	ADP
cana-4165	9	51	the	the	DET
cana-4165	9	52	pillar	pillar	NOUN
cana-4165	9	53	successes	success	NOUN
cana-4165	9	54	of	of	ADP
cana-4165	9	55	modern	modern	ADJ
cana-4165	9	56	physics	physic	NOUN
cana-4165	9	57	.	.	PUNCT
cana-4165	10	1	the	the	DET
cana-4165	10	2	idea	idea	NOUN
cana-4165	10	3	of	of	ADP
cana-4165	10	4	electron	electron	NOUN
cana-4165	10	5	mean	mean	NOUN
cana-4165	10	6	velocity	velocity	NOUN
cana-4165	10	7	—	—	PUNCT
cana-4165	10	8	a	a	DET
cana-4165	10	9	quantity	quantity	NOUN
cana-4165	10	10	that	that	PRON
cana-4165	10	11	defines	define	VERB
cana-4165	10	12	important	important	ADJ
cana-4165	10	13	device	device	NOUN
cana-4165	10	14	properties	property	NOUN
cana-4165	10	15	including	include	VERB
cana-4165	10	16	mobility	mobility	NOUN
cana-4165	10	17	,	,	PUNCT
cana-4165	10	18	conductivity	conductivity	NOUN
cana-4165	10	19	,	,	PUNCT
cana-4165	10	20	and	and	CCONJ
cana-4165	10	21	switching	switch	VERB
cana-4165	10	22	speed	speed	NOUN
cana-4165	10	23	—	—	PUNCT
cana-4165	10	24	is	be	AUX
cana-4165	10	25	fundamental	fundamental	ADJ
cana-4165	10	26	in	in	ADP
cana-4165	10	27	this	this	DET
cana-4165	10	28	knowledge	knowledge	NOUN
cana-4165	10	29	.	.	PUNCT
cana-4165	11	1	classical	classical	ADJ
cana-4165	11	2	models	model	NOUN
cana-4165	11	3	based	base	VERB
cana-4165	11	4	on	on	ADP
cana-4165	11	5	the	the	DET
cana-4165	11	6	drude	drude	ADJ
cana-4165	11	7	theory	theory	NOUN
cana-4165	11	8	fail	fail	VERB
cana-4165	11	9	down	down	ADP
cana-4165	11	10	when	when	SCONJ
cana-4165	11	11	confronted	confront	VERB
cana-4165	11	12	with	with	ADP
cana-4165	11	13	quantum	quantum	ADJ
cana-4165	11	14	events	event	NOUN
cana-4165	11	15	,	,	PUNCT
cana-4165	11	16	strong	strong	ADJ
cana-4165	11	17	fields	field	NOUN
cana-4165	11	18	,	,	PUNCT
cana-4165	11	19	or	or	CCONJ
cana-4165	11	20	nanoscale	nanoscale	NOUN
cana-4165	11	21	confinement	confinement	NOUN
cana-4165	11	22	even	even	ADV
cana-4165	11	23	if	if	SCONJ
cana-4165	11	24	they	they	PRON
cana-4165	11	25	offer	offer	VERB
cana-4165	11	26	sufficient	sufficient	ADJ
cana-4165	11	27	descriptions	description	NOUN
cana-4165	11	28	at	at	ADP
cana-4165	11	29	macroscopic	macroscopic	ADJ
cana-4165	11	30	levels	level	NOUN
cana-4165	11	31	.	.	PUNCT
cana-4165	12	1	using	use	VERB
cana-4165	12	2	the	the	DET
cana-4165	12	3	simplified	simplified	ADJ
cana-4165	12	4	relationship	relationship	NOUN
cana-4165	12	5	v	v	ADP
cana-4165	12	6	=	=	SYM
cana-4165	12	7	μe	μe	NOUN
cana-4165	12	8	,	,	PUNCT
cana-4165	12	9	where	where	SCONJ
cana-4165	12	10	μ	μ	PROPN
cana-4165	12	11	denotes	denote	VERB
cana-4165	12	12	the	the	DET
cana-4165	12	13	mobility	mobility	NOUN
cana-4165	12	14	and	and	CCONJ
cana-4165	12	15	e	e	X
cana-4165	12	16	the	the	DET
cana-4165	12	17	applied	apply	VERB
cana-4165	12	18	electric	electric	ADJ
cana-4165	12	19	field	field	NOUN
cana-4165	12	20	,	,	PUNCT
cana-4165	12	21	the	the	DET
cana-4165	12	22	asymptotic	asymptotic	ADJ
cana-4165	12	23	behavior	behavior	NOUN
cana-4165	12	24	of	of	ADP
cana-4165	12	25	electron	electron	NOUN
cana-4165	12	26	mean	mean	NOUN
cana-4165	12	27	velocities	velocity	NOUN
cana-4165	12	28	has	have	AUX
cana-4165	12	29	historically	historically	ADV
cana-4165	12	30	been	be	AUX
cana-4165	12	31	characterized	characterize	VERB
cana-4165	12	32	.	.	PUNCT
cana-4165	13	1	but	but	CCONJ
cana-4165	13	2	this	this	DET
cana-4165	13	3	linear	linear	ADJ
cana-4165	13	4	approximation	approximation	NOUN
cana-4165	13	5	misses	miss	VERB
cana-4165	13	6	the	the	DET
cana-4165	13	7	interesting	interesting	ADJ
cana-4165	13	8	physics	physics	NOUN
cana-4165	13	9	revealed	reveal	VERB
cana-4165	13	10	in	in	ADP
cana-4165	13	11	certain	certain	ADJ
cana-4165	13	12	limiting	limit	VERB
cana-4165	13	13	situations	situation	NOUN
cana-4165	13	14	.	.	PUNCT
cana-4165	14	1	rising	rise	VERB
cana-4165	14	2	scattering	scatter	VERB
cana-4165	14	3	with	with	ADP
cana-4165	14	4	optical	optical	ADJ
cana-4165	14	5	phonons	phonon	NOUN
cana-4165	14	6	causes	cause	VERB
cana-4165	14	7	velocity	velocity	NOUN
cana-4165	14	8	saturation	saturation	NOUN
cana-4165	14	9	in	in	ADP
cana-4165	14	10	high	high	ADJ
cana-4165	14	11	-	-	PUNCT
cana-4165	14	12	field	field	NOUN
cana-4165	14	13	regimes	regime	NOUN
cana-4165	14	14	.	.	PUNCT
cana-4165	15	1	on	on	ADP
cana-4165	15	2	low	low	ADJ
cana-4165	15	3	temperatures	temperature	NOUN
cana-4165	15	4	or	or	CCONJ
cana-4165	15	5	in	in	ADP
cana-4165	15	6	ultrapure	ultrapure	ADJ
cana-4165	15	7	materials	material	NOUN
cana-4165	15	8	,	,	PUNCT
cana-4165	15	9	on	on	ADP
cana-4165	15	10	the	the	DET
cana-4165	15	11	other	other	ADJ
cana-4165	15	12	hand	hand	NOUN
cana-4165	15	13	,	,	PUNCT
cana-4165	15	14	ballistic	ballistic	ADJ
cana-4165	15	15	transport	transport	NOUN
cana-4165	15	16	predominates	predominate	VERB
cana-4165	15	17	and	and	CCONJ
cana-4165	15	18	generates	generate	VERB
cana-4165	15	19	quite	quite	ADV
cana-4165	15	20	distinct	distinct	ADJ
cana-4165	15	21	scaling	scaling	NOUN
cana-4165	15	22	relations	relation	NOUN
cana-4165	15	23	.	.	PUNCT
cana-4165	16	1	though	though	SCONJ
cana-4165	16	2	its	its	PRON
cana-4165	16	3	crucial	crucial	ADJ
cana-4165	16	4	relevance	relevance	NOUN
cana-4165	16	5	for	for	ADP
cana-4165	16	6	modern	modern	ADJ
cana-4165	16	7	electronics	electronic	NOUN
cana-4165	16	8	,	,	PUNCT
cana-4165	16	9	the	the	DET
cana-4165	16	10	change	change	NOUN
cana-4165	16	11	between	between	ADP
cana-4165	16	12	these	these	DET
cana-4165	16	13	regimes	regime	NOUN
cana-4165	16	14	is	be	AUX
cana-4165	16	15	still	still	ADV
cana-4165	16	16	poorly	poorly	ADV
cana-4165	16	17	known	know	VERB
cana-4165	16	18	.	.	PUNCT
cana-4165	17	1	materials	material	NOUN
cana-4165	17	2	research	research	NOUN
cana-4165	17	3	has	have	AUX
cana-4165	17	4	recently	recently	ADV
cana-4165	17	5	made	make	VERB
cana-4165	17	6	experimental	experimental	ADJ
cana-4165	17	7	progress	progress	NOUN
cana-4165	17	8	allowing	allow	VERB
cana-4165	17	9	the	the	DET
cana-4165	17	10	construction	construction	NOUN
cana-4165	17	11	of	of	ADP
cana-4165	17	12	atomically	atomically	ADV
cana-4165	17	13	exact	exact	ADJ
cana-4165	17	14	structures	structure	NOUN
cana-4165	17	15	where	where	SCONJ
cana-4165	17	16	electrons	electron	NOUN
cana-4165	17	17	can	can	AUX
cana-4165	17	18	be	be	AUX
cana-4165	17	19	confined	confine	VERB
cana-4165	17	20	to	to	ADP
cana-4165	17	21	efficiently	efficiently	ADV
cana-4165	17	22	lower	lower	ADV
cana-4165	17	23	-	-	PUNCT
cana-4165	17	24	dimensional	dimensional	ADJ
cana-4165	17	25	systems	system	NOUN
cana-4165	17	26	.	.	PUNCT
cana-4165	18	1	from	from	ADP
cana-4165	18	2	twodimensional	twodimensional	ADJ
cana-4165	18	3	electron	electron	NOUN
cana-4165	18	4	vapors	vapor	NOUN
cana-4165	18	5	in	in	ADP
cana-4165	18	6	semiconductor	semiconductor	NOUN
cana-4165	18	7	heterostructures	heterostructure	NOUN
cana-4165	18	8	to	to	ADP
cana-4165	18	9	really	really	ADV
cana-4165	18	10	one	one	NUM
cana-4165	18	11	-	-	PUNCT
cana-4165	18	12	dimensional	dimensional	ADJ
cana-4165	18	13	carbon	carbon	NOUN
cana-4165	18	14	communications	communication	NOUN
cana-4165	18	15	on	on	ADP
cana-4165	18	16	applied	apply	VERB
cana-4165	18	17	nonlinear	nonlinear	ADJ
cana-4165	18	18	analysis	analysis	NOUN
cana-4165	18	19	issn	issn	NOUN
cana-4165	18	20	:	:	PUNCT
cana-4165	18	21	1074	1074	NUM
cana-4165	18	22	-	-	PUNCT
cana-4165	18	23	133x	133x	NUM
cana-4165	18	24	vol	vol	NOUN
cana-4165	18	25	32	32	NUM
cana-4165	18	26	no	no	NOUN
cana-4165	18	27	.	.	PUNCT
cana-4165	19	1	9s	9s	NUM
cana-4165	19	2	(	(	PUNCT
cana-4165	19	3	2025	2025	NUM
cana-4165	19	4	)	)	PUNCT
cana-4165	19	5	1389	1389	NUM
cana-4165	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	19	7	nanotubes	nanotube	NOUN
cana-4165	19	8	and	and	CCONJ
cana-4165	19	9	zero	zero	NUM
cana-4165	19	10	-	-	PUNCT
cana-4165	19	11	dimensional	dimensional	ADJ
cana-4165	19	12	quantum	quantum	ADJ
cana-4165	19	13	dots	dot	NOUN
cana-4165	19	14	,	,	PUNCT
cana-4165	19	15	the	the	DET
cana-4165	19	16	conventional	conventional	ADJ
cana-4165	19	17	theoretical	theoretical	ADJ
cana-4165	19	18	frameworks	framework	NOUN
cana-4165	19	19	need	need	VERB
cana-4165	19	20	significant	significant	ADJ
cana-4165	19	21	adjustment	adjustment	NOUN
cana-4165	19	22	in	in	ADP
cana-4165	19	23	these	these	DET
cana-4165	19	24	environments	environment	NOUN
cana-4165	19	25	.	.	PUNCT
cana-4165	20	1	unprecedented	unprecedented	ADJ
cana-4165	20	2	characteristics	characteristic	NOUN
cana-4165	20	3	of	of	ADP
cana-4165	20	4	the	the	DET
cana-4165	20	5	asymptotic	asymptotic	ADJ
cana-4165	20	6	expansion	expansion	NOUN
cana-4165	20	7	of	of	ADP
cana-4165	20	8	mean	mean	ADJ
cana-4165	20	9	velocities	velocity	NOUN
cana-4165	20	10	in	in	ADP
cana-4165	20	11	these	these	DET
cana-4165	20	12	systems	system	NOUN
cana-4165	20	13	can	can	AUX
cana-4165	20	14	not	not	PART
cana-4165	20	15	be	be	AUX
cana-4165	20	16	justified	justify	VERB
cana-4165	20	17	with	with	ADP
cana-4165	20	18	current	current	ADJ
cana-4165	20	19	theories	theory	NOUN
cana-4165	20	20	.	.	PUNCT
cana-4165	21	1	asymptotic	asymptotic	ADJ
cana-4165	21	2	expansions	expansion	NOUN
cana-4165	21	3	for	for	ADP
cana-4165	21	4	electron	electron	NOUN
cana-4165	21	5	velocities	velocity	NOUN
cana-4165	21	6	provide	provide	VERB
cana-4165	21	7	various	various	ADJ
cana-4165	21	8	mathematical	mathematical	ADJ
cana-4165	21	9	difficulties	difficulty	NOUN
cana-4165	21	10	in	in	ADP
cana-4165	21	11	formulation	formulation	NOUN
cana-4165	21	12	.	.	PUNCT
cana-4165	22	1	these	these	DET
cana-4165	22	2	developments	development	NOUN
cana-4165	22	3	have	have	VERB
cana-4165	22	4	to	to	PART
cana-4165	22	5	consider	consider	VERB
cana-4165	22	6	the	the	DET
cana-4165	22	7	quantum	quantum	ADJ
cana-4165	22	8	character	character	NOUN
cana-4165	22	9	of	of	ADP
cana-4165	22	10	electrons	electron	NOUN
cana-4165	22	11	,	,	PUNCT
cana-4165	22	12	many	many	ADJ
cana-4165	22	13	-	-	PUNCT
cana-4165	22	14	body	body	NOUN
cana-4165	22	15	interactions	interaction	NOUN
cana-4165	22	16	,	,	PUNCT
cana-4165	22	17	and	and	CCONJ
cana-4165	22	18	statistical	statistical	ADJ
cana-4165	22	19	physics	physics	NOUN
cana-4165	22	20	controlling	control	VERB
cana-4165	22	21	ensemble	ensemble	ADJ
cana-4165	22	22	averages	average	NOUN
cana-4165	22	23	at	at	ADP
cana-4165	22	24	once	once	ADV
cana-4165	22	25	.	.	PUNCT
cana-4165	23	1	one	one	NUM
cana-4165	23	2	method	method	NOUN
cana-4165	23	3	is	be	AUX
cana-4165	23	4	provided	provide	VERB
cana-4165	23	5	by	by	ADP
cana-4165	23	6	perturbation	perturbation	NOUN
cana-4165	23	7	theory	theory	NOUN
cana-4165	23	8	;	;	PUNCT
cana-4165	23	9	nonetheless	nonetheless	ADV
cana-4165	23	10	,	,	PUNCT
cana-4165	23	11	the	the	DET
cana-4165	23	12	identification	identification	NOUN
cana-4165	23	13	of	of	ADP
cana-4165	23	14	suitable	suitable	ADJ
cana-4165	23	15	small	small	ADJ
cana-4165	23	16	parameters	parameter	NOUN
cana-4165	23	17	and	and	CCONJ
cana-4165	23	18	the	the	DET
cana-4165	23	19	computation	computation	NOUN
cana-4165	23	20	of	of	ADP
cana-4165	23	21	convergence	convergence	NOUN
cana-4165	23	22	conditions	condition	NOUN
cana-4165	23	23	remain	remain	VERB
cana-4165	23	24	non	non	ADJ
cana-4165	23	25	-	-	ADJ
cana-4165	23	26	trivial	trivial	ADJ
cana-4165	23	27	issues	issue	NOUN
cana-4165	23	28	.	.	PUNCT
cana-4165	24	1	different	different	ADJ
cana-4165	24	2	formulations	formulation	NOUN
cana-4165	24	3	depending	depend	VERB
cana-4165	24	4	on	on	ADP
cana-4165	24	5	path	path	NOUN
cana-4165	24	6	integrals	integral	NOUN
cana-4165	24	7	or	or	CCONJ
cana-4165	24	8	diagrammatic	diagrammatic	ADJ
cana-4165	24	9	approaches	approach	NOUN
cana-4165	24	10	bring	bring	VERB
cana-4165	24	11	their	their	PRON
cana-4165	24	12	own	own	ADJ
cana-4165	24	13	complexity	complexity	NOUN
cana-4165	24	14	but	but	CCONJ
cana-4165	24	15	might	might	AUX
cana-4165	24	16	provide	provide	VERB
cana-4165	24	17	more	more	ADJ
cana-4165	24	18	natural	natural	ADJ
cana-4165	24	19	representations	representation	NOUN
cana-4165	24	20	in	in	ADP
cana-4165	24	21	some	some	DET
cana-4165	24	22	limits	limit	NOUN
cana-4165	24	23	.	.	PUNCT
cana-4165	25	1	from	from	ADP
cana-4165	25	2	an	an	DET
cana-4165	25	3	experimental	experimental	ADJ
cana-4165	25	4	standpoint	standpoint	NOUN
cana-4165	25	5	,	,	PUNCT
cana-4165	25	6	direct	direct	ADJ
cana-4165	25	7	microscopic	microscopic	ADJ
cana-4165	25	8	scale	scale	NOUN
cana-4165	25	9	electron	electron	NOUN
cana-4165	25	10	velocity	velocity	NOUN
cana-4165	25	11	measurement	measurement	NOUN
cana-4165	25	12	offers	offer	VERB
cana-4165	25	13	considerable	considerable	ADJ
cana-4165	25	14	difficulties	difficulty	NOUN
cana-4165	25	15	.	.	PUNCT
cana-4165	26	1	indirect	indirect	ADJ
cana-4165	26	2	access	access	NOUN
cana-4165	26	3	to	to	ADP
cana-4165	26	4	velocity	velocity	NOUN
cana-4165	26	5	distributions	distribution	NOUN
cana-4165	26	6	is	be	AUX
cana-4165	26	7	provided	provide	VERB
cana-4165	26	8	by	by	ADP
cana-4165	26	9	techniques	technique	NOUN
cana-4165	26	10	including	include	VERB
cana-4165	26	11	time	time	NOUN
cana-4165	26	12	-	-	PUNCT
cana-4165	26	13	resolved	resolve	VERB
cana-4165	26	14	photoemission	photoemission	NOUN
cana-4165	26	15	spectroscopy	spectroscopy	NOUN
cana-4165	26	16	,	,	PUNCT
cana-4165	26	17	scanning	scan	VERB
cana-4165	26	18	tunneling	tunneling	NOUN
cana-4165	26	19	microscopy	microscopy	NOUN
cana-4165	26	20	,	,	PUNCT
cana-4165	26	21	and	and	CCONJ
cana-4165	26	22	microwave	microwave	NOUN
cana-4165	26	23	resonance	resonance	NOUN
cana-4165	26	24	approaches	approach	NOUN
cana-4165	26	25	;	;	PUNCT
cana-4165	26	26	each	each	PRON
cana-4165	26	27	generates	generate	VERB
cana-4165	26	28	artifacts	artifact	NOUN
cana-4165	26	29	and	and	CCONJ
cana-4165	26	30	uncertainty	uncertainty	NOUN
cana-4165	26	31	.	.	PUNCT
cana-4165	27	1	therefore	therefore	ADV
cana-4165	27	2	,	,	PUNCT
cana-4165	27	3	careful	careful	ADJ
cana-4165	27	4	attention	attention	NOUN
cana-4165	27	5	of	of	ADP
cana-4165	27	6	these	these	DET
cana-4165	27	7	constraints	constraint	NOUN
cana-4165	27	8	is	be	AUX
cana-4165	27	9	necessary	necessary	ADJ
cana-4165	27	10	in	in	ADP
cana-4165	27	11	the	the	DET
cana-4165	27	12	comparison	comparison	NOUN
cana-4165	27	13	between	between	ADP
cana-4165	27	14	experimental	experimental	ADJ
cana-4165	27	15	data	datum	NOUN
cana-4165	27	16	and	and	CCONJ
cana-4165	27	17	theoretical	theoretical	ADJ
cana-4165	27	18	forecasts	forecast	NOUN
cana-4165	27	19	.	.	PUNCT
cana-4165	28	1	through	through	ADP
cana-4165	28	2	wave	wave	NOUN
cana-4165	28	3	-	-	PUNCT
cana-4165	28	4	particle	particle	NOUN
cana-4165	28	5	duality	duality	NOUN
cana-4165	28	6	,	,	PUNCT
cana-4165	28	7	the	the	DET
cana-4165	28	8	quantum	quantum	ADJ
cana-4165	28	9	mechanical	mechanical	ADJ
cana-4165	28	10	character	character	NOUN
cana-4165	28	11	of	of	ADP
cana-4165	28	12	electrons	electron	NOUN
cana-4165	28	13	brings	bring	VERB
cana-4165	28	14	still	still	ADV
cana-4165	28	15	more	more	ADJ
cana-4165	28	16	complexity	complexity	NOUN
cana-4165	28	17	.	.	PUNCT
cana-4165	29	1	the	the	DET
cana-4165	29	2	expectation	expectation	NOUN
cana-4165	29	3	value	value	NOUN
cana-4165	29	4	of	of	ADP
cana-4165	29	5	the	the	DET
cana-4165	29	6	velocity	velocity	NOUN
cana-4165	29	7	operator	operator	NOUN
cana-4165	29	8	with	with	ADP
cana-4165	29	9	regard	regard	NOUN
cana-4165	29	10	to	to	ADP
cana-4165	29	11	the	the	DET
cana-4165	29	12	relevant	relevant	ADJ
cana-4165	29	13	quantum	quantum	NOUN
cana-4165	29	14	state	state	NOUN
cana-4165	29	15	must	must	AUX
cana-4165	29	16	be	be	AUX
cana-4165	29	17	obtained	obtain	VERB
cana-4165	29	18	from	from	ADP
cana-4165	29	19	which	which	PRON
cana-4165	29	20	one	one	PRON
cana-4165	29	21	derives	derive	VERB
cana-4165	29	22	the	the	DET
cana-4165	29	23	mean	mean	ADJ
cana-4165	29	24	velocity	velocity	NOUN
cana-4165	29	25	,	,	PUNCT
cana-4165	29	26	maybe	maybe	ADV
cana-4165	29	27	via	via	ADP
cana-4165	29	28	entangled	entangled	ADJ
cana-4165	29	29	configurations	configuration	NOUN
cana-4165	29	30	or	or	CCONJ
cana-4165	29	31	coherent	coherent	ADJ
cana-4165	29	32	superpositions	superposition	NOUN
cana-4165	29	33	.	.	PUNCT
cana-4165	30	1	the	the	DET
cana-4165	30	2	band	band	NOUN
cana-4165	30	3	structure	structure	NOUN
cana-4165	30	4	in	in	ADP
cana-4165	30	5	crystals	crystal	NOUN
cana-4165	30	6	alters	alter	VERB
cana-4165	30	7	the	the	DET
cana-4165	30	8	momentum	momentum	NOUN
cana-4165	30	9	-	-	PUNCT
cana-4165	30	10	velocity	velocity	NOUN
cana-4165	30	11	link	link	NOUN
cana-4165	30	12	even	even	ADV
cana-4165	30	13	more	more	ADV
cana-4165	30	14	,	,	PUNCT
cana-4165	30	15	resulting	result	VERB
cana-4165	30	16	in	in	ADP
cana-4165	30	17	conditions	condition	NOUN
cana-4165	30	18	whereby	whereby	SCONJ
cana-4165	30	19	the	the	DET
cana-4165	30	20	group	group	NOUN
cana-4165	30	21	velocity	velocity	NOUN
cana-4165	30	22	may	may	AUX
cana-4165	30	23	even	even	ADV
cana-4165	30	24	turn	turn	VERB
cana-4165	30	25	negative	negative	ADJ
cana-4165	30	26	in	in	ADP
cana-4165	30	27	some	some	DET
cana-4165	30	28	energy	energy	NOUN
cana-4165	30	29	ranges	range	NOUN
cana-4165	30	30	.	.	PUNCT
cana-4165	31	1	temperature	temperature	NOUN
cana-4165	31	2	impacts	impact	NOUN
cana-4165	31	3	bring	bring	VERB
cana-4165	31	4	still	still	ADV
cana-4165	31	5	another	another	DET
cana-4165	31	6	level	level	NOUN
cana-4165	31	7	of	of	ADP
cana-4165	31	8	complexity	complexity	NOUN
cana-4165	31	9	to	to	ADP
cana-4165	31	10	the	the	DET
cana-4165	31	11	issue	issue	NOUN
cana-4165	31	12	.	.	PUNCT
cana-4165	32	1	the	the	DET
cana-4165	32	2	population	population	NOUN
cana-4165	32	3	of	of	ADP
cana-4165	32	4	phonon	phonon	NOUN
cana-4165	32	5	modes	mode	NOUN
cana-4165	32	6	changes	change	NOUN
cana-4165	32	7	with	with	ADP
cana-4165	32	8	temperature	temperature	NOUN
cana-4165	32	9	,	,	PUNCT
cana-4165	32	10	therefore	therefore	ADV
cana-4165	32	11	changing	change	VERB
cana-4165	32	12	the	the	DET
cana-4165	32	13	electron	electron	NOUN
cana-4165	32	14	scattering	scatter	VERB
cana-4165	32	15	scene	scene	NOUN
cana-4165	32	16	.	.	PUNCT
cana-4165	33	1	with	with	ADP
cana-4165	33	2	different	different	ADJ
cana-4165	33	3	physics	physics	NOUN
cana-4165	33	4	dominating	dominating	NOUN
cana-4165	33	5	in	in	ADP
cana-4165	33	6	different	different	ADJ
cana-4165	33	7	temperature	temperature	NOUN
cana-4165	33	8	regimes	regime	NOUN
cana-4165	33	9	,	,	PUNCT
cana-4165	33	10	the	the	DET
cana-4165	33	11	asymptotic	asymptotic	ADJ
cana-4165	33	12	expansions	expansion	NOUN
cana-4165	33	13	must	must	AUX
cana-4165	33	14	hence	hence	ADV
cana-4165	33	15	integrate	integrate	VERB
cana-4165	33	16	temperature	temperature	NOUN
cana-4165	33	17	-	-	PUNCT
cana-4165	33	18	dependent	dependent	ADJ
cana-4165	33	19	factors	factor	NOUN
cana-4165	33	20	.	.	PUNCT
cana-4165	34	1	quantum	quantum	ADJ
cana-4165	34	2	coherence	coherence	NOUN
cana-4165	34	3	effects	effect	NOUN
cana-4165	34	4	become	become	VERB
cana-4165	34	5	noticeable	noticeable	ADJ
cana-4165	34	6	at	at	ADP
cana-4165	34	7	extremely	extremely	ADV
cana-4165	34	8	low	low	ADJ
cana-4165	34	9	temperatures	temperature	NOUN
cana-4165	34	10	and	and	CCONJ
cana-4165	34	11	a	a	DET
cana-4165	34	12	more	more	ADV
cana-4165	34	13	suitable	suitable	ADJ
cana-4165	34	14	description	description	NOUN
cana-4165	34	15	is	be	AUX
cana-4165	34	16	provided	provide	VERB
cana-4165	34	17	by	by	ADP
cana-4165	34	18	the	the	DET
cana-4165	34	19	classical	classical	ADJ
cana-4165	34	20	boltzmann	boltzmann	PROPN
cana-4165	34	21	statistics	statistic	NOUN
cana-4165	34	22	at	at	ADP
cana-4165	34	23	high	high	ADJ
cana-4165	34	24	temperatures	temperature	NOUN
cana-4165	34	25	.	.	PUNCT
cana-4165	35	1	in	in	ADP
cana-4165	35	2	nanoscale	nanoscale	NOUN
cana-4165	35	3	systems	system	NOUN
cana-4165	35	4	,	,	PUNCT
cana-4165	35	5	the	the	DET
cana-4165	35	6	effect	effect	NOUN
cana-4165	35	7	of	of	ADP
cana-4165	35	8	interfaces	interface	NOUN
cana-4165	35	9	and	and	CCONJ
cana-4165	35	10	limits	limit	NOUN
cana-4165	35	11	can	can	AUX
cana-4165	35	12	not	not	PART
cana-4165	35	13	be	be	AUX
cana-4165	35	14	underlined	underline	VERB
cana-4165	35	15	.	.	PUNCT
cana-4165	36	1	asymptotic	asymptotic	ADJ
cana-4165	36	2	behavior	behavior	NOUN
cana-4165	36	3	of	of	ADP
cana-4165	36	4	electron	electron	NOUN
cana-4165	36	5	velocities	velocity	NOUN
cana-4165	36	6	is	be	AUX
cana-4165	36	7	modified	modify	VERB
cana-4165	36	8	by	by	ADP
cana-4165	36	9	surface	surface	NOUN
cana-4165	36	10	scattering	scattering	NOUN
cana-4165	36	11	,	,	PUNCT
cana-4165	36	12	quantum	quantum	ADJ
cana-4165	36	13	confinement	confinement	NOUN
cana-4165	36	14	,	,	PUNCT
cana-4165	36	15	and	and	CCONJ
cana-4165	36	16	tunneling	tunnel	VERB
cana-4165	36	17	over	over	ADP
cana-4165	36	18	obstacles	obstacle	NOUN
cana-4165	36	19	.	.	PUNCT
cana-4165	37	1	these	these	DET
cana-4165	37	2	consequences	consequence	NOUN
cana-4165	37	3	get	get	VERB
cana-4165	37	4	especially	especially	ADV
cana-4165	37	5	important	important	ADJ
cana-4165	37	6	when	when	SCONJ
cana-4165	37	7	the	the	DET
cana-4165	37	8	characteristic	characteristic	ADJ
cana-4165	37	9	length	length	NOUN
cana-4165	37	10	scales	scale	NOUN
cana-4165	37	11	of	of	ADP
cana-4165	37	12	the	the	DET
cana-4165	37	13	system	system	NOUN
cana-4165	37	14	approach	approach	VERB
cana-4165	37	15	the	the	DET
cana-4165	37	16	electron	electron	NOUN
cana-4165	37	17	mean	mean	VERB
cana-4165	37	18	free	free	ADJ
cana-4165	37	19	path	path	NOUN
cana-4165	37	20	or	or	CCONJ
cana-4165	37	21	the	the	DET
cana-4165	37	22	de	de	X
cana-4165	37	23	broglie	broglie	PROPN
cana-4165	37	24	wavelength	wavelength	NOUN
cana-4165	37	25	.	.	PUNCT
cana-4165	38	1	by	by	ADP
cana-4165	38	2	means	mean	NOUN
cana-4165	38	3	of	of	ADP
cana-4165	38	4	scaling	scale	VERB
cana-4165	38	5	theories	theory	NOUN
cana-4165	38	6	and	and	CCONJ
cana-4165	38	7	renormalization	renormalization	NOUN
cana-4165	38	8	group	group	NOUN
cana-4165	38	9	techniques	technique	NOUN
cana-4165	38	10	,	,	PUNCT
cana-4165	38	11	recent	recent	ADJ
cana-4165	38	12	theoretical	theoretical	ADJ
cana-4165	38	13	discoveries	discovery	NOUN
cana-4165	38	14	aim	aim	VERB
cana-4165	38	15	to	to	PART
cana-4165	38	16	unite	unite	VERB
cana-4165	38	17	these	these	DET
cana-4165	38	18	several	several	ADJ
cana-4165	38	19	regimes	regime	NOUN
cana-4165	38	20	.	.	PUNCT
cana-4165	39	1	more	more	ADJ
cana-4165	39	2	general	general	ADJ
cana-4165	39	3	asymptotic	asymptotic	ADJ
cana-4165	39	4	expansions	expansion	NOUN
cana-4165	39	5	can	can	AUX
cana-4165	39	6	be	be	AUX
cana-4165	39	7	developed	develop	VERB
cana-4165	39	8	by	by	ADP
cana-4165	39	9	knowing	know	VERB
cana-4165	39	10	the	the	DET
cana-4165	39	11	pertinent	pertinent	ADJ
cana-4165	39	12	dimensionless	dimensionless	NOUN
cana-4165	39	13	parameters	parameter	NOUN
cana-4165	39	14	,	,	PUNCT
cana-4165	39	15	including	include	VERB
cana-4165	39	16	the	the	DET
cana-4165	39	17	ratio	ratio	NOUN
cana-4165	39	18	of	of	ADP
cana-4165	39	19	the	the	DET
cana-4165	39	20	mean	mean	ADJ
cana-4165	39	21	free	free	ADJ
cana-4165	39	22	path	path	NOUN
cana-4165	39	23	to	to	ADP
cana-4165	39	24	the	the	DET
cana-4165	39	25	system	system	NOUN
cana-4165	39	26	size	size	NOUN
cana-4165	39	27	or	or	CCONJ
cana-4165	39	28	the	the	DET
cana-4165	39	29	thermal	thermal	ADJ
cana-4165	39	30	energy	energy	NOUN
cana-4165	39	31	to	to	ADP
cana-4165	39	32	the	the	DET
cana-4165	39	33	fermi	fermi	NOUN
cana-4165	39	34	energy	energy	NOUN
cana-4165	39	35	.	.	PUNCT
cana-4165	40	1	these	these	DET
cana-4165	40	2	expansions	expansion	NOUN
cana-4165	40	3	expose	expose	VERB
cana-4165	40	4	universal	universal	ADJ
cana-4165	40	5	characteristics	characteristic	NOUN
cana-4165	40	6	either	either	CCONJ
cana-4165	40	7	in	in	ADP
cana-4165	40	8	particular	particular	ADJ
cana-4165	40	9	limiting	limiting	NOUN
cana-4165	40	10	situations	situation	NOUN
cana-4165	40	11	or	or	CCONJ
cana-4165	40	12	close	close	ADJ
cana-4165	40	13	to	to	ADP
cana-4165	40	14	key	key	ADJ
cana-4165	40	15	spots	spot	NOUN
cana-4165	40	16	.	.	PUNCT
cana-4165	41	1	our	our	PRON
cana-4165	41	2	work	work	NOUN
cana-4165	41	3	expands	expand	VERB
cana-4165	41	4	on	on	ADP
cana-4165	41	5	these	these	DET
cana-4165	41	6	bases	basis	NOUN
cana-4165	41	7	and	and	CCONJ
cana-4165	41	8	fills	fill	VERB
cana-4165	41	9	in	in	ADP
cana-4165	41	10	some	some	DET
cana-4165	41	11	important	important	ADJ
cana-4165	41	12	voids	voids	NOUN
cana-4165	41	13	in	in	ADP
cana-4165	41	14	the	the	DET
cana-4165	41	15	body	body	NOUN
cana-4165	41	16	of	of	ADP
cana-4165	41	17	current	current	ADJ
cana-4165	41	18	knowledge	knowledge	NOUN
cana-4165	41	19	.	.	PUNCT
cana-4165	42	1	we	we	PRON
cana-4165	42	2	present	present	VERB
cana-4165	42	3	a	a	DET
cana-4165	42	4	methodical	methodical	ADJ
cana-4165	42	5	approach	approach	NOUN
cana-4165	42	6	to	to	PART
cana-4165	42	7	derive	derive	VERB
cana-4165	42	8	asymptotic	asymptotic	ADJ
cana-4165	42	9	expansions	expansion	NOUN
cana-4165	42	10	of	of	ADP
cana-4165	42	11	electron	electron	NOUN
cana-4165	42	12	mean	mean	NOUN
cana-4165	42	13	velocities	velocity	NOUN
cana-4165	42	14	that	that	PRON
cana-4165	42	15	holds	hold	VERB
cana-4165	42	16	true	true	ADJ
cana-4165	42	17	over	over	ADP
cana-4165	42	18	several	several	ADJ
cana-4165	42	19	regimes	regime	NOUN
cana-4165	42	20	.	.	PUNCT
cana-4165	43	1	many	many	ADJ
cana-4165	43	2	-	-	PUNCT
cana-4165	43	3	body	body	NOUN
cana-4165	43	4	interactions	interaction	NOUN
cana-4165	43	5	,	,	PUNCT
cana-4165	43	6	dimensional	dimensional	ADJ
cana-4165	43	7	scaling	scaling	NOUN
cana-4165	43	8	,	,	PUNCT
cana-4165	43	9	and	and	CCONJ
cana-4165	43	10	quantum	quantum	NOUN
cana-4165	43	11	effects	effect	NOUN
cana-4165	43	12	let	let	VERB
cana-4165	43	13	our	our	PRON
cana-4165	43	14	method	method	NOUN
cana-4165	43	15	offer	offer	VERB
cana-4165	43	16	a	a	DET
cana-4165	43	17	more	more	ADV
cana-4165	43	18	complete	complete	ADJ
cana-4165	43	19	framework	framework	NOUN
cana-4165	43	20	than	than	ADP
cana-4165	43	21	earlier	early	ADJ
cana-4165	43	22	theories	theory	NOUN
cana-4165	43	23	.	.	PUNCT
cana-4165	44	1	this	this	DET
cana-4165	44	2	methodology	methodology	NOUN
cana-4165	44	3	provides	provide	VERB
cana-4165	44	4	communications	communication	NOUN
cana-4165	44	5	on	on	ADP
cana-4165	44	6	applied	apply	VERB
cana-4165	44	7	nonlinear	nonlinear	ADJ
cana-4165	44	8	analysis	analysis	NOUN
cana-4165	44	9	issn	issn	NOUN
cana-4165	44	10	:	:	PUNCT
cana-4165	44	11	1074	1074	NUM
cana-4165	44	12	-	-	PUNCT
cana-4165	44	13	133x	133x	NUM
cana-4165	44	14	vol	vol	NOUN
cana-4165	44	15	32	32	NUM
cana-4165	44	16	no	no	NOUN
cana-4165	44	17	.	.	PUNCT
cana-4165	45	1	9s	9s	NUM
cana-4165	45	2	(	(	PUNCT
cana-4165	45	3	2025	2025	NUM
cana-4165	45	4	)	)	PUNCT
cana-4165	45	5	1390	1390	NUM
cana-4165	46	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	46	2	predictive	predictive	ADJ
cana-4165	46	3	capability	capability	NOUN
cana-4165	46	4	for	for	ADP
cana-4165	46	5	new	new	ADJ
cana-4165	46	6	materials	material	NOUN
cana-4165	46	7	and	and	CCONJ
cana-4165	46	8	device	device	NOUN
cana-4165	46	9	configurations	configuration	NOUN
cana-4165	46	10	in	in	ADP
cana-4165	46	11	addition	addition	NOUN
cana-4165	46	12	to	to	ADP
cana-4165	46	13	reconciling	reconcile	VERB
cana-4165	46	14	apparently	apparently	ADV
cana-4165	46	15	contradicting	contradict	VERB
cana-4165	46	16	experimental	experimental	ADJ
cana-4165	46	17	results	result	NOUN
cana-4165	46	18	.	.	PUNCT
cana-4165	47	1	objectives	objective	NOUN
cana-4165	47	2	1	1	NUM
cana-4165	47	3	.	.	PUNCT
cana-4165	47	4	to	to	PART
cana-4165	47	5	derive	derive	VERB
cana-4165	47	6	comprehensive	comprehensive	ADJ
cana-4165	47	7	analytical	analytical	ADJ
cana-4165	47	8	expressions	expression	NOUN
cana-4165	47	9	for	for	ADP
cana-4165	47	10	the	the	DET
cana-4165	47	11	asymptotic	asymptotic	ADJ
cana-4165	47	12	expansion	expansion	NOUN
cana-4165	47	13	of	of	ADP
cana-4165	47	14	electron	electron	NOUN
cana-4165	47	15	mean	mean	NOUN
cana-4165	47	16	velocities	velocity	NOUN
cana-4165	47	17	in	in	ADP
cana-4165	47	18	quantum	quantum	ADJ
cana-4165	47	19	transport	transport	NOUN
cana-4165	47	20	systems	system	NOUN
cana-4165	47	21	across	across	ADP
cana-4165	47	22	different	different	ADJ
cana-4165	47	23	dimensional	dimensional	ADJ
cana-4165	47	24	confinements	confinement	NOUN
cana-4165	47	25	(	(	PUNCT
cana-4165	47	26	3d	3d	NOUN
cana-4165	47	27	,	,	PUNCT
cana-4165	47	28	2d	2d	NOUN
cana-4165	47	29	,	,	PUNCT
cana-4165	47	30	and	and	CCONJ
cana-4165	47	31	1d	1d	NUM
cana-4165	47	32	systems	system	NOUN
cana-4165	47	33	)	)	PUNCT
cana-4165	47	34	.	.	PUNCT
cana-4165	48	1	2	2	X
cana-4165	48	2	.	.	PUNCT
cana-4165	48	3	to	to	PART
cana-4165	48	4	establish	establish	VERB
cana-4165	48	5	a	a	DET
cana-4165	48	6	unified	unified	ADJ
cana-4165	48	7	scaling	scaling	NOUN
cana-4165	48	8	theory	theory	NOUN
cana-4165	48	9	that	that	PRON
cana-4165	48	10	quantifies	quantify	VERB
cana-4165	48	11	the	the	DET
cana-4165	48	12	transition	transition	NOUN
cana-4165	48	13	between	between	ADP
cana-4165	48	14	diffusive	diffusive	ADJ
cana-4165	48	15	and	and	CCONJ
cana-4165	48	16	ballistic	ballistic	ADJ
cana-4165	48	17	transport	transport	NOUN
cana-4165	48	18	regimes	regime	NOUN
cana-4165	48	19	through	through	ADP
cana-4165	48	20	rigorous	rigorous	ADJ
cana-4165	48	21	mathematical	mathematical	ADJ
cana-4165	48	22	formulation	formulation	NOUN
cana-4165	48	23	and	and	CCONJ
cana-4165	48	24	experimental	experimental	ADJ
cana-4165	48	25	validation	validation	NOUN
cana-4165	48	26	.	.	PUNCT
cana-4165	49	1	3	3	X
cana-4165	49	2	.	.	X
cana-4165	49	3	to	to	PART
cana-4165	49	4	investigate	investigate	VERB
cana-4165	49	5	the	the	DET
cana-4165	49	6	influence	influence	NOUN
cana-4165	49	7	of	of	ADP
cana-4165	49	8	quantum	quantum	ADJ
cana-4165	49	9	effects	effect	NOUN
cana-4165	49	10	,	,	PUNCT
cana-4165	49	11	many	many	ADJ
cana-4165	49	12	-	-	PUNCT
cana-4165	49	13	body	body	NOUN
cana-4165	49	14	interactions	interaction	NOUN
cana-4165	49	15	,	,	PUNCT
cana-4165	49	16	and	and	CCONJ
cana-4165	49	17	temperature	temperature	NOUN
cana-4165	49	18	dependence	dependence	NOUN
cana-4165	49	19	on	on	ADP
cana-4165	49	20	the	the	DET
cana-4165	49	21	asymptotic	asymptotic	ADJ
cana-4165	49	22	behavior	behavior	NOUN
cana-4165	49	23	of	of	ADP
cana-4165	49	24	electron	electron	NOUN
cana-4165	49	25	velocities	velocity	NOUN
cana-4165	49	26	in	in	ADP
cana-4165	49	27	advanced	advanced	ADJ
cana-4165	49	28	materials	material	NOUN
cana-4165	49	29	such	such	ADJ
cana-4165	49	30	as	as	ADP
cana-4165	49	31	graphene	graphene	NOUN
cana-4165	49	32	,	,	PUNCT
cana-4165	49	33	topological	topological	ADJ
cana-4165	49	34	insulators	insulator	NOUN
cana-4165	49	35	,	,	PUNCT
cana-4165	49	36	and	and	CCONJ
cana-4165	49	37	semiconductor	semiconductor	NOUN
cana-4165	49	38	heterostructures	heterostructure	NOUN
cana-4165	49	39	.	.	PUNCT
cana-4165	50	1	scope	scope	VERB
cana-4165	50	2	theoretical	theoretical	ADJ
cana-4165	50	3	modeling	modeling	NOUN
cana-4165	50	4	,	,	PUNCT
cana-4165	50	5	numerical	numerical	ADJ
cana-4165	50	6	simulations	simulation	NOUN
cana-4165	50	7	,	,	PUNCT
cana-4165	50	8	and	and	CCONJ
cana-4165	50	9	comparison	comparison	NOUN
cana-4165	50	10	with	with	ADP
cana-4165	50	11	experimental	experimental	ADJ
cana-4165	50	12	data	datum	NOUN
cana-4165	50	13	on	on	ADP
cana-4165	50	14	electron	electron	NOUN
cana-4165	50	15	transport	transport	NOUN
cana-4165	50	16	in	in	ADP
cana-4165	50	17	semiconductors	semiconductor	NOUN
cana-4165	50	18	and	and	CCONJ
cana-4165	50	19	low	low	ADJ
cana-4165	50	20	-	-	PUNCT
cana-4165	50	21	dimensional	dimensional	ADJ
cana-4165	50	22	materials	material	NOUN
cana-4165	50	23	comprise	comprise	VERB
cana-4165	50	24	this	this	DET
cana-4165	50	25	work	work	NOUN
cana-4165	50	26	.	.	PUNCT
cana-4165	51	1	using	use	VERB
cana-4165	51	2	perturbative	perturbative	ADJ
cana-4165	51	3	approaches	approach	NOUN
cana-4165	51	4	,	,	PUNCT
cana-4165	51	5	non	non	ADJ
cana-4165	51	6	-	-	ADJ
cana-4165	51	7	equilibrium	equilibrium	ADJ
cana-4165	51	8	green	green	NOUN
cana-4165	51	9	's	's	PART
cana-4165	51	10	function	function	NOUN
cana-4165	51	11	techniques	technique	NOUN
cana-4165	51	12	,	,	PUNCT
cana-4165	51	13	and	and	CCONJ
cana-4165	51	14	boltzmann	boltzmann	PROPN
cana-4165	51	15	transport	transport	NOUN
cana-4165	51	16	formulations	formulation	NOUN
cana-4165	51	17	,	,	PUNCT
cana-4165	51	18	the	the	DET
cana-4165	51	19	scope	scope	NOUN
cana-4165	51	20	covers	cover	VERB
cana-4165	51	21	the	the	DET
cana-4165	51	22	derivation	derivation	NOUN
cana-4165	51	23	of	of	ADP
cana-4165	51	24	analytical	analytical	ADJ
cana-4165	51	25	formulas	formula	NOUN
cana-4165	51	26	for	for	ADP
cana-4165	51	27	electron	electron	NOUN
cana-4165	51	28	mean	mean	NOUN
cana-4165	51	29	velocities	velocity	NOUN
cana-4165	51	30	.	.	PUNCT
cana-4165	52	1	we	we	PRON
cana-4165	52	2	especially	especially	ADV
cana-4165	52	3	address	address	VERB
cana-4165	52	4	situations	situation	NOUN
cana-4165	52	5	where	where	SCONJ
cana-4165	52	6	quantum	quantum	ADJ
cana-4165	52	7	effects	effect	NOUN
cana-4165	52	8	become	become	VERB
cana-4165	52	9	important	important	ADJ
cana-4165	52	10	:	:	PUNCT
cana-4165	52	11	two	two	NUM
cana-4165	52	12	-	-	PUNCT
cana-4165	52	13	dimensional	dimensional	ADJ
cana-4165	52	14	electron	electron	NOUN
cana-4165	52	15	vapors	vapor	NOUN
cana-4165	52	16	in	in	ADP
cana-4165	52	17	semiconductor	semiconductor	NOUN
cana-4165	52	18	heterostructures	heterostructure	NOUN
cana-4165	52	19	,	,	PUNCT
cana-4165	52	20	graphene	graphene	ADJ
cana-4165	52	21	monolayers	monolayer	NOUN
cana-4165	52	22	,	,	PUNCT
cana-4165	52	23	topological	topological	ADJ
cana-4165	52	24	insulators	insulator	NOUN
cana-4165	52	25	,	,	PUNCT
cana-4165	52	26	and	and	CCONJ
cana-4165	52	27	one	one	NUM
cana-4165	52	28	-	-	PUNCT
cana-4165	52	29	dimensional	dimensional	ADJ
cana-4165	52	30	quantum	quantum	ADJ
cana-4165	52	31	wires	wire	NOUN
cana-4165	52	32	.	.	PUNCT
cana-4165	53	1	considered	consider	VERB
cana-4165	53	2	are	be	AUX
cana-4165	53	3	electric	electric	ADJ
cana-4165	53	4	fields	field	NOUN
cana-4165	53	5	from	from	ADP
cana-4165	53	6	10²	10²	NUM
cana-4165	53	7	v	v	NOUN
cana-4165	53	8	/	/	SYM
cana-4165	53	9	m	m	NOUN
cana-4165	53	10	to	to	ADP
cana-4165	53	11	10⁶	10⁶	NUM
cana-4165	53	12	v	v	NOUN
cana-4165	53	13	/	/	SYM
cana-4165	53	14	m	m	NOUN
cana-4165	53	15	and	and	CCONJ
cana-4165	53	16	temperature	temperature	NOUN
cana-4165	53	17	ranges	ranges	AUX
cana-4165	53	18	from	from	ADP
cana-4165	53	19	4k	4k	NUM
cana-4165	53	20	to	to	ADP
cana-4165	53	21	300k	300k	PROPN
cana-4165	53	22	.	.	PUNCT
cana-4165	54	1	with	with	ADP
cana-4165	54	2	specific	specific	ADJ
cana-4165	54	3	focus	focus	NOUN
cana-4165	54	4	on	on	ADP
cana-4165	54	5	the	the	DET
cana-4165	54	6	asymptotic	asymptotic	ADJ
cana-4165	54	7	behavior	behavior	NOUN
cana-4165	54	8	under	under	ADP
cana-4165	54	9	different	different	ADJ
cana-4165	54	10	limiting	limiting	NOUN
cana-4165	54	11	conditions	condition	NOUN
cana-4165	54	12	,	,	PUNCT
cana-4165	54	13	the	the	DET
cana-4165	54	14	analysis	analysis	NOUN
cana-4165	54	15	covers	cover	VERB
cana-4165	54	16	both	both	DET
cana-4165	54	17	steady	steady	ADJ
cana-4165	54	18	-	-	PUNCT
cana-4165	54	19	state	state	NOUN
cana-4165	54	20	and	and	CCONJ
cana-4165	54	21	transient	transient	ADJ
cana-4165	54	22	reactions	reaction	NOUN
cana-4165	54	23	.	.	PUNCT
cana-4165	55	1	limitations	limitation	NOUN
cana-4165	55	2	1	1	NUM
cana-4165	55	3	.	.	PUNCT
cana-4165	56	1	our	our	PRON
cana-4165	56	2	analytical	analytical	ADJ
cana-4165	56	3	framework	framework	NOUN
cana-4165	56	4	neglects	neglect	VERB
cana-4165	56	5	certain	certain	ADJ
cana-4165	56	6	many	many	ADJ
cana-4165	56	7	-	-	PUNCT
cana-4165	56	8	body	body	NOUN
cana-4165	56	9	effects	effect	NOUN
cana-4165	56	10	such	such	ADJ
cana-4165	56	11	as	as	ADP
cana-4165	56	12	electron	electron	NOUN
cana-4165	56	13	-	-	PUNCT
cana-4165	56	14	electron	electron	NOUN
cana-4165	56	15	interactions	interaction	NOUN
cana-4165	56	16	beyond	beyond	ADP
cana-4165	56	17	the	the	DET
cana-4165	56	18	mean	mean	ADJ
cana-4165	56	19	-	-	PUNCT
cana-4165	56	20	field	field	NOUN
cana-4165	56	21	approximation	approximation	NOUN
cana-4165	56	22	,	,	PUNCT
cana-4165	56	23	which	which	PRON
cana-4165	56	24	may	may	AUX
cana-4165	56	25	become	become	VERB
cana-4165	56	26	significant	significant	ADJ
cana-4165	56	27	in	in	ADP
cana-4165	56	28	strongly	strongly	ADV
cana-4165	56	29	correlated	correlate	VERB
cana-4165	56	30	systems	system	NOUN
cana-4165	56	31	at	at	ADP
cana-4165	56	32	low	low	ADJ
cana-4165	56	33	temperatures	temperature	NOUN
cana-4165	56	34	or	or	CCONJ
cana-4165	56	35	high	high	ADJ
cana-4165	56	36	carrier	carrier	NOUN
cana-4165	56	37	densities	density	NOUN
cana-4165	56	38	.	.	PUNCT
cana-4165	57	1	2	2	X
cana-4165	57	2	.	.	X
cana-4165	57	3	the	the	DET
cana-4165	57	4	derived	derive	VERB
cana-4165	57	5	asymptotic	asymptotic	ADJ
cana-4165	57	6	expansions	expansion	NOUN
cana-4165	57	7	assume	assume	VERB
cana-4165	57	8	perfect	perfect	ADJ
cana-4165	57	9	crystalline	crystalline	NOUN
cana-4165	57	10	structures	structure	NOUN
cana-4165	57	11	and	and	CCONJ
cana-4165	57	12	may	may	AUX
cana-4165	57	13	require	require	VERB
cana-4165	57	14	substantial	substantial	ADJ
cana-4165	57	15	modifications	modification	NOUN
cana-4165	57	16	when	when	SCONJ
cana-4165	57	17	applied	apply	VERB
cana-4165	57	18	to	to	ADP
cana-4165	57	19	systems	system	NOUN
cana-4165	57	20	with	with	ADP
cana-4165	57	21	significant	significant	ADJ
cana-4165	57	22	disorder	disorder	NOUN
cana-4165	57	23	,	,	PUNCT
cana-4165	57	24	impurities	impurity	NOUN
cana-4165	57	25	,	,	PUNCT
cana-4165	57	26	or	or	CCONJ
cana-4165	57	27	structural	structural	ADJ
cana-4165	57	28	defects	defect	NOUN
cana-4165	57	29	that	that	PRON
cana-4165	57	30	dominate	dominate	VERB
cana-4165	57	31	the	the	DET
cana-4165	57	32	scattering	scatter	VERB
cana-4165	57	33	mechanisms	mechanism	NOUN
cana-4165	57	34	.	.	PUNCT
cana-4165	58	1	3	3	X
cana-4165	58	2	.	.	X
cana-4165	58	3	the	the	DET
cana-4165	58	4	present	present	ADJ
cana-4165	58	5	work	work	NOUN
cana-4165	58	6	focuses	focus	VERB
cana-4165	58	7	primarily	primarily	ADV
cana-4165	58	8	on	on	ADP
cana-4165	58	9	steady	steady	ADJ
cana-4165	58	10	-	-	PUNCT
cana-4165	58	11	state	state	NOUN
cana-4165	58	12	behavior	behavior	NOUN
cana-4165	58	13	,	,	PUNCT
cana-4165	58	14	with	with	ADP
cana-4165	58	15	limited	limited	ADJ
cana-4165	58	16	treatment	treatment	NOUN
cana-4165	58	17	of	of	ADP
cana-4165	58	18	highfrequency	highfrequency	NOUN
cana-4165	58	19	dynamic	dynamic	ADJ
cana-4165	58	20	responses	response	NOUN
cana-4165	58	21	where	where	SCONJ
cana-4165	58	22	displacement	displacement	ADJ
cana-4165	58	23	currents	current	NOUN
cana-4165	58	24	and	and	CCONJ
cana-4165	58	25	electromagnetic	electromagnetic	ADJ
cana-4165	58	26	wave	wave	NOUN
cana-4165	58	27	propagation	propagation	NOUN
cana-4165	58	28	effects	effect	NOUN
cana-4165	58	29	become	become	VERB
cana-4165	58	30	important	important	ADJ
cana-4165	58	31	.	.	PUNCT
cana-4165	59	1	literature	literature	NOUN
cana-4165	59	2	review	review	PROPN
cana-4165	59	3	since	since	SCONJ
cana-4165	59	4	the	the	DET
cana-4165	59	5	pioneering	pioneering	ADJ
cana-4165	59	6	work	work	NOUN
cana-4165	59	7	of	of	ADP
cana-4165	59	8	drude	drude	ADJ
cana-4165	59	9	in	in	ADP
cana-4165	59	10	the	the	DET
cana-4165	59	11	early	early	ADJ
cana-4165	59	12	20th	20th	ADJ
cana-4165	59	13	century	century	NOUN
cana-4165	59	14	,	,	PUNCT
cana-4165	59	15	theoretical	theoretical	ADJ
cana-4165	59	16	theory	theory	NOUN
cana-4165	59	17	of	of	ADP
cana-4165	59	18	electron	electron	NOUN
cana-4165	59	19	transport	transport	NOUN
cana-4165	59	20	has	have	AUX
cana-4165	59	21	changed	change	VERB
cana-4165	59	22	drastically	drastically	ADV
cana-4165	59	23	.	.	PUNCT
cana-4165	60	1	based	base	VERB
cana-4165	60	2	on	on	ADP
cana-4165	60	3	the	the	DET
cana-4165	60	4	kinetic	kinetic	ADJ
cana-4165	60	5	theory	theory	NOUN
cana-4165	60	6	of	of	ADP
cana-4165	60	7	gases	gas	NOUN
cana-4165	60	8	applied	apply	VERB
cana-4165	60	9	to	to	ADP
cana-4165	60	10	electrons	electron	NOUN
cana-4165	60	11	,	,	PUNCT
cana-4165	60	12	drude	drude	PROPN
cana-4165	60	13	's	's	PART
cana-4165	60	14	model	model	NOUN
cana-4165	60	15	offered	offer	VERB
cana-4165	60	16	the	the	DET
cana-4165	60	17	first	first	ADJ
cana-4165	60	18	quantitative	quantitative	ADJ
cana-4165	60	19	foundation	foundation	NOUN
cana-4165	60	20	for	for	ADP
cana-4165	60	21	grasp	grasp	NOUN
cana-4165	60	22	of	of	ADP
cana-4165	60	23	electrical	electrical	ADJ
cana-4165	60	24	conductivity	conductivity	NOUN
cana-4165	60	25	.	.	PUNCT
cana-4165	61	1	up	up	ADV
cana-4165	61	2	until	until	ADP
cana-4165	61	3	the	the	DET
cana-4165	61	4	arrival	arrival	NOUN
cana-4165	61	5	of	of	ADP
cana-4165	61	6	quantum	quantum	ADJ
cana-4165	61	7	physics	physics	NOUN
cana-4165	61	8	,	,	PUNCT
cana-4165	61	9	this	this	DET
cana-4165	61	10	classical	classical	ADJ
cana-4165	61	11	method	method	NOUN
cana-4165	61	12	—	—	PUNCT
cana-4165	61	13	later	later	ADV
cana-4165	61	14	improved	improve	VERB
cana-4165	61	15	by	by	ADP
cana-4165	61	16	lorentz	lorentz	PROPN
cana-4165	61	17	to	to	PART
cana-4165	61	18	include	include	VERB
cana-4165	61	19	the	the	DET
cana-4165	61	20	consequences	consequence	NOUN
cana-4165	61	21	of	of	ADP
cana-4165	61	22	the	the	DET
cana-4165	61	23	lattice	lattice	NOUN
cana-4165	61	24	structure	structure	NOUN
cana-4165	61	25	—	—	PUNCT
cana-4165	61	26	remained	remain	VERB
cana-4165	61	27	the	the	DET
cana-4165	61	28	main	main	ADJ
cana-4165	61	29	paradigm	paradigm	NOUN
cana-4165	61	30	.	.	PUNCT
cana-4165	62	1	communications	communication	NOUN
cana-4165	62	2	on	on	ADP
cana-4165	62	3	applied	apply	VERB
cana-4165	62	4	nonlinear	nonlinear	ADJ
cana-4165	62	5	analysis	analysis	NOUN
cana-4165	62	6	issn	issn	NOUN
cana-4165	62	7	:	:	PUNCT
cana-4165	62	8	1074	1074	NUM
cana-4165	62	9	-	-	PUNCT
cana-4165	62	10	133x	133x	NUM
cana-4165	62	11	vol	vol	NOUN
cana-4165	62	12	32	32	NUM
cana-4165	62	13	no	no	NOUN
cana-4165	62	14	.	.	PUNCT
cana-4165	63	1	9s	9s	NUM
cana-4165	63	2	(	(	PUNCT
cana-4165	63	3	2025	2025	NUM
cana-4165	63	4	)	)	PUNCT
cana-4165	63	5	1391	1391	NUM
cana-4165	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	63	7	with	with	ADP
cana-4165	63	8	his	his	PRON
cana-4165	63	9	addition	addition	NOUN
cana-4165	63	10	of	of	ADP
cana-4165	63	11	quantum	quantum	ADJ
cana-4165	63	12	statistics	statistic	NOUN
cana-4165	63	13	,	,	PUNCT
cana-4165	63	14	sommerfeld	sommerfeld	PROPN
cana-4165	63	15	's	's	PART
cana-4165	63	16	version	version	NOUN
cana-4165	63	17	of	of	ADP
cana-4165	63	18	the	the	DET
cana-4165	63	19	drude	drude	ADJ
cana-4165	63	20	model	model	NOUN
cana-4165	63	21	marked	mark	VERB
cana-4165	63	22	a	a	DET
cana-4165	63	23	major	major	ADJ
cana-4165	63	24	breakthrough	breakthrough	NOUN
cana-4165	63	25	.	.	PUNCT
cana-4165	64	1	sommerfeld	sommerfeld	PROPN
cana-4165	64	2	fixed	fix	VERB
cana-4165	64	3	various	various	ADJ
cana-4165	64	4	contradictions	contradiction	NOUN
cana-4165	64	5	in	in	ADP
cana-4165	64	6	the	the	DET
cana-4165	64	7	original	original	ADJ
cana-4165	64	8	theory	theory	NOUN
cana-4165	64	9	,	,	PUNCT
cana-4165	64	10	especially	especially	ADV
cana-4165	64	11	with	with	ADP
cana-4165	64	12	relation	relation	NOUN
cana-4165	64	13	to	to	ADP
cana-4165	64	14	the	the	DET
cana-4165	64	15	temperature	temperature	NOUN
cana-4165	64	16	dependence	dependence	NOUN
cana-4165	64	17	of	of	ADP
cana-4165	64	18	conductivity	conductivity	NOUN
cana-4165	64	19	and	and	CCONJ
cana-4165	64	20	the	the	DET
cana-4165	64	21	electronic	electronic	ADJ
cana-4165	64	22	contribution	contribution	NOUN
cana-4165	64	23	to	to	ADP
cana-4165	64	24	specific	specific	ADJ
cana-4165	64	25	heat	heat	NOUN
cana-4165	64	26	,	,	PUNCT
cana-4165	64	27	by	by	ADP
cana-4165	64	28	realizing	realize	VERB
cana-4165	64	29	that	that	SCONJ
cana-4165	64	30	electrons	electron	NOUN
cana-4165	64	31	follow	follow	VERB
cana-4165	64	32	fermi	fermi	NOUN
cana-4165	64	33	-	-	PUNCT
cana-4165	64	34	dirac	dirac	NOUN
cana-4165	64	35	statistics	statistic	NOUN
cana-4165	64	36	rather	rather	ADV
cana-4165	64	37	than	than	ADP
cana-4165	64	38	the	the	DET
cana-4165	64	39	conventional	conventional	ADJ
cana-4165	64	40	maxwell	maxwell	PROPN
cana-4165	64	41	-	-	PUNCT
cana-4165	64	42	boltzmann	boltzmann	PROPN
cana-4165	64	43	distribution	distribution	NOUN
cana-4165	64	44	.	.	PUNCT
cana-4165	65	1	still	still	ADV
cana-4165	65	2	,	,	PUNCT
cana-4165	65	3	this	this	DET
cana-4165	65	4	quantum	quantum	NOUN
cana-4165	65	5	refinement	refinement	NOUN
cana-4165	65	6	handled	handle	VERB
cana-4165	65	7	electrons	electron	NOUN
cana-4165	65	8	as	as	ADP
cana-4165	65	9	basically	basically	ADV
cana-4165	65	10	free	free	ADJ
cana-4165	65	11	particles	particle	NOUN
cana-4165	65	12	dispersed	disperse	VERB
cana-4165	65	13	by	by	ADP
cana-4165	65	14	stationary	stationary	ADJ
cana-4165	65	15	ions	ion	NOUN
cana-4165	65	16	.	.	PUNCT
cana-4165	66	1	bloch	bloch	PROPN
cana-4165	66	2	's	's	PART
cana-4165	66	3	theorem	theorem	NOUN
cana-4165	66	4	(	(	PUNCT
cana-4165	66	5	1928	1928	NUM
cana-4165	66	6	)	)	PUNCT
cana-4165	66	7	showed	show	VERB
cana-4165	66	8	that	that	SCONJ
cana-4165	66	9	electrons	electron	NOUN
cana-4165	66	10	in	in	ADP
cana-4165	66	11	periodic	periodic	ADJ
cana-4165	66	12	potentials	potential	NOUN
cana-4165	66	13	should	should	AUX
cana-4165	66	14	be	be	AUX
cana-4165	66	15	characterized	characterize	VERB
cana-4165	66	16	by	by	ADP
cana-4165	66	17	wave	wave	NOUN
cana-4165	66	18	functions	function	NOUN
cana-4165	66	19	with	with	ADP
cana-4165	66	20	the	the	DET
cana-4165	66	21	periodicity	periodicity	NOUN
cana-4165	66	22	of	of	ADP
cana-4165	66	23	the	the	DET
cana-4165	66	24	lattice	lattice	NOUN
cana-4165	66	25	,	,	PUNCT
cana-4165	66	26	hence	hence	ADV
cana-4165	66	27	transforming	transform	VERB
cana-4165	66	28	the	the	DET
cana-4165	66	29	quantum	quantum	ADJ
cana-4165	66	30	mechanical	mechanical	ADJ
cana-4165	66	31	knowledge	knowledge	NOUN
cana-4165	66	32	of	of	ADP
cana-4165	66	33	electron	electron	NOUN
cana-4165	66	34	transport	transport	NOUN
cana-4165	66	35	in	in	ADP
cana-4165	66	36	crystals	crystal	NOUN
cana-4165	66	37	.	.	PUNCT
cana-4165	67	1	this	this	DET
cana-4165	67	2	realization	realization	NOUN
cana-4165	67	3	resulted	result	VERB
cana-4165	67	4	in	in	ADP
cana-4165	67	5	the	the	DET
cana-4165	67	6	idea	idea	NOUN
cana-4165	67	7	of	of	ADP
cana-4165	67	8	electron	electron	NOUN
cana-4165	67	9	bands	band	NOUN
cana-4165	67	10	and	and	CCONJ
cana-4165	67	11	clarified	clarify	VERB
cana-4165	67	12	phenomena	phenomenon	NOUN
cana-4165	67	13	including	include	VERB
cana-4165	67	14	the	the	DET
cana-4165	67	15	presence	presence	NOUN
cana-4165	67	16	of	of	ADP
cana-4165	67	17	semiconductors	semiconductor	NOUN
cana-4165	67	18	and	and	CCONJ
cana-4165	67	19	insulators	insulator	NOUN
cana-4165	67	20	.	.	PUNCT
cana-4165	68	1	almost	almost	ADV
cana-4165	68	2	all	all	PRON
cana-4165	68	3	later	late	ADJ
cana-4165	68	4	ideas	idea	NOUN
cana-4165	68	5	of	of	ADP
cana-4165	68	6	electron	electron	NOUN
cana-4165	68	7	transport	transport	NOUN
cana-4165	68	8	in	in	ADP
cana-4165	68	9	crystalline	crystalline	ADJ
cana-4165	68	10	solids	solid	NOUN
cana-4165	68	11	derived	derive	VERB
cana-4165	68	12	from	from	ADP
cana-4165	68	13	bloch	bloch	PROPN
cana-4165	68	14	's	's	PART
cana-4165	68	15	work	work	NOUN
cana-4165	68	16	.	.	PUNCT
cana-4165	69	1	the	the	DET
cana-4165	69	2	semiclassical	semiclassical	ADJ
cana-4165	69	3	theory	theory	NOUN
cana-4165	69	4	of	of	ADP
cana-4165	69	5	electron	electron	NOUN
cana-4165	69	6	dynamics	dynamic	NOUN
cana-4165	69	7	in	in	ADP
cana-4165	69	8	crystals	crystal	NOUN
cana-4165	69	9	was	be	AUX
cana-4165	69	10	established	establish	VERB
cana-4165	69	11	by	by	ADP
cana-4165	69	12	peierls	peierl	NOUN
cana-4165	69	13	(	(	PUNCT
cana-4165	69	14	1929	1929	NUM
cana-4165	69	15	)	)	PUNCT
cana-4165	69	16	and	and	CCONJ
cana-4165	69	17	subsequently	subsequently	ADV
cana-4165	69	18	wilson	wilson	PROPN
cana-4165	69	19	(	(	PUNCT
cana-4165	69	20	1931	1931	NUM
cana-4165	69	21	)	)	PUNCT
cana-4165	69	22	,	,	PUNCT
cana-4165	69	23	therefore	therefore	ADV
cana-4165	69	24	introducing	introduce	VERB
cana-4165	69	25	the	the	DET
cana-4165	69	26	idea	idea	NOUN
cana-4165	69	27	of	of	ADP
cana-4165	69	28	effective	effective	ADJ
cana-4165	69	29	mass	mass	NOUN
cana-4165	69	30	to	to	PART
cana-4165	69	31	explain	explain	VERB
cana-4165	69	32	the	the	DET
cana-4165	69	33	effect	effect	NOUN
cana-4165	69	34	of	of	ADP
cana-4165	69	35	the	the	DET
cana-4165	69	36	band	band	NOUN
cana-4165	69	37	structure	structure	NOUN
cana-4165	69	38	on	on	ADP
cana-4165	69	39	electron	electron	NOUN
cana-4165	69	40	mobility	mobility	NOUN
cana-4165	69	41	.	.	PUNCT
cana-4165	70	1	with	with	ADP
cana-4165	70	2	k	k	PROPN
cana-4165	70	3	as	as	ADP
cana-4165	70	4	the	the	DET
cana-4165	70	5	crystal	crystal	NOUN
cana-4165	70	6	momentum	momentum	NOUN
cana-4165	70	7	,	,	PUNCT
cana-4165	70	8	the	the	DET
cana-4165	70	9	equation	equation	NOUN
cana-4165	70	10	of	of	ADP
cana-4165	70	11	motion	motion	NOUN
cana-4165	70	12	in	in	ADP
cana-4165	70	13	this	this	DET
cana-4165	70	14	system	system	NOUN
cana-4165	70	15	takes	take	VERB
cana-4165	70	16	the	the	DET
cana-4165	70	17	form	form	NOUN
cana-4165	70	18	ℐdk	ℐdk	PROPN
cana-4165	70	19	/	/	SYM
cana-4165	70	20	dt	dt	NOUN
cana-4165	70	21	=	=	NOUN
cana-4165	71	1	-ee	-ee	NOUN
cana-4165	71	2	.	.	PUNCT
cana-4165	72	1	although	although	SCONJ
cana-4165	72	2	still	still	ADV
cana-4165	72	3	approximative	approximative	ADJ
cana-4165	72	4	,	,	PUNCT
cana-4165	72	5	this	this	DET
cana-4165	72	6	formulation	formulation	NOUN
cana-4165	72	7	remains	remain	VERB
cana-4165	72	8	extensively	extensively	ADV
cana-4165	72	9	applied	apply	VERB
cana-4165	72	10	in	in	ADP
cana-4165	72	11	device	device	NOUN
cana-4165	72	12	physics	physics	NOUN
cana-4165	72	13	and	and	CCONJ
cana-4165	72	14	effectively	effectively	ADV
cana-4165	72	15	captured	capture	VERB
cana-4165	72	16	fundamental	fundamental	ADJ
cana-4165	72	17	aspects	aspect	NOUN
cana-4165	72	18	of	of	ADP
cana-4165	72	19	electron	electron	NOUN
cana-4165	72	20	transport	transport	NOUN
cana-4165	72	21	in	in	ADP
cana-4165	72	22	semiconductors	semiconductor	NOUN
cana-4165	72	23	.	.	PUNCT
cana-4165	73	1	originally	originally	ADV
cana-4165	73	2	developed	develop	VERB
cana-4165	73	3	for	for	ADP
cana-4165	73	4	classical	classical	ADJ
cana-4165	73	5	gases	gas	NOUN
cana-4165	73	6	,	,	PUNCT
cana-4165	73	7	several	several	ADJ
cana-4165	73	8	1930s	1930	NOUN
cana-4165	73	9	researchers	researcher	NOUN
cana-4165	73	10	modified	modify	VERB
cana-4165	73	11	the	the	DET
cana-4165	73	12	boltzmann	boltzmann	PROPN
cana-4165	73	13	transport	transport	NOUN
cana-4165	73	14	equation	equation	NOUN
cana-4165	73	15	(	(	PUNCT
cana-4165	73	16	bte	bte	NOUN
cana-4165	73	17	)	)	PUNCT
cana-4165	73	18	to	to	PART
cana-4165	73	19	fit	fit	VERB
cana-4165	73	20	electronic	electronic	ADJ
cana-4165	73	21	systems	system	NOUN
cana-4165	73	22	.	.	PUNCT
cana-4165	74	1	under	under	ADP
cana-4165	74	2	the	the	DET
cana-4165	74	3	impact	impact	NOUN
cana-4165	74	4	of	of	ADP
cana-4165	74	5	fields	field	NOUN
cana-4165	74	6	and	and	CCONJ
cana-4165	74	7	scattering	scatter	VERB
cana-4165	74	8	events	event	NOUN
cana-4165	74	9	,	,	PUNCT
cana-4165	74	10	this	this	DET
cana-4165	74	11	statistical	statistical	ADJ
cana-4165	74	12	method	method	NOUN
cana-4165	74	13	explains	explain	VERB
cana-4165	74	14	the	the	DET
cana-4165	74	15	change	change	NOUN
cana-4165	74	16	of	of	ADP
cana-4165	74	17	the	the	DET
cana-4165	74	18	electron	electron	NOUN
cana-4165	74	19	distribution	distribution	NOUN
cana-4165	74	20	function	function	NOUN
cana-4165	74	21	in	in	ADP
cana-4165	74	22	phase	phase	NOUN
cana-4165	74	23	space	space	NOUN
cana-4165	74	24	.	.	PUNCT
cana-4165	75	1	the	the	DET
cana-4165	75	2	linearized	linearize	VERB
cana-4165	75	3	bte	bte	NOUN
cana-4165	75	4	offers	offer	VERB
cana-4165	75	5	the	the	DET
cana-4165	75	6	conventional	conventional	ADJ
cana-4165	75	7	structure	structure	NOUN
cana-4165	75	8	for	for	ADP
cana-4165	75	9	computing	compute	VERB
cana-4165	75	10	conductivity	conductivity	NOUN
cana-4165	75	11	and	and	CCONJ
cana-4165	75	12	mobility	mobility	NOUN
cana-4165	75	13	as	as	ADV
cana-4165	75	14	well	well	ADV
cana-4165	75	15	as	as	ADP
cana-4165	75	16	transport	transport	NOUN
cana-4165	75	17	coefficients	coefficient	NOUN
cana-4165	75	18	.	.	PUNCT
cana-4165	76	1	landau	landau	NOUN
cana-4165	76	2	,	,	PUNCT
cana-4165	76	3	peierls	peierl	NOUN
cana-4165	76	4	,	,	PUNCT
cana-4165	76	5	and	and	CCONJ
cana-4165	76	6	others	other	NOUN
cana-4165	76	7	developed	develop	VERB
cana-4165	76	8	techniques	technique	NOUN
cana-4165	76	9	for	for	ADP
cana-4165	76	10	solving	solve	VERB
cana-4165	76	11	this	this	DET
cana-4165	76	12	equation	equation	NOUN
cana-4165	76	13	in	in	ADP
cana-4165	76	14	several	several	ADJ
cana-4165	76	15	approximations	approximation	NOUN
cana-4165	76	16	via	via	ADP
cana-4165	76	17	extensive	extensive	ADJ
cana-4165	76	18	labor	labor	NOUN
cana-4165	76	19	.	.	PUNCT
cana-4165	77	1	introduced	introduce	VERB
cana-4165	77	2	in	in	ADP
cana-4165	77	3	the	the	DET
cana-4165	77	4	1940s	1940	NOUN
cana-4165	77	5	,	,	PUNCT
cana-4165	77	6	feynman	feynman	PROPN
cana-4165	77	7	's	's	PART
cana-4165	77	8	path	path	NOUN
cana-4165	77	9	integral	integral	ADJ
cana-4165	77	10	formulation	formulation	NOUN
cana-4165	77	11	of	of	ADP
cana-4165	77	12	quantum	quantum	ADJ
cana-4165	77	13	mechanics	mechanic	NOUN
cana-4165	77	14	finally	finally	ADV
cana-4165	77	15	produced	produce	VERB
cana-4165	77	16	effective	effective	ADJ
cana-4165	77	17	methods	method	NOUN
cana-4165	77	18	for	for	ADP
cana-4165	77	19	treating	treat	VERB
cana-4165	77	20	electron	electron	NOUN
cana-4165	77	21	flow	flow	NOUN
cana-4165	77	22	.	.	PUNCT
cana-4165	78	1	establishing	establish	VERB
cana-4165	78	2	links	link	NOUN
cana-4165	78	3	between	between	ADP
cana-4165	78	4	quantum	quantum	ADJ
cana-4165	78	5	propagation	propagation	NOUN
cana-4165	78	6	and	and	CCONJ
cana-4165	78	7	stochastic	stochastic	NOUN
cana-4165	78	8	processes	process	NOUN
cana-4165	78	9	,	,	PUNCT
cana-4165	78	10	the	the	DET
cana-4165	78	11	feynman	feynman	PROPN
cana-4165	78	12	-	-	PUNCT
cana-4165	78	13	kac	kac	PROPN
cana-4165	78	14	formula	formula	NOUN
cana-4165	78	15	offers	offer	VERB
cana-4165	78	16	substitute	substitute	ADJ
cana-4165	78	17	methods	method	NOUN
cana-4165	78	18	of	of	ADP
cana-4165	78	19	transport	transport	NOUN
cana-4165	78	20	computation	computation	NOUN
cana-4165	78	21	.	.	PUNCT
cana-4165	79	1	these	these	DET
cana-4165	79	2	techniques	technique	NOUN
cana-4165	79	3	were	be	AUX
cana-4165	79	4	especially	especially	ADV
cana-4165	79	5	useful	useful	ADJ
cana-4165	79	6	for	for	ADP
cana-4165	79	7	handling	handle	VERB
cana-4165	79	8	disordered	disordered	ADJ
cana-4165	79	9	systems	system	NOUN
cana-4165	79	10	in	in	ADP
cana-4165	79	11	which	which	PRON
cana-4165	79	12	conventional	conventional	ADJ
cana-4165	79	13	blochbased	blochbase	VERB
cana-4165	79	14	solutions	solution	NOUN
cana-4165	79	15	become	become	VERB
cana-4165	79	16	impractical	impractical	ADJ
cana-4165	79	17	.	.	PUNCT
cana-4165	80	1	establishing	establish	VERB
cana-4165	80	2	a	a	DET
cana-4165	80	3	broad	broad	ADJ
cana-4165	80	4	framework	framework	NOUN
cana-4165	80	5	for	for	ADP
cana-4165	80	6	computing	compute	VERB
cana-4165	80	7	transport	transport	NOUN
cana-4165	80	8	coefficients	coefficient	NOUN
cana-4165	80	9	from	from	ADP
cana-4165	80	10	equilibrium	equilibrium	NOUN
cana-4165	80	11	correlation	correlation	NOUN
cana-4165	80	12	functions	function	NOUN
cana-4165	80	13	,	,	PUNCT
cana-4165	80	14	kubo	kubo	PROPN
cana-4165	80	15	's	's	PART
cana-4165	80	16	linear	linear	ADJ
cana-4165	80	17	response	response	NOUN
cana-4165	80	18	theory	theory	NOUN
cana-4165	80	19	(	(	PUNCT
cana-4165	80	20	1957	1957	NUM
cana-4165	80	21	)	)	PUNCT
cana-4165	80	22	marked	mark	VERB
cana-4165	80	23	still	still	ADV
cana-4165	80	24	another	another	DET
cana-4165	80	25	milestone	milestone	NOUN
cana-4165	80	26	.	.	PUNCT
cana-4165	81	1	the	the	DET
cana-4165	81	2	kubo	kubo	PROPN
cana-4165	81	3	formula	formula	NOUN
cana-4165	81	4	offers	offer	VERB
cana-4165	81	5	a	a	DET
cana-4165	81	6	logical	logical	ADJ
cana-4165	81	7	basis	basis	NOUN
cana-4165	81	8	for	for	ADP
cana-4165	81	9	transport	transport	NOUN
cana-4165	81	10	theory	theory	NOUN
cana-4165	81	11	that	that	PRON
cana-4165	81	12	inevitably	inevitably	ADV
cana-4165	81	13	integrates	integrate	VERB
cana-4165	81	14	quantum	quantum	ADJ
cana-4165	81	15	phenomena	phenomenon	NOUN
cana-4165	81	16	by	by	ADP
cana-4165	81	17	relating	relate	VERB
cana-4165	81	18	conductivity	conductivity	NOUN
cana-4165	81	19	to	to	ADP
cana-4165	81	20	the	the	DET
cana-4165	81	21	current	current	ADJ
cana-4165	81	22	-	-	PUNCT
cana-4165	81	23	current	current	ADJ
cana-4165	81	24	correlation	correlation	NOUN
cana-4165	81	25	function	function	NOUN
cana-4165	81	26	.	.	PUNCT
cana-4165	82	1	particularly	particularly	ADV
cana-4165	82	2	with	with	ADP
cana-4165	82	3	relation	relation	NOUN
cana-4165	82	4	to	to	ADP
cana-4165	82	5	quantum	quantum	ADJ
cana-4165	82	6	coherence	coherence	NOUN
cana-4165	82	7	,	,	PUNCT
cana-4165	82	8	this	this	DET
cana-4165	82	9	method	method	NOUN
cana-4165	82	10	avoids	avoid	VERB
cana-4165	82	11	several	several	ADJ
cana-4165	82	12	restrictions	restriction	NOUN
cana-4165	82	13	of	of	ADP
cana-4165	82	14	the	the	DET
cana-4165	82	15	boltzmann	boltzmann	PROPN
cana-4165	82	16	equation	equation	NOUN
cana-4165	82	17	.	.	PUNCT
cana-4165	83	1	based	base	VERB
cana-4165	83	2	on	on	ADP
cana-4165	83	3	transmission	transmission	NOUN
cana-4165	83	4	probability	probability	NOUN
cana-4165	83	5	between	between	ADP
cana-4165	83	6	leads	lead	NOUN
cana-4165	83	7	,	,	PUNCT
cana-4165	83	8	landauer	landauer	NOUN
cana-4165	83	9	(	(	PUNCT
cana-4165	83	10	1957	1957	NUM
cana-4165	83	11	)	)	PUNCT
cana-4165	83	12	and	and	CCONJ
cana-4165	83	13	later	later	ADV
cana-4165	83	14	büttiker	büttiker	NOUN
cana-4165	83	15	devised	devise	VERB
cana-4165	83	16	a	a	DET
cana-4165	83	17	new	new	ADJ
cana-4165	83	18	method	method	NOUN
cana-4165	83	19	of	of	ADP
cana-4165	83	20	quantum	quantum	ADJ
cana-4165	83	21	transport	transport	NOUN
cana-4165	83	22	.	.	PUNCT
cana-4165	84	1	mesoscopic	mesoscopic	NOUN
cana-4165	84	2	systems	system	NOUN
cana-4165	84	3	,	,	PUNCT
cana-4165	84	4	where	where	SCONJ
cana-4165	84	5	sample	sample	NOUN
cana-4165	84	6	dimensions	dimension	NOUN
cana-4165	84	7	approach	approach	VERB
cana-4165	84	8	typical	typical	ADJ
cana-4165	84	9	quantum	quantum	ADJ
cana-4165	84	10	lengths	length	NOUN
cana-4165	84	11	like	like	ADP
cana-4165	84	12	the	the	DET
cana-4165	84	13	phase	phase	NOUN
cana-4165	84	14	coherence	coherence	NOUN
cana-4165	84	15	length	length	NOUN
cana-4165	84	16	,	,	PUNCT
cana-4165	84	17	found	find	VERB
cana-4165	84	18	particular	particular	ADJ
cana-4165	84	19	fit	fit	NOUN
cana-4165	84	20	for	for	ADP
cana-4165	84	21	this	this	DET
cana-4165	84	22	scattering	scatter	VERB
cana-4165	84	23	theory	theory	NOUN
cana-4165	84	24	of	of	ADP
cana-4165	84	25	transport	transport	NOUN
cana-4165	84	26	.	.	PUNCT
cana-4165	85	1	natural	natural	ADJ
cana-4165	85	2	description	description	NOUN
cana-4165	85	3	of	of	ADP
cana-4165	85	4	conductance	conductance	NOUN
cana-4165	85	5	quantization	quantization	NOUN
cana-4165	85	6	and	and	CCONJ
cana-4165	85	7	resonant	resonant	ADJ
cana-4165	85	8	tunneling	tunneling	NOUN
cana-4165	85	9	events	event	NOUN
cana-4165	85	10	is	be	AUX
cana-4165	85	11	given	give	VERB
cana-4165	85	12	by	by	ADP
cana-4165	85	13	the	the	DET
cana-4165	85	14	landauer	landauer	NOUN
cana-4165	85	15	-	-	PUNCT
cana-4165	85	16	büttiker	büttiker	NOUN
cana-4165	85	17	formalism	formalism	NOUN
cana-4165	85	18	.	.	PUNCT
cana-4165	86	1	communications	communication	NOUN
cana-4165	86	2	on	on	ADP
cana-4165	86	3	applied	apply	VERB
cana-4165	86	4	nonlinear	nonlinear	ADJ
cana-4165	86	5	analysis	analysis	NOUN
cana-4165	86	6	issn	issn	NOUN
cana-4165	86	7	:	:	PUNCT
cana-4165	86	8	1074	1074	NUM
cana-4165	86	9	-	-	PUNCT
cana-4165	86	10	133x	133x	NUM
cana-4165	86	11	vol	vol	NOUN
cana-4165	86	12	32	32	NUM
cana-4165	86	13	no	no	NOUN
cana-4165	86	14	.	.	PUNCT
cana-4165	87	1	9s	9s	NUM
cana-4165	87	2	(	(	PUNCT
cana-4165	87	3	2025	2025	NUM
cana-4165	87	4	)	)	PUNCT
cana-4165	87	5	1392	1392	NUM
cana-4165	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	87	7	thekeldysh	thekeldysh	NOUN
cana-4165	87	8	non	non	ADJ
cana-4165	87	9	-	-	ADJ
cana-4165	87	10	equilibrium	equilibrium	NOUN
cana-4165	87	11	developed	develop	VERB
cana-4165	87	12	in	in	ADP
cana-4165	87	13	the	the	DET
cana-4165	87	14	1960s	1960	NOUN
cana-4165	87	15	,	,	PUNCT
cana-4165	87	16	green	green	PROPN
cana-4165	87	17	's	's	PART
cana-4165	87	18	function	function	NOUN
cana-4165	87	19	methodology	methodology	NOUN
cana-4165	87	20	combined	combine	VERB
cana-4165	87	21	several	several	ADJ
cana-4165	87	22	earlier	early	ADJ
cana-4165	87	23	methods	method	NOUN
cana-4165	87	24	and	and	CCONJ
cana-4165	87	25	expanded	expand	VERB
cana-4165	87	26	its	its	PRON
cana-4165	87	27	relevance	relevance	NOUN
cana-4165	87	28	to	to	ADP
cana-4165	87	29	highly	highly	ADV
cana-4165	87	30	non	non	ADJ
cana-4165	87	31	-	-	ADJ
cana-4165	87	32	equilibrium	equilibrium	ADJ
cana-4165	87	33	conditions	condition	NOUN
cana-4165	87	34	.	.	PUNCT
cana-4165	88	1	for	for	ADP
cana-4165	88	2	numerical	numerical	ADJ
cana-4165	88	3	simulations	simulation	NOUN
cana-4165	88	4	of	of	ADP
cana-4165	88	5	quantum	quantum	ADJ
cana-4165	88	6	transport	transport	NOUN
cana-4165	88	7	in	in	ADP
cana-4165	88	8	nanoscale	nanoscale	NOUN
cana-4165	88	9	devices	device	NOUN
cana-4165	88	10	,	,	PUNCT
cana-4165	88	11	this	this	DET
cana-4165	88	12	strong	strong	ADJ
cana-4165	88	13	formalism	formalism	NOUN
cana-4165	88	14	offers	offer	VERB
cana-4165	88	15	a	a	DET
cana-4165	88	16	methodical	methodical	ADJ
cana-4165	88	17	approach	approach	NOUN
cana-4165	88	18	to	to	PART
cana-4165	88	19	include	include	VERB
cana-4165	88	20	many	many	ADJ
cana-4165	88	21	-	-	PUNCT
cana-4165	88	22	body	body	NOUN
cana-4165	88	23	effects	effect	NOUN
cana-4165	88	24	and	and	CCONJ
cana-4165	88	25	has	have	AUX
cana-4165	88	26	evolved	evolve	VERB
cana-4165	88	27	as	as	ADP
cana-4165	88	28	the	the	DET
cana-4165	88	29	preferred	preferred	ADJ
cana-4165	88	30	technique	technique	NOUN
cana-4165	88	31	.	.	PUNCT
cana-4165	89	1	kadanoff	kadanoff	NOUN
cana-4165	89	2	and	and	CCONJ
cana-4165	89	3	baym	baym	PROPN
cana-4165	89	4	's	's	PART
cana-4165	89	5	work	work	NOUN
cana-4165	89	6	established	establish	VERB
cana-4165	89	7	the	the	DET
cana-4165	89	8	link	link	NOUN
cana-4165	89	9	in	in	ADP
cana-4165	89	10	suitable	suitable	ADJ
cana-4165	89	11	limits	limit	NOUN
cana-4165	89	12	between	between	ADP
cana-4165	89	13	this	this	DET
cana-4165	89	14	method	method	NOUN
cana-4165	89	15	and	and	CCONJ
cana-4165	89	16	the	the	DET
cana-4165	89	17	boltzmann	boltzmann	PROPN
cana-4165	89	18	equation	equation	NOUN
cana-4165	89	19	.	.	PUNCT
cana-4165	90	1	pioneered	pioneer	VERB
cana-4165	90	2	in	in	ADP
cana-4165	90	3	the	the	DET
cana-4165	90	4	framework	framework	NOUN
cana-4165	90	5	of	of	ADP
cana-4165	90	6	localization	localization	NOUN
cana-4165	90	7	by	by	ADP
cana-4165	90	8	anderson	anderson	PROPN
cana-4165	90	9	,	,	PUNCT
cana-4165	90	10	thouless	thouless	NOUN
cana-4165	90	11	,	,	PUNCT
cana-4165	90	12	and	and	CCONJ
cana-4165	90	13	others	other	NOUN
cana-4165	90	14	,	,	PUNCT
cana-4165	90	15	scaling	scale	VERB
cana-4165	90	16	theory	theory	NOUN
cana-4165	90	17	offered	offer	VERB
cana-4165	90	18	vital	vital	ADJ
cana-4165	90	19	new	new	ADJ
cana-4165	90	20	perspectives	perspective	NOUN
cana-4165	90	21	on	on	ADP
cana-4165	90	22	the	the	DET
cana-4165	90	23	dimensional	dimensional	ADJ
cana-4165	90	24	dependency	dependency	NOUN
cana-4165	90	25	of	of	ADP
cana-4165	90	26	transport	transport	NOUN
cana-4165	90	27	events	event	NOUN
cana-4165	90	28	.	.	PUNCT
cana-4165	91	1	our	our	PRON
cana-4165	91	2	knowledge	knowledge	NOUN
cana-4165	91	3	of	of	ADP
cana-4165	91	4	transport	transport	NOUN
cana-4165	91	5	in	in	ADP
cana-4165	91	6	low	low	ADJ
cana-4165	91	7	-	-	PUNCT
cana-4165	91	8	dimensional	dimensional	ADJ
cana-4165	91	9	systems	system	NOUN
cana-4165	91	10	was	be	AUX
cana-4165	91	11	transformed	transform	VERB
cana-4165	91	12	when	when	SCONJ
cana-4165	91	13	we	we	PRON
cana-4165	91	14	realised	realise	VERB
cana-4165	91	15	all	all	DET
cana-4165	91	16	states	state	NOUN
cana-4165	91	17	in	in	ADP
cana-4165	91	18	disordered	disordered	ADJ
cana-4165	91	19	one	one	NUM
cana-4165	91	20	-	-	PUNCT
cana-4165	91	21	dimensional	dimensional	ADJ
cana-4165	91	22	and	and	CCONJ
cana-4165	91	23	two	two	NUM
cana-4165	91	24	-	-	PUNCT
cana-4165	91	25	dimensional	dimensional	ADJ
cana-4165	91	26	systems	system	NOUN
cana-4165	91	27	should	should	AUX
cana-4165	91	28	be	be	AUX
cana-4165	91	29	localized	localize	VERB
cana-4165	91	30	at	at	ADP
cana-4165	91	31	zero	zero	NUM
cana-4165	91	32	temperature	temperature	NOUN
cana-4165	91	33	(	(	PUNCT
cana-4165	91	34	in	in	ADP
cana-4165	91	35	the	the	DET
cana-4165	91	36	absence	absence	NOUN
cana-4165	91	37	of	of	ADP
cana-4165	91	38	particular	particular	ADJ
cana-4165	91	39	symmetries	symmetry	NOUN
cana-4165	91	40	)	)	PUNCT
cana-4165	91	41	.	.	PUNCT
cana-4165	92	1	by	by	ADP
cana-4165	92	2	means	mean	NOUN
cana-4165	92	3	of	of	ADP
cana-4165	92	4	the	the	DET
cana-4165	92	5	beta	beta	ADJ
cana-4165	92	6	function	function	NOUN
cana-4165	92	7	for	for	ADP
cana-4165	92	8	conductance	conductance	NOUN
cana-4165	92	9	,	,	PUNCT
cana-4165	92	10	a	a	DET
cana-4165	92	11	consistent	consistent	ADJ
cana-4165	92	12	explanation	explanation	NOUN
cana-4165	92	13	of	of	ADP
cana-4165	92	14	metalinsulator	metalinsulator	NOUN
cana-4165	92	15	transitions	transition	NOUN
cana-4165	92	16	was	be	AUX
cana-4165	92	17	possible	possible	ADJ
cana-4165	92	18	.	.	PUNCT
cana-4165	93	1	found	find	VERB
cana-4165	93	2	experimentally	experimentally	ADV
cana-4165	93	3	by	by	ADP
cana-4165	93	4	von	von	PROPN
cana-4165	93	5	klitzing	klitzing	PROPN
cana-4165	93	6	in	in	ADP
cana-4165	93	7	1980	1980	NUM
cana-4165	93	8	,	,	PUNCT
cana-4165	93	9	the	the	DET
cana-4165	93	10	quantum	quantum	PROPN
cana-4165	93	11	hall	hall	NOUN
cana-4165	93	12	effect	effect	NOUN
cana-4165	93	13	exposed	expose	VERB
cana-4165	93	14	essentially	essentially	ADV
cana-4165	93	15	fresh	fresh	ADJ
cana-4165	93	16	transport	transport	NOUN
cana-4165	93	17	mechanics	mechanic	NOUN
cana-4165	93	18	in	in	ADP
cana-4165	93	19	two	two	NUM
cana-4165	93	20	-	-	PUNCT
cana-4165	93	21	dimensional	dimensional	ADJ
cana-4165	93	22	electron	electron	NOUN
cana-4165	93	23	systems	system	NOUN
cana-4165	93	24	exposed	expose	VERB
cana-4165	93	25	to	to	ADP
cana-4165	93	26	strong	strong	ADJ
cana-4165	93	27	magnetic	magnetic	ADJ
cana-4165	93	28	fields	field	NOUN
cana-4165	93	29	.	.	PUNCT
cana-4165	94	1	developed	develop	VERB
cana-4165	94	2	by	by	ADP
cana-4165	94	3	laughlin	laughlin	PROPN
cana-4165	94	4	,	,	PUNCT
cana-4165	94	5	thouless	thouless	NOUN
cana-4165	94	6	,	,	PUNCT
cana-4165	94	7	and	and	CCONJ
cana-4165	94	8	others	other	NOUN
cana-4165	94	9	,	,	PUNCT
cana-4165	94	10	the	the	DET
cana-4165	94	11	theoretical	theoretical	ADJ
cana-4165	94	12	justification	justification	NOUN
cana-4165	94	13	used	use	VERB
cana-4165	94	14	topological	topological	ADJ
cana-4165	94	15	ideas	idea	NOUN
cana-4165	94	16	that	that	PRON
cana-4165	94	17	have	have	AUX
cana-4165	94	18	since	since	SCONJ
cana-4165	94	19	proven	prove	VERB
cana-4165	94	20	fundamental	fundamental	ADJ
cana-4165	94	21	in	in	ADP
cana-4165	94	22	modern	modern	ADJ
cana-4165	94	23	condensed	condense	VERB
cana-4165	94	24	matter	matter	NOUN
cana-4165	94	25	physics	physics	NOUN
cana-4165	94	26	.	.	PUNCT
cana-4165	95	1	topological	topological	ADJ
cana-4165	95	2	band	band	NOUN
cana-4165	95	3	theory	theory	NOUN
cana-4165	95	4	's	's	PART
cana-4165	95	5	resultant	resultant	NOUN
cana-4165	95	6	paradigm	paradigm	NOUN
cana-4165	95	7	has	have	VERB
cana-4165	95	8	significant	significant	ADJ
cana-4165	95	9	consequences	consequence	NOUN
cana-4165	95	10	for	for	ADP
cana-4165	95	11	electron	electron	NOUN
cana-4165	95	12	transport	transport	NOUN
cana-4165	95	13	in	in	ADP
cana-4165	95	14	many	many	ADJ
cana-4165	95	15	systems	system	NOUN
cana-4165	95	16	.	.	PUNCT
cana-4165	96	1	the	the	DET
cana-4165	96	2	1980s	1980s	NUM
cana-4165	96	3	saw	see	VERB
cana-4165	96	4	the	the	DET
cana-4165	96	5	discovery	discovery	NOUN
cana-4165	96	6	of	of	ADP
cana-4165	96	7	high	high	ADJ
cana-4165	96	8	-	-	PUNCT
cana-4165	96	9	temperature	temperature	NOUN
cana-4165	96	10	superconductors	superconductor	NOUN
cana-4165	96	11	,	,	PUNCT
cana-4165	96	12	therefore	therefore	ADV
cana-4165	96	13	undermining	undermine	VERB
cana-4165	96	14	accepted	accepted	ADJ
cana-4165	96	15	transport	transport	NOUN
cana-4165	96	16	models	model	NOUN
cana-4165	96	17	.	.	PUNCT
cana-4165	97	1	behavior	behavior	NOUN
cana-4165	97	2	of	of	ADP
cana-4165	97	3	these	these	DET
cana-4165	97	4	strongly	strongly	ADV
cana-4165	97	5	correlated	correlate	VERB
cana-4165	97	6	materials	material	NOUN
cana-4165	97	7	can	can	AUX
cana-4165	97	8	not	not	PART
cana-4165	97	9	be	be	AUX
cana-4165	97	10	sufficiently	sufficiently	ADV
cana-4165	97	11	explained	explain	VERB
cana-4165	97	12	by	by	ADP
cana-4165	97	13	independent	independent	ADJ
cana-4165	97	14	-	-	PUNCT
cana-4165	97	15	electron	electron	NOUN
cana-4165	97	16	approximations	approximation	NOUN
cana-4165	97	17	.	.	PUNCT
cana-4165	98	1	several	several	ADJ
cana-4165	98	2	theoretical	theoretical	ADJ
cana-4165	98	3	models	model	NOUN
cana-4165	98	4	have	have	AUX
cana-4165	98	5	been	be	AUX
cana-4165	98	6	developed	develop	VERB
cana-4165	98	7	to	to	PART
cana-4165	98	8	solve	solve	VERB
cana-4165	98	9	these	these	DET
cana-4165	98	10	difficulties	difficulty	NOUN
cana-4165	98	11	with	with	ADP
cana-4165	98	12	important	important	ADJ
cana-4165	98	13	consequences	consequence	NOUN
cana-4165	98	14	for	for	ADP
cana-4165	98	15	normal	normal	ADJ
cana-4165	98	16	-	-	PUNCT
cana-4165	98	17	state	state	NOUN
cana-4165	98	18	transport	transport	NOUN
cana-4165	98	19	properties	property	NOUN
cana-4165	98	20	:	:	PUNCT
cana-4165	98	21	dynamical	dynamical	ADJ
cana-4165	98	22	mean	mean	ADJ
cana-4165	98	23	-	-	PUNCT
cana-4165	98	24	field	field	NOUN
cana-4165	98	25	theory	theory	NOUN
cana-4165	98	26	and	and	CCONJ
cana-4165	98	27	resonating	resonate	VERB
cana-4165	98	28	valence	valence	NOUN
cana-4165	98	29	bond	bond	NOUN
cana-4165	98	30	theory	theory	NOUN
cana-4165	98	31	among	among	ADP
cana-4165	98	32	others	other	NOUN
cana-4165	98	33	.	.	PUNCT
cana-4165	99	1	focusing	focus	VERB
cana-4165	99	2	on	on	ADP
cana-4165	99	3	systems	system	NOUN
cana-4165	99	4	midway	midway	ADV
cana-4165	99	5	between	between	ADP
cana-4165	99	6	the	the	DET
cana-4165	99	7	microscopic	microscopic	ADJ
cana-4165	99	8	quantum	quantum	ADJ
cana-4165	99	9	realm	realm	NOUN
cana-4165	99	10	and	and	CCONJ
cana-4165	99	11	the	the	DET
cana-4165	99	12	macroscopic	macroscopic	ADJ
cana-4165	99	13	classical	classical	ADJ
cana-4165	99	14	world	world	NOUN
cana-4165	99	15	,	,	PUNCT
cana-4165	99	16	mesoscopic	mesoscopic	NOUN
cana-4165	99	17	physics	physics	NOUN
cana-4165	99	18	first	first	ADV
cana-4165	99	19	developed	develop	VERB
cana-4165	99	20	as	as	ADP
cana-4165	99	21	a	a	DET
cana-4165	99	22	separate	separate	ADJ
cana-4165	99	23	field	field	NOUN
cana-4165	99	24	in	in	ADP
cana-4165	99	25	the	the	DET
cana-4165	99	26	1980s	1980	NOUN
cana-4165	99	27	and	and	CCONJ
cana-4165	99	28	1990s	1990	NOUN
cana-4165	99	29	important	important	ADJ
cana-4165	99	30	events	event	NOUN
cana-4165	99	31	in	in	ADP
cana-4165	99	32	this	this	DET
cana-4165	99	33	regime	regime	NOUN
cana-4165	99	34	consist	consist	VERB
cana-4165	99	35	in	in	ADP
cana-4165	99	36	weak	weak	ADJ
cana-4165	99	37	localization	localization	NOUN
cana-4165	99	38	,	,	PUNCT
cana-4165	99	39	universal	universal	ADJ
cana-4165	99	40	conductance	conductance	NOUN
cana-4165	99	41	fluctuations	fluctuation	NOUN
cana-4165	99	42	,	,	PUNCT
cana-4165	99	43	and	and	CCONJ
cana-4165	99	44	aharonov	aharonov	PROPN
cana-4165	99	45	-	-	PUNCT
cana-4165	99	46	bohm	bohm	PROPN
cana-4165	99	47	oscillations	oscillation	NOUN
cana-4165	99	48	.	.	PUNCT
cana-4165	100	1	these	these	DET
cana-4165	100	2	effects	effect	NOUN
cana-4165	100	3	have	have	AUX
cana-4165	100	4	been	be	AUX
cana-4165	100	5	refined	refine	VERB
cana-4165	100	6	in	in	ADP
cana-4165	100	7	transport	transport	NOUN
cana-4165	100	8	theory	theory	NOUN
cana-4165	100	9	by	by	ADP
cana-4165	100	10	means	mean	NOUN
cana-4165	100	11	of	of	ADP
cana-4165	100	12	thorough	thorough	ADJ
cana-4165	100	13	study	study	NOUN
cana-4165	100	14	of	of	ADP
cana-4165	100	15	quantum	quantum	ADJ
cana-4165	100	16	coherence	coherence	NOUN
cana-4165	100	17	in	in	ADP
cana-4165	100	18	the	the	DET
cana-4165	100	19	theoretical	theoretical	ADJ
cana-4165	100	20	description	description	NOUN
cana-4165	100	21	.	.	PUNCT
cana-4165	101	1	starting	start	VERB
cana-4165	101	2	with	with	ADP
cana-4165	101	3	graphene	graphene	NOUN
cana-4165	101	4	in	in	ADP
cana-4165	101	5	2004	2004	NUM
cana-4165	101	6	,	,	PUNCT
cana-4165	101	7	the	the	DET
cana-4165	101	8	development	development	NOUN
cana-4165	101	9	of	of	ADP
cana-4165	101	10	two	two	NUM
cana-4165	101	11	-	-	PUNCT
cana-4165	101	12	dimensional	dimensional	ADJ
cana-4165	101	13	materials	material	NOUN
cana-4165	101	14	has	have	AUX
cana-4165	101	15	driven	drive	VERB
cana-4165	101	16	more	more	ADJ
cana-4165	101	17	progress	progress	NOUN
cana-4165	101	18	in	in	ADP
cana-4165	101	19	transport	transport	NOUN
cana-4165	101	20	theory	theory	NOUN
cana-4165	101	21	.	.	PUNCT
cana-4165	102	1	unusual	unusual	ADJ
cana-4165	102	2	transport	transport	NOUN
cana-4165	102	3	characteristics	characteristic	NOUN
cana-4165	102	4	including	include	VERB
cana-4165	102	5	minimal	minimal	ADJ
cana-4165	102	6	conductivity	conductivity	NOUN
cana-4165	102	7	at	at	ADP
cana-4165	102	8	the	the	DET
cana-4165	102	9	neutrality	neutrality	NOUN
cana-4165	102	10	point	point	NOUN
cana-4165	102	11	and	and	CCONJ
cana-4165	102	12	klein	klein	PROPN
cana-4165	102	13	tunneling	tunneling	PROPN
cana-4165	102	14	are	be	AUX
cana-4165	102	15	obtained	obtain	VERB
cana-4165	102	16	from	from	ADP
cana-4165	102	17	the	the	DET
cana-4165	102	18	linear	linear	ADJ
cana-4165	102	19	dispersion	dispersion	NOUN
cana-4165	102	20	relation	relation	NOUN
cana-4165	102	21	close	close	ADJ
cana-4165	102	22	to	to	ADP
cana-4165	102	23	the	the	DET
cana-4165	102	24	dirac	dirac	NOUN
cana-4165	102	25	points	point	NOUN
cana-4165	102	26	in	in	ADP
cana-4165	102	27	graphene	graphene	NOUN
cana-4165	102	28	.	.	PUNCT
cana-4165	103	1	these	these	DET
cana-4165	103	2	results	result	NOUN
cana-4165	103	3	have	have	AUX
cana-4165	103	4	motivated	motivate	VERB
cana-4165	103	5	the	the	DET
cana-4165	103	6	investigation	investigation	NOUN
cana-4165	103	7	of	of	ADP
cana-4165	103	8	pseudospin	pseudospin	ADJ
cana-4165	103	9	-	-	PUNCT
cana-4165	103	10	dependent	dependent	ADJ
cana-4165	103	11	transport	transport	NOUN
cana-4165	103	12	events	event	NOUN
cana-4165	103	13	and	and	CCONJ
cana-4165	103	14	the	the	DET
cana-4165	103	15	creation	creation	NOUN
cana-4165	103	16	of	of	ADP
cana-4165	103	17	relativistic	relativistic	ADJ
cana-4165	103	18	analogies	analogy	NOUN
cana-4165	103	19	in	in	ADP
cana-4165	103	20	condensed	condense	VERB
cana-4165	103	21	matter	matter	NOUN
cana-4165	103	22	physics	physics	NOUN
cana-4165	103	23	.	.	PUNCT
cana-4165	104	1	another	another	DET
cana-4165	104	2	frontier	frontier	NOUN
cana-4165	104	3	in	in	ADP
cana-4165	104	4	transport	transport	NOUN
cana-4165	104	5	physics	physic	NOUN
cana-4165	104	6	are	be	AUX
cana-4165	104	7	theoretically	theoretically	ADV
cana-4165	104	8	anticipated	anticipate	VERB
cana-4165	104	9	and	and	CCONJ
cana-4165	104	10	experimentally	experimentally	ADV
cana-4165	104	11	verified	verify	VERB
cana-4165	104	12	topological	topological	ADJ
cana-4165	104	13	insulators	insulator	NOUN
cana-4165	104	14	from	from	ADP
cana-4165	104	15	the	the	DET
cana-4165	104	16	2000s	2000s	NUM
cana-4165	104	17	.	.	PUNCT
cana-4165	105	1	these	these	DET
cana-4165	105	2	materials	material	NOUN
cana-4165	105	3	have	have	AUX
cana-4165	105	4	conducting	conduct	VERB
cana-4165	105	5	surface	surface	NOUN
cana-4165	105	6	states	state	NOUN
cana-4165	105	7	sheltered	shelter	VERB
cana-4165	105	8	by	by	ADP
cana-4165	105	9	time	time	NOUN
cana-4165	105	10	-	-	PUNCT
cana-4165	105	11	reversal	reversal	NOUN
cana-4165	105	12	symmetry	symmetry	NOUN
cana-4165	105	13	yet	yet	ADV
cana-4165	105	14	insulating	insulate	VERB
cana-4165	105	15	bulk	bulk	ADJ
cana-4165	105	16	states	state	NOUN
cana-4165	105	17	.	.	PUNCT
cana-4165	106	1	these	these	DET
cana-4165	106	2	surface	surface	NOUN
cana-4165	106	3	states	state	NOUN
cana-4165	106	4	'	'	PART
cana-4165	106	5	strong	strong	ADJ
cana-4165	106	6	transport	transport	NOUN
cana-4165	106	7	characteristics	characteristic	NOUN
cana-4165	106	8	find	find	VERB
cana-4165	106	9	use	use	NOUN
cana-4165	106	10	in	in	ADP
cana-4165	106	11	spintronics	spintronic	NOUN
cana-4165	106	12	and	and	CCONJ
cana-4165	106	13	quantum	quantum	NOUN
cana-4165	106	14	computing	computing	NOUN
cana-4165	106	15	.	.	PUNCT
cana-4165	107	1	non	non	ADJ
cana-4165	107	2	-	-	ADJ
cana-4165	107	3	equilibrium	equilibrium	ADJ
cana-4165	107	4	quantum	quantum	NOUN
cana-4165	107	5	transport	transport	NOUN
cana-4165	107	6	has	have	AUX
cana-4165	107	7	lately	lately	ADV
cana-4165	107	8	attracted	attract	VERB
cana-4165	107	9	more	more	ADV
cana-4165	107	10	and	and	CCONJ
cana-4165	107	11	more	more	ADJ
cana-4165	107	12	attention	attention	NOUN
cana-4165	107	13	in	in	ADP
cana-4165	107	14	theoretical	theoretical	ADJ
cana-4165	107	15	studies	study	NOUN
cana-4165	107	16	.	.	PUNCT
cana-4165	108	1	first	first	ADJ
cana-4165	108	2	-	-	PUNCT
cana-4165	108	3	principles	principle	NOUN
cana-4165	108	4	computations	computation	NOUN
cana-4165	108	5	of	of	ADP
cana-4165	108	6	transient	transient	ADJ
cana-4165	108	7	responses	response	NOUN
cana-4165	108	8	are	be	AUX
cana-4165	108	9	made	make	VERB
cana-4165	108	10	possible	possible	ADJ
cana-4165	108	11	by	by	ADP
cana-4165	108	12	the	the	DET
cana-4165	108	13	advent	advent	NOUN
cana-4165	108	14	of	of	ADP
cana-4165	108	15	time	time	NOUN
cana-4165	108	16	-	-	PUNCT
cana-4165	108	17	dependent	dependent	ADJ
cana-4165	108	18	density	density	NOUN
cana-4165	108	19	functional	functional	ADJ
cana-4165	108	20	theory	theory	NOUN
cana-4165	108	21	and	and	CCONJ
cana-4165	108	22	its	its	PRON
cana-4165	108	23	application	application	NOUN
cana-4165	108	24	to	to	PART
cana-4165	108	25	transport	transport	NOUN
cana-4165	108	26	concerns	concern	NOUN
cana-4165	108	27	.	.	PUNCT
cana-4165	109	1	concurrently	concurrently	ADV
cana-4165	109	2	,	,	PUNCT
cana-4165	109	3	the	the	DET
cana-4165	109	4	connection	connection	NOUN
cana-4165	109	5	communications	communication	NOUN
cana-4165	109	6	on	on	ADP
cana-4165	109	7	applied	apply	VERB
cana-4165	109	8	nonlinear	nonlinear	ADJ
cana-4165	109	9	analysis	analysis	NOUN
cana-4165	109	10	issn	issn	NOUN
cana-4165	109	11	:	:	PUNCT
cana-4165	109	12	1074	1074	NUM
cana-4165	109	13	-	-	PUNCT
cana-4165	109	14	133x	133x	NUM
cana-4165	109	15	vol	vol	NOUN
cana-4165	109	16	32	32	NUM
cana-4165	109	17	no	no	NOUN
cana-4165	109	18	.	.	PUNCT
cana-4165	110	1	9s	9s	NUM
cana-4165	110	2	(	(	PUNCT
cana-4165	110	3	2025	2025	NUM
cana-4165	110	4	)	)	PUNCT
cana-4165	110	5	1393	1393	NUM
cana-4165	110	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	110	7	between	between	ADP
cana-4165	110	8	noise	noise	NOUN
cana-4165	110	9	characteristics	characteristic	NOUN
cana-4165	110	10	and	and	CCONJ
cana-4165	110	11	fundamental	fundamental	ADJ
cana-4165	110	12	transport	transport	NOUN
cana-4165	110	13	features	feature	NOUN
cana-4165	110	14	has	have	AUX
cana-4165	110	15	been	be	AUX
cana-4165	110	16	explained	explain	VERB
cana-4165	110	17	by	by	ADP
cana-4165	110	18	the	the	DET
cana-4165	110	19	fluctuationdissipation	fluctuationdissipation	NOUN
cana-4165	110	20	theorem	theorem	NOUN
cana-4165	110	21	and	and	CCONJ
cana-4165	110	22	its	its	PRON
cana-4165	110	23	generalizations	generalization	NOUN
cana-4165	110	24	to	to	ADP
cana-4165	110	25	non	non	ADJ
cana-4165	110	26	-	-	ADJ
cana-4165	110	27	equilibrium	equilibrium	ADJ
cana-4165	110	28	conditions	condition	NOUN
cana-4165	110	29	.	.	PUNCT
cana-4165	111	1	from	from	ADP
cana-4165	111	2	basic	basic	ADJ
cana-4165	111	3	monte	monte	PROPN
cana-4165	111	4	carlo	carlo	PROPN
cana-4165	111	5	simulations	simulation	NOUN
cana-4165	111	6	of	of	ADP
cana-4165	111	7	the	the	DET
cana-4165	111	8	boltzmann	boltzmann	PROPN
cana-4165	111	9	equation	equation	NOUN
cana-4165	111	10	to	to	ADP
cana-4165	111	11	advanced	advanced	ADJ
cana-4165	111	12	quantum	quantum	NOUN
cana-4165	111	13	transport	transport	NOUN
cana-4165	111	14	codes	code	NOUN
cana-4165	111	15	based	base	VERB
cana-4165	111	16	on	on	ADP
cana-4165	111	17	non	non	ADJ
cana-4165	111	18	-	-	ADJ
cana-4165	111	19	equilibrium	equilibrium	ADJ
cana-4165	111	20	green	green	NOUN
cana-4165	111	21	's	's	PART
cana-4165	111	22	functions	function	NOUN
cana-4165	111	23	or	or	CCONJ
cana-4165	111	24	wave	wave	NOUN
cana-4165	111	25	function	function	NOUN
cana-4165	111	26	matching	matching	NOUN
cana-4165	111	27	approaches	approach	NOUN
cana-4165	111	28	,	,	PUNCT
cana-4165	111	29	computational	computational	ADJ
cana-4165	111	30	methods	method	NOUN
cana-4165	111	31	have	have	AUX
cana-4165	111	32	evolved	evolve	VERB
cana-4165	111	33	substantially	substantially	ADV
cana-4165	111	34	.	.	PUNCT
cana-4165	112	1	particularly	particularly	ADV
cana-4165	112	2	as	as	SCONJ
cana-4165	112	3	dimensions	dimension	NOUN
cana-4165	112	4	reduce	reduce	VERB
cana-4165	112	5	and	and	CCONJ
cana-4165	112	6	quantum	quantum	NOUN
cana-4165	112	7	phenomena	phenomenon	NOUN
cana-4165	112	8	take	take	VERB
cana-4165	112	9	front	front	ADJ
cana-4165	112	10	stage	stage	NOUN
cana-4165	112	11	,	,	PUNCT
cana-4165	112	12	these	these	DET
cana-4165	112	13	numerical	numerical	ADJ
cana-4165	112	14	techniques	technique	NOUN
cana-4165	112	15	have	have	AUX
cana-4165	112	16	become	become	VERB
cana-4165	112	17	indispensable	indispensable	ADJ
cana-4165	112	18	for	for	ADP
cana-4165	112	19	analyzing	analyze	VERB
cana-4165	112	20	experiments	experiment	NOUN
cana-4165	112	21	and	and	CCONJ
cana-4165	112	22	projecting	project	VERB
cana-4165	112	23	device	device	NOUN
cana-4165	112	24	properties	property	NOUN
cana-4165	112	25	.	.	PUNCT
cana-4165	113	1	regarding	regard	VERB
cana-4165	113	2	the	the	DET
cana-4165	113	3	asymptotic	asymptotic	ADJ
cana-4165	113	4	behavior	behavior	NOUN
cana-4165	113	5	of	of	ADP
cana-4165	113	6	electron	electron	NOUN
cana-4165	113	7	mean	mean	NOUN
cana-4165	113	8	velocities	velocity	NOUN
cana-4165	113	9	especially	especially	ADV
cana-4165	113	10	,	,	PUNCT
cana-4165	113	11	numerous	numerous	ADJ
cana-4165	113	12	important	important	ADJ
cana-4165	113	13	contributions	contribution	NOUN
cana-4165	113	14	merit	merit	NOUN
cana-4165	113	15	discussion	discussion	NOUN
cana-4165	113	16	.	.	PUNCT
cana-4165	114	1	shockley	shockley	PROPN
cana-4165	114	2	investigated	investigate	VERB
cana-4165	114	3	the	the	DET
cana-4165	114	4	high	high	ADJ
cana-4165	114	5	-	-	PUNCT
cana-4165	114	6	field	field	NOUN
cana-4165	114	7	velocity	velocity	NOUN
cana-4165	114	8	saturation	saturation	NOUN
cana-4165	114	9	in	in	ADP
cana-4165	114	10	semiconductors	semiconductor	NOUN
cana-4165	114	11	in	in	ADP
cana-4165	114	12	great	great	ADJ
cana-4165	114	13	detail	detail	NOUN
cana-4165	114	14	and	and	CCONJ
cana-4165	114	15	developed	develop	VERB
cana-4165	114	16	the	the	DET
cana-4165	114	17	link	link	NOUN
cana-4165	114	18	between	between	ADP
cana-4165	114	19	saturation	saturation	NOUN
cana-4165	114	20	velocity	velocity	NOUN
cana-4165	114	21	and	and	CCONJ
cana-4165	114	22	optical	optical	ADJ
cana-4165	114	23	phonon	phonon	NOUN
cana-4165	114	24	energy	energy	NOUN
cana-4165	114	25	.	.	PUNCT
cana-4165	115	1	later	later	ADJ
cana-4165	115	2	improvements	improvement	NOUN
cana-4165	115	3	by	by	ADP
cana-4165	115	4	fischetti	fischetti	ADJ
cana-4165	115	5	and	and	CCONJ
cana-4165	115	6	others	other	NOUN
cana-4165	115	7	included	include	VERB
cana-4165	115	8	more	more	ADV
cana-4165	115	9	realistic	realistic	ADJ
cana-4165	115	10	scattering	scatter	VERB
cana-4165	115	11	models	model	NOUN
cana-4165	115	12	and	and	CCONJ
cana-4165	115	13	thorough	thorough	ADJ
cana-4165	115	14	band	band	NOUN
cana-4165	115	15	structural	structural	ADJ
cana-4165	115	16	computations	computation	NOUN
cana-4165	115	17	.	.	PUNCT
cana-4165	116	1	quantum	quantum	ADJ
cana-4165	116	2	corrections	correction	NOUN
cana-4165	116	3	to	to	ADP
cana-4165	116	4	the	the	DET
cana-4165	116	5	classical	classical	ADJ
cana-4165	116	6	drude	drude	ADJ
cana-4165	116	7	outcome	outcome	NOUN
cana-4165	116	8	have	have	AUX
cana-4165	116	9	been	be	AUX
cana-4165	116	10	found	find	VERB
cana-4165	116	11	theoretically	theoretically	ADV
cana-4165	116	12	from	from	ADP
cana-4165	116	13	the	the	DET
cana-4165	116	14	lowtemperature	lowtemperature	NOUN
cana-4165	116	15	limit	limit	NOUN
cana-4165	116	16	.	.	PUNCT
cana-4165	117	1	developed	develop	VERB
cana-4165	117	2	by	by	ADP
cana-4165	117	3	anderson	anderson	PROPN
cana-4165	117	4	,	,	PUNCT
cana-4165	117	5	gorkov	gorkov	PROPN
cana-4165	117	6	,	,	PUNCT
cana-4165	117	7	and	and	CCONJ
cana-4165	117	8	others	other	NOUN
cana-4165	117	9	,	,	PUNCT
cana-4165	117	10	weak	weak	ADJ
cana-4165	117	11	localization	localization	NOUN
cana-4165	117	12	theory	theory	NOUN
cana-4165	117	13	forecasts	forecast	VERB
cana-4165	117	14	a	a	DET
cana-4165	117	15	logarithmic	logarithmic	ADJ
cana-4165	117	16	temperature	temperature	NOUN
cana-4165	117	17	dependence	dependence	NOUN
cana-4165	117	18	of	of	ADP
cana-4165	117	19	conductivity	conductivity	NOUN
cana-4165	117	20	in	in	ADP
cana-4165	117	21	two	two	NUM
cana-4165	117	22	-	-	PUNCT
cana-4165	117	23	dimensional	dimensional	ADJ
cana-4165	117	24	systems	system	NOUN
cana-4165	117	25	by	by	ADP
cana-4165	117	26	means	mean	NOUN
cana-4165	117	27	of	of	ADP
cana-4165	117	28	quantum	quantum	ADJ
cana-4165	117	29	interference	interference	NOUN
cana-4165	117	30	phenomena	phenomenon	NOUN
cana-4165	117	31	.	.	PUNCT
cana-4165	118	1	experimentally	experimentally	ADV
cana-4165	118	2	confirmed	confirm	VERB
cana-4165	118	3	in	in	ADP
cana-4165	118	4	several	several	ADJ
cana-4165	118	5	materials	material	NOUN
cana-4165	118	6	,	,	PUNCT
cana-4165	118	7	these	these	DET
cana-4165	118	8	corrections	correction	NOUN
cana-4165	118	9	are	be	AUX
cana-4165	118	10	fundamental	fundamental	ADJ
cana-4165	118	11	elements	element	NOUN
cana-4165	118	12	of	of	ADP
cana-4165	118	13	a	a	DET
cana-4165	118	14	complete	complete	ADJ
cana-4165	118	15	asymptotic	asymptotic	ADJ
cana-4165	118	16	growth	growth	NOUN
cana-4165	118	17	.	.	PUNCT
cana-4165	119	1	via	via	ADP
cana-4165	119	2	both	both	DET
cana-4165	119	3	analytical	analytical	ADJ
cana-4165	119	4	theory	theory	NOUN
cana-4165	119	5	and	and	CCONJ
cana-4165	119	6	numerical	numerical	ADJ
cana-4165	119	7	simulations	simulation	NOUN
cana-4165	119	8	,	,	PUNCT
cana-4165	119	9	the	the	DET
cana-4165	119	10	dimensional	dimensional	ADJ
cana-4165	119	11	scaling	scaling	NOUN
cana-4165	119	12	of	of	ADP
cana-4165	119	13	transport	transport	NOUN
cana-4165	119	14	coefficients	coefficient	NOUN
cana-4165	119	15	has	have	AUX
cana-4165	119	16	been	be	AUX
cana-4165	119	17	methodically	methodically	ADV
cana-4165	119	18	investigated	investigate	VERB
cana-4165	119	19	.	.	PUNCT
cana-4165	120	1	quantum	quantum	ADJ
cana-4165	120	2	confinement	confinement	NOUN
cana-4165	120	3	changes	change	VERB
cana-4165	120	4	the	the	DET
cana-4165	120	5	density	density	NOUN
cana-4165	120	6	of	of	ADP
cana-4165	120	7	states	state	NOUN
cana-4165	120	8	and	and	CCONJ
cana-4165	120	9	scattering	scatter	VERB
cana-4165	120	10	rates	rate	NOUN
cana-4165	120	11	as	as	ADP
cana-4165	120	12	dimensionality	dimensionality	NOUN
cana-4165	120	13	reduces	reduce	NOUN
cana-4165	120	14	,	,	PUNCT
cana-4165	120	15	therefore	therefore	ADV
cana-4165	120	16	producing	produce	VERB
cana-4165	120	17	distinct	distinct	ADJ
cana-4165	120	18	functional	functional	ADJ
cana-4165	120	19	dependence	dependence	NOUN
cana-4165	120	20	on	on	ADP
cana-4165	120	21	parameters	parameter	NOUN
cana-4165	120	22	including	include	VERB
cana-4165	120	23	carrier	carrier	NOUN
cana-4165	120	24	density	density	NOUN
cana-4165	120	25	and	and	CCONJ
cana-4165	120	26	temperature	temperature	NOUN
cana-4165	120	27	.	.	PUNCT
cana-4165	121	1	any	any	DET
cana-4165	121	2	thorough	thorough	ADJ
cana-4165	121	3	asymptotic	asymptotic	ADJ
cana-4165	121	4	growth	growth	NOUN
cana-4165	121	5	depends	depend	VERB
cana-4165	121	6	on	on	ADP
cana-4165	121	7	these	these	DET
cana-4165	121	8	scaling	scale	VERB
cana-4165	121	9	relations	relation	NOUN
cana-4165	121	10	in	in	ADP
cana-4165	121	11	great	great	ADJ
cana-4165	121	12	part	part	NOUN
cana-4165	121	13	.	.	PUNCT
cana-4165	122	1	notwithstanding	notwithstanding	ADP
cana-4165	122	2	these	these	DET
cana-4165	122	3	developments	development	NOUN
cana-4165	122	4	,	,	PUNCT
cana-4165	122	5	our	our	PRON
cana-4165	122	6	knowledge	knowledge	NOUN
cana-4165	122	7	of	of	ADP
cana-4165	122	8	asymptotic	asymptotic	ADJ
cana-4165	122	9	behaviors	behavior	NOUN
cana-4165	122	10	throughout	throughout	ADP
cana-4165	122	11	several	several	ADJ
cana-4165	122	12	transport	transport	NOUN
cana-4165	122	13	regimes	regime	NOUN
cana-4165	122	14	still	still	ADV
cana-4165	122	15	lags	lag	VERB
cana-4165	122	16	far	far	ADV
cana-4165	122	17	behind	behind	ADV
cana-4165	122	18	.	.	PUNCT
cana-4165	123	1	there	there	PRON
cana-4165	123	2	is	be	VERB
cana-4165	123	3	no	no	DET
cana-4165	123	4	consistent	consistent	ADJ
cana-4165	123	5	theoretical	theoretical	ADJ
cana-4165	123	6	explanation	explanation	NOUN
cana-4165	123	7	that	that	PRON
cana-4165	123	8	holds	hold	VERB
cana-4165	123	9	true	true	ADJ
cana-4165	123	10	over	over	ADP
cana-4165	123	11	the	the	DET
cana-4165	123	12	intermediate	intermediate	ADJ
cana-4165	123	13	zone	zone	NOUN
cana-4165	123	14	for	for	ADP
cana-4165	123	15	the	the	DET
cana-4165	123	16	change	change	NOUN
cana-4165	123	17	between	between	ADP
cana-4165	123	18	diffusive	diffusive	ADJ
cana-4165	123	19	and	and	CCONJ
cana-4165	123	20	ballistic	ballistic	ADJ
cana-4165	123	21	transfer	transfer	NOUN
cana-4165	123	22	.	.	PUNCT
cana-4165	124	1	likewise	likewise	ADV
cana-4165	124	2	,	,	PUNCT
cana-4165	124	3	greater	great	ADJ
cana-4165	124	4	explanation	explanation	NOUN
cana-4165	124	5	is	be	AUX
cana-4165	124	6	needed	need	VERB
cana-4165	124	7	regarding	regard	VERB
cana-4165	124	8	the	the	DET
cana-4165	124	9	interaction	interaction	NOUN
cana-4165	124	10	among	among	ADP
cana-4165	124	11	several	several	ADJ
cana-4165	124	12	scattering	scatter	VERB
cana-4165	124	13	mechanisms	mechanism	NOUN
cana-4165	124	14	in	in	ADP
cana-4165	124	15	determining	determine	VERB
cana-4165	124	16	asymptotic	asymptotic	ADJ
cana-4165	124	17	velocity	velocity	NOUN
cana-4165	124	18	.	.	PUNCT
cana-4165	125	1	we	we	PRON
cana-4165	125	2	systematically	systematically	ADV
cana-4165	125	3	derive	derive	VERB
cana-4165	125	4	asymptotic	asymptotic	ADJ
cana-4165	125	5	expansions	expansion	NOUN
cana-4165	125	6	including	include	VERB
cana-4165	125	7	quantum	quantum	ADJ
cana-4165	125	8	effects	effect	NOUN
cana-4165	125	9	,	,	PUNCT
cana-4165	125	10	dimensional	dimensional	ADJ
cana-4165	125	11	scaling	scaling	NOUN
cana-4165	125	12	,	,	PUNCT
cana-4165	125	13	and	and	CCONJ
cana-4165	125	14	suitable	suitable	ADJ
cana-4165	125	15	limiting	limiting	NOUN
cana-4165	125	16	behaviours	behaviour	NOUN
cana-4165	125	17	to	to	PART
cana-4165	125	18	fill	fill	VERB
cana-4165	125	19	in	in	ADP
cana-4165	125	20	these	these	DET
cana-4165	125	21	voids	void	NOUN
cana-4165	125	22	.	.	PUNCT
cana-4165	126	1	conceptual	conceptual	ADJ
cana-4165	126	2	background	background	NOUN
cana-4165	126	3	the	the	DET
cana-4165	126	4	asymptotic	asymptotic	ADJ
cana-4165	126	5	expansion	expansion	NOUN
cana-4165	126	6	of	of	ADP
cana-4165	126	7	electron	electron	NOUN
cana-4165	126	8	mean	mean	NOUN
cana-4165	126	9	velocities	velocity	NOUN
cana-4165	126	10	calls	call	VERB
cana-4165	126	11	for	for	ADP
cana-4165	126	12	detailed	detailed	ADJ
cana-4165	126	13	study	study	NOUN
cana-4165	126	14	of	of	ADP
cana-4165	126	15	the	the	DET
cana-4165	126	16	basic	basic	ADJ
cana-4165	126	17	physics	physics	NOUN
cana-4165	126	18	ideas	idea	NOUN
cana-4165	126	19	controlling	control	VERB
cana-4165	126	20	electron	electron	NOUN
cana-4165	126	21	transport	transport	NOUN
cana-4165	126	22	.	.	PUNCT
cana-4165	127	1	beginning	begin	VERB
cana-4165	127	2	with	with	ADP
cana-4165	127	3	the	the	DET
cana-4165	127	4	fundamental	fundamental	ADJ
cana-4165	127	5	definitions	definition	NOUN
cana-4165	127	6	and	and	CCONJ
cana-4165	127	7	working	work	VERB
cana-4165	127	8	towards	towards	ADP
cana-4165	127	9	more	more	ADV
cana-4165	127	10	complex	complex	ADJ
cana-4165	127	11	quantum	quantum	ADJ
cana-4165	127	12	mechanical	mechanical	ADJ
cana-4165	127	13	treatments	treatment	NOUN
cana-4165	127	14	,	,	PUNCT
cana-4165	127	15	this	this	DET
cana-4165	127	16	part	part	NOUN
cana-4165	127	17	lays	lay	VERB
cana-4165	127	18	the	the	DET
cana-4165	127	19	theoretical	theoretical	ADJ
cana-4165	127	20	framework	framework	NOUN
cana-4165	127	21	supporting	support	VERB
cana-4165	127	22	our	our	PRON
cana-4165	127	23	investigation	investigation	NOUN
cana-4165	127	24	.	.	PUNCT
cana-4165	128	1	the	the	DET
cana-4165	128	2	velocity	velocity	NOUN
cana-4165	128	3	of	of	ADP
cana-4165	128	4	a	a	DET
cana-4165	128	5	particle	particle	NOUN
cana-4165	128	6	in	in	ADP
cana-4165	128	7	classical	classical	ADJ
cana-4165	128	8	mechanics	mechanic	NOUN
cana-4165	128	9	is	be	AUX
cana-4165	128	10	only	only	ADV
cana-4165	128	11	defined	define	VERB
cana-4165	128	12	as	as	ADP
cana-4165	128	13	the	the	DET
cana-4165	128	14	time	time	NOUN
cana-4165	128	15	derivative	derivative	NOUN
cana-4165	128	16	of	of	ADP
cana-4165	128	17	its	its	PRON
cana-4165	128	18	position	position	NOUN
cana-4165	128	19	.	.	PUNCT
cana-4165	129	1	but	but	CCONJ
cana-4165	129	2	for	for	ADP
cana-4165	129	3	an	an	DET
cana-4165	129	4	electron	electron	NOUN
cana-4165	129	5	in	in	ADP
cana-4165	129	6	a	a	DET
cana-4165	129	7	crystal	crystal	NOUN
cana-4165	129	8	,	,	PUNCT
cana-4165	129	9	the	the	DET
cana-4165	129	10	periodic	periodic	ADJ
cana-4165	129	11	potential	potential	NOUN
cana-4165	129	12	of	of	ADP
cana-4165	129	13	the	the	DET
cana-4165	129	14	lattice	lattice	NOUN
cana-4165	129	15	complicates	complicate	VERB
cana-4165	129	16	the	the	DET
cana-4165	129	17	situation	situation	NOUN
cana-4165	129	18	.	.	PUNCT
cana-4165	130	1	the	the	DET
cana-4165	130	2	electron	electron	NOUN
cana-4165	130	3	's	's	PART
cana-4165	130	4	state	state	NOUN
cana-4165	130	5	in	in	ADP
cana-4165	130	6	the	the	DET
cana-4165	130	7	quantum	quantum	ADJ
cana-4165	130	8	mechanical	mechanical	ADJ
cana-4165	130	9	model	model	NOUN
cana-4165	130	10	is	be	AUX
cana-4165	130	11	expressed	express	VERB
cana-4165	130	12	either	either	CCONJ
cana-4165	130	13	generally	generally	ADV
cana-4165	130	14	by	by	ADP
cana-4165	130	15	a	a	DET
cana-4165	130	16	density	density	NOUN
cana-4165	130	17	matrix	matrix	NOUN
cana-4165	130	18	or	or	CCONJ
cana-4165	130	19	by	by	ADP
cana-4165	130	20	a	a	DET
cana-4165	130	21	wave	wave	NOUN
cana-4165	130	22	function	function	NOUN
cana-4165	130	23	.	.	PUNCT
cana-4165	131	1	then	then	ADV
cana-4165	131	2	the	the	DET
cana-4165	131	3	expectation	expectation	NOUN
cana-4165	131	4	value	value	NOUN
cana-4165	131	5	of	of	ADP
cana-4165	131	6	the	the	DET
cana-4165	131	7	velocity	velocity	NOUN
cana-4165	131	8	operator	operator	NOUN
cana-4165	131	9	offers	offer	VERB
cana-4165	131	10	the	the	DET
cana-4165	131	11	quantum	quantum	ADJ
cana-4165	131	12	mechanical	mechanical	ADJ
cana-4165	131	13	counterpart	counterpart	NOUN
cana-4165	131	14	of	of	ADP
cana-4165	131	15	the	the	DET
cana-4165	131	16	classical	classical	ADJ
cana-4165	131	17	velocity	velocity	NOUN
cana-4165	131	18	.	.	PUNCT
cana-4165	132	1	communications	communication	NOUN
cana-4165	132	2	on	on	ADP
cana-4165	132	3	applied	apply	VERB
cana-4165	132	4	nonlinear	nonlinear	ADJ
cana-4165	132	5	analysis	analysis	NOUN
cana-4165	132	6	issn	issn	NOUN
cana-4165	132	7	:	:	PUNCT
cana-4165	132	8	1074	1074	NUM
cana-4165	132	9	-	-	PUNCT
cana-4165	132	10	133x	133x	NUM
cana-4165	132	11	vol	vol	NOUN
cana-4165	132	12	32	32	NUM
cana-4165	132	13	no	no	NOUN
cana-4165	132	14	.	.	PUNCT
cana-4165	133	1	9s	9s	NUM
cana-4165	133	2	(	(	PUNCT
cana-4165	133	3	2025	2025	NUM
cana-4165	133	4	)	)	PUNCT
cana-4165	133	5	1394	1394	NUM
cana-4165	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	133	7	in	in	ADP
cana-4165	133	8	quantum	quantum	ADJ
cana-4165	133	9	physics	physics	NOUN
cana-4165	133	10	,	,	PUNCT
cana-4165	133	11	the	the	DET
cana-4165	133	12	velocity	velocity	NOUN
cana-4165	133	13	operator	operator	NOUN
cana-4165	133	14	is	be	AUX
cana-4165	133	15	obtained	obtain	VERB
cana-4165	133	16	from	from	ADP
cana-4165	133	17	the	the	DET
cana-4165	133	18	position	position	NOUN
cana-4165	133	19	operator	operator	NOUN
cana-4165	133	20	using	use	VERB
cana-4165	133	21	the	the	DET
cana-4165	133	22	heisenberg	heisenberg	PROPN
cana-4165	133	23	equation	equation	NOUN
cana-4165	133	24	of	of	ADP
cana-4165	133	25	motion	motion	NOUN
cana-4165	133	26	:	:	PUNCT
cana-4165	133	27	v	v	X
cana-4165	133	28	=	=	SYM
cana-4165	133	29	(	(	PUNCT
cana-4165	133	30	i/ℐ-[h	i/ℐ-[h	X
cana-4165	133	31	,	,	PUNCT
cana-4165	133	32	r	r	NOUN
cana-4165	133	33	]	]	X
cana-4165	133	34	)	)	PUNCT
cana-4165	133	35	where	where	SCONJ
cana-4165	133	36	h	h	NOUN
cana-4165	133	37	is	be	AUX
cana-4165	133	38	the	the	DET
cana-4165	133	39	hamiltonian	hamiltonian	NOUN
cana-4165	133	40	of	of	ADP
cana-4165	133	41	the	the	DET
cana-4165	133	42	system	system	NOUN
cana-4165	133	43	and	and	CCONJ
cana-4165	133	44	r	r	X
cana-4165	133	45	the	the	DET
cana-4165	133	46	position	position	NOUN
cana-4165	133	47	operator	operator	NOUN
cana-4165	133	48	.	.	PUNCT
cana-4165	134	1	this	this	PRON
cana-4165	134	2	lowers	lower	VERB
cana-4165	134	3	for	for	ADP
cana-4165	134	4	a	a	DET
cana-4165	134	5	free	free	ADJ
cana-4165	134	6	electron	electron	NOUN
cana-4165	134	7	to	to	ADP
cana-4165	134	8	the	the	DET
cana-4165	134	9	well	well	ADV
cana-4165	134	10	-	-	PUNCT
cana-4165	134	11	known	know	VERB
cana-4165	134	12	relationship	relationship	NOUN
cana-4165	134	13	v	v	ADP
cana-4165	134	14	=	=	NOUN
cana-4165	134	15	p	p	X
cana-4165	134	16	/	/	SYM
cana-4165	134	17	m	m	VERB
cana-4165	134	18	between	between	ADP
cana-4165	134	19	momentum	momentum	NOUN
cana-4165	134	20	and	and	CCONJ
cana-4165	134	21	velocity	velocity	NOUN
cana-4165	134	22	.	.	PUNCT
cana-4165	135	1	but	but	CCONJ
cana-4165	135	2	in	in	ADP
cana-4165	135	3	a	a	DET
cana-4165	135	4	crystal	crystal	NOUN
cana-4165	135	5	the	the	DET
cana-4165	135	6	band	band	NOUN
cana-4165	135	7	structure	structure	NOUN
cana-4165	135	8	makes	make	VERB
cana-4165	135	9	the	the	DET
cana-4165	135	10	interaction	interaction	NOUN
cana-4165	135	11	more	more	ADV
cana-4165	135	12	complicated	complicated	ADJ
cana-4165	135	13	.	.	PUNCT
cana-4165	136	1	the	the	DET
cana-4165	136	2	energy	energy	NOUN
cana-4165	136	3	dispersion	dispersion	NOUN
cana-4165	136	4	relation	relation	NOUN
cana-4165	136	5	for	for	ADP
cana-4165	136	6	the	the	DET
cana-4165	136	7	band	band	NOUN
cana-4165	136	8	determines	determine	VERB
cana-4165	136	9	the	the	DET
cana-4165	136	10	group	group	NOUN
cana-4165	136	11	velocity	velocity	NOUN
cana-4165	136	12	of	of	ADP
cana-4165	136	13	an	an	DET
cana-4165	136	14	electron	electron	NOUN
cana-4165	136	15	in	in	ADP
cana-4165	136	16	band	band	NOUN
cana-4165	136	17	n	n	CCONJ
cana-4165	136	18	with	with	ADP
cana-4165	136	19	crystal	crystal	NOUN
cana-4165	136	20	momentum	momentum	NOUN
cana-4165	136	21	k	k	X
cana-4165	136	22	by	by	ADP
cana-4165	136	23	vn(k	vn(k	PRON
cana-4165	136	24	)	)	PUNCT
cana-4165	136	25	=	=	PRON
cana-4165	136	26	(	(	PUNCT
cana-4165	136	27	1/ℐ∆ken(k	1/ℐ∆ken(k	NUM
cana-4165	136	28	)	)	PUNCT
cana-4165	136	29	.	.	PUNCT
cana-4165	137	1	the	the	DET
cana-4165	137	2	way	way	NOUN
cana-4165	137	3	electrons	electron	NOUN
cana-4165	137	4	distribute	distribute	VERB
cana-4165	137	5	in	in	ADP
cana-4165	137	6	phase	phase	NOUN
cana-4165	137	7	space	space	NOUN
cana-4165	137	8	determines	determine	VERB
cana-4165	137	9	the	the	DET
cana-4165	137	10	mean	mean	ADJ
cana-4165	137	11	speed	speed	NOUN
cana-4165	137	12	of	of	ADP
cana-4165	137	13	electrons	electron	NOUN
cana-4165	137	14	in	in	ADP
cana-4165	137	15	a	a	DET
cana-4165	137	16	substance	substance	NOUN
cana-4165	137	17	.	.	PUNCT
cana-4165	138	1	with	with	ADP
cana-4165	138	2	ef	ef	PROPN
cana-4165	138	3	as	as	ADP
cana-4165	138	4	the	the	DET
cana-4165	138	5	fermi	fermi	NOUN
cana-4165	138	6	energy	energy	NOUN
cana-4165	138	7	,	,	PUNCT
cana-4165	138	8	this	this	DET
cana-4165	138	9	distribution	distribution	NOUN
cana-4165	138	10	is	be	AUX
cana-4165	138	11	obtained	obtain	VERB
cana-4165	138	12	in	in	ADP
cana-4165	138	13	equilibrium	equilibrium	NOUN
cana-4165	138	14	from	from	ADP
cana-4165	138	15	the	the	DET
cana-4165	138	16	fermi	fermi	NOUN
cana-4165	138	17	-	-	PUNCT
cana-4165	138	18	dirac	dirac	NOUN
cana-4165	138	19	function	function	NOUN
cana-4165	138	20	f0(e	f0(e	PROPN
cana-4165	138	21	)	)	PUNCT
cana-4165	138	22	=	=	PUNCT
cana-4165	139	1	[	[	PUNCT
cana-4165	139	2	exp((e	exp((e	PROPN
cana-4165	139	3	-	-	PUNCT
cana-4165	139	4	ef)/kbt	ef)/kbt	NOUN
cana-4165	139	5	)	)	PUNCT
cana-4165	139	6	+	+	CCONJ
cana-4165	139	7	1]^(-1	1]^(-1	NUM
cana-4165	139	8	)	)	PUNCT
cana-4165	139	9	.	.	PUNCT
cana-4165	140	1	the	the	DET
cana-4165	140	2	distribution	distribution	NOUN
cana-4165	140	3	function	function	NOUN
cana-4165	140	4	strays	stray	NOUN
cana-4165	140	5	from	from	ADP
cana-4165	140	6	equilibrium	equilibrium	NOUN
cana-4165	140	7	with	with	ADP
cana-4165	140	8	an	an	DET
cana-4165	140	9	applied	apply	VERB
cana-4165	140	10	electric	electric	ADJ
cana-4165	140	11	field	field	NOUN
cana-4165	140	12	.	.	PUNCT
cana-4165	141	1	in	in	ADP
cana-4165	141	2	transport	transport	NOUN
cana-4165	141	3	theory	theory	NOUN
cana-4165	141	4	,	,	PUNCT
cana-4165	141	5	the	the	DET
cana-4165	141	6	computation	computation	NOUN
cana-4165	141	7	of	of	ADP
cana-4165	141	8	this	this	DET
cana-4165	141	9	non	non	ADJ
cana-4165	141	10	-	-	ADJ
cana-4165	141	11	equilibrium	equilibrium	ADJ
cana-4165	141	12	distribution	distribution	NOUN
cana-4165	141	13	and	and	CCONJ
cana-4165	141	14	hence	hence	ADV
cana-4165	141	15	the	the	DET
cana-4165	141	16	mean	mean	ADJ
cana-4165	141	17	velocity	velocity	NOUN
cana-4165	141	18	poses	pose	VERB
cana-4165	141	19	a	a	DET
cana-4165	141	20	major	major	ADJ
cana-4165	141	21	difficulty	difficulty	NOUN
cana-4165	141	22	.	.	PUNCT
cana-4165	142	1	one	one	NUM
cana-4165	142	2	foundation	foundation	NOUN
cana-4165	142	3	for	for	ADP
cana-4165	142	4	establishing	establish	VERB
cana-4165	142	5	the	the	DET
cana-4165	142	6	non	non	ADJ
cana-4165	142	7	-	-	ADJ
cana-4165	142	8	equilibrium	equilibrium	ADJ
cana-4165	142	9	distribution	distribution	NOUN
cana-4165	142	10	function	function	NOUN
cana-4165	142	11	is	be	AUX
cana-4165	142	12	given	give	VERB
cana-4165	142	13	by	by	ADP
cana-4165	142	14	the	the	DET
cana-4165	142	15	boltzmann	boltzmann	PROPN
cana-4165	142	16	transport	transport	NOUN
cana-4165	142	17	equation	equation	NOUN
cana-4165	142	18	.	.	PUNCT
cana-4165	143	1	general	general	ADJ
cana-4165	143	2	form	form	NOUN
cana-4165	143	3	of	of	ADP
cana-4165	143	4	this	this	DET
cana-4165	143	5	equation	equation	NOUN
cana-4165	143	6	is	be	AUX
cana-4165	143	7	:	:	PUNCT
cana-4165	143	8	∂f/∂t	∂f/∂t	NOUN
cana-4165	143	9	+	+	CCONJ
cana-4165	143	10	v·∇rf	v·∇rf	PROPN
cana-4165	143	11	+	+	CCONJ
cana-4165	143	12	f·∇pf	f·∇pf	NOUN
cana-4165	143	13	=	=	SYM
cana-4165	143	14	(	(	PUNCT
cana-4165	143	15	∂f/∂t)coll	∂f/∂t)coll	PROPN
cana-4165	143	16	f	f	PROPN
cana-4165	143	17	the	the	DET
cana-4165	143	18	applied	applied	ADJ
cana-4165	143	19	force	force	NOUN
cana-4165	143	20	;	;	PUNCT
cana-4165	143	21	the	the	DET
cana-4165	143	22	right	right	ADJ
cana-4165	143	23	-	-	PUNCT
cana-4165	143	24	hand	hand	NOUN
cana-4165	143	25	side	side	NOUN
cana-4165	143	26	denotes	denote	VERB
cana-4165	143	27	the	the	DET
cana-4165	143	28	collision	collision	NOUN
cana-4165	143	29	integral	integral	ADJ
cana-4165	143	30	accounting	accounting	NOUN
cana-4165	143	31	for	for	ADP
cana-4165	143	32	all	all	DET
cana-4165	143	33	scattering	scatter	VERB
cana-4165	143	34	processes	process	NOUN
cana-4165	143	35	;	;	PUNCT
cana-4165	143	36	f(r	f(r	NOUN
cana-4165	143	37	,	,	PUNCT
cana-4165	143	38	p	p	X
cana-4165	143	39	,	,	PUNCT
cana-4165	143	40	t	t	PROPN
cana-4165	143	41	)	)	PUNCT
cana-4165	143	42	is	be	AUX
cana-4165	143	43	the	the	DET
cana-4165	143	44	distribution	distribution	NOUN
cana-4165	143	45	function	function	NOUN
cana-4165	143	46	.	.	PUNCT
cana-4165	144	1	this	this	DET
cana-4165	144	2	equation	equation	NOUN
cana-4165	144	3	reduces	reduce	VERB
cana-4165	144	4	in	in	ADP
cana-4165	144	5	the	the	DET
cana-4165	144	6	steady	steady	ADJ
cana-4165	144	7	state	state	NOUN
cana-4165	144	8	and	and	CCONJ
cana-4165	144	9	under	under	ADP
cana-4165	144	10	a	a	DET
cana-4165	144	11	homogeneous	homogeneous	ADJ
cana-4165	144	12	electric	electric	ADJ
cana-4165	144	13	field	field	NOUN
cana-4165	144	14	to	to	ADP
cana-4165	144	15	:	:	PUNCT
cana-4165	144	16	-ee·∇kf	-ee·∇kf	PROPN
cana-4165	144	17	=	=	PUNCT
cana-4165	144	18	(	(	PUNCT
cana-4165	144	19	∂f/∂t)coll	∂f/∂t)coll	PROPN
cana-4165	144	20	there	there	PRON
cana-4165	144	21	exist	exist	VERB
cana-4165	144	22	several	several	ADJ
cana-4165	144	23	approximations	approximation	NOUN
cana-4165	144	24	to	to	PART
cana-4165	144	25	assess	assess	VERB
cana-4165	144	26	the	the	DET
cana-4165	144	27	collision	collision	NOUN
cana-4165	144	28	integral	integral	ADJ
cana-4165	144	29	.	.	PUNCT
cana-4165	145	1	with	with	ADP
cana-4165	145	2	a	a	DET
cana-4165	145	3	characteristic	characteristic	ADJ
cana-4165	145	4	time	time	NOUN
cana-4165	145	5	τ	τ	X
cana-4165	145	6	:	:	PUNCT
cana-4165	145	7	(	(	PUNCT
cana-4165	145	8	∂f/∂t)coll	∂f/∂t)coll	NOUN
cana-4165	145	9	=	=	SYM
cana-4165	145	10	-(f	-(f	PUNCT
cana-4165	145	11	-	-	PUNCT
cana-4165	145	12	f0)/τ	f0)/τ	NOUN
cana-4165	145	13	,	,	PUNCT
cana-4165	145	14	the	the	DET
cana-4165	145	15	relaxation	relaxation	NOUN
cana-4165	145	16	time	time	NOUN
cana-4165	145	17	approximation	approximation	NOUN
cana-4165	145	18	supposes	suppose	VERB
cana-4165	145	19	that	that	SCONJ
cana-4165	145	20	scattering	scatter	VERB
cana-4165	145	21	tends	tend	VERB
cana-4165	145	22	to	to	PART
cana-4165	145	23	reestablish	reestablish	VERB
cana-4165	145	24	the	the	DET
cana-4165	145	25	equilibrium	equilibrium	NOUN
cana-4165	145	26	distribution	distribution	NOUN
cana-4165	145	27	.	.	PUNCT
cana-4165	146	1	more	more	ADV
cana-4165	146	2	advanced	advanced	ADJ
cana-4165	146	3	methods	method	NOUN
cana-4165	146	4	include	include	VERB
cana-4165	146	5	careful	careful	ADJ
cana-4165	146	6	attention	attention	NOUN
cana-4165	146	7	to	to	ADP
cana-4165	146	8	certain	certain	ADJ
cana-4165	146	9	scattering	scattering	NOUN
cana-4165	146	10	processes	process	NOUN
cana-4165	146	11	like	like	ADP
cana-4165	146	12	electron	electron	NOUN
cana-4165	146	13	-	-	PUNCT
cana-4165	146	14	electron	electron	NOUN
cana-4165	146	15	interactions	interaction	NOUN
cana-4165	146	16	,	,	PUNCT
cana-4165	146	17	phonon	phonon	NOUN
cana-4165	146	18	scattering	scattering	NOUN
cana-4165	146	19	,	,	PUNCT
cana-4165	146	20	and	and	CCONJ
cana-4165	146	21	impurity	impurity	NOUN
cana-4165	146	22	scattering	scattering	NOUN
cana-4165	146	23	.	.	PUNCT
cana-4165	147	1	under	under	ADP
cana-4165	147	2	the	the	DET
cana-4165	147	3	linear	linear	ADJ
cana-4165	147	4	response	response	NOUN
cana-4165	147	5	regime	regime	NOUN
cana-4165	147	6	,	,	PUNCT
cana-4165	147	7	the	the	DET
cana-4165	147	8	mean	mean	ADJ
cana-4165	147	9	velocity	velocity	NOUN
cana-4165	147	10	follows	follow	VERB
cana-4165	147	11	ohm	ohm	PROPN
cana-4165	147	12	's	's	PART
cana-4165	147	13	law	law	NOUN
cana-4165	147	14	:	:	PUNCT
cana-4165	147	15	v	v	NOUN
cana-4165	147	16	=	=	SYM
cana-4165	147	17	μe	μe	NOUN
cana-4165	147	18	,	,	PUNCT
cana-4165	147	19	where	where	SCONJ
cana-4165	147	20	μ	μ	PROPN
cana-4165	147	21	denotes	denote	VERB
cana-4165	147	22	the	the	DET
cana-4165	147	23	mobility	mobility	NOUN
cana-4165	147	24	tensor	tensor	NOUN
cana-4165	147	25	;	;	PUNCT
cana-4165	147	26	the	the	DET
cana-4165	147	27	variance	variance	NOUN
cana-4165	147	28	from	from	ADP
cana-4165	147	29	equilibrium	equilibrium	NOUN
cana-4165	147	30	is	be	AUX
cana-4165	147	31	proportional	proportional	ADJ
cana-4165	147	32	to	to	ADP
cana-4165	147	33	the	the	DET
cana-4165	147	34	applied	apply	VERB
cana-4165	147	35	field	field	NOUN
cana-4165	147	36	.	.	PUNCT
cana-4165	148	1	at	at	ADP
cana-4165	148	2	high	high	ADJ
cana-4165	148	3	fields	field	NOUN
cana-4165	148	4	,	,	PUNCT
cana-4165	148	5	where	where	SCONJ
cana-4165	148	6	several	several	ADJ
cana-4165	148	7	saturation	saturation	NOUN
cana-4165	148	8	mechanisms	mechanism	NOUN
cana-4165	148	9	are	be	AUX
cana-4165	148	10	active	active	ADJ
cana-4165	148	11	,	,	PUNCT
cana-4165	148	12	this	this	DET
cana-4165	148	13	linear	linear	ADJ
cana-4165	148	14	approximation	approximation	NOUN
cana-4165	148	15	fails	fail	VERB
cana-4165	148	16	.	.	PUNCT
cana-4165	149	1	one	one	NUM
cana-4165	149	2	often	often	ADV
cana-4165	149	3	used	use	VERB
cana-4165	149	4	phenomenological	phenomenological	ADJ
cana-4165	149	5	model	model	NOUN
cana-4165	149	6	for	for	SCONJ
cana-4165	149	7	the	the	DET
cana-4165	149	8	field	field	NOUN
cana-4165	149	9	dependence	dependence	NOUN
cana-4165	149	10	of	of	ADP
cana-4165	149	11	velocity	velocity	NOUN
cana-4165	149	12	consists	consist	VERB
cana-4165	149	13	in	in	ADP
cana-4165	149	14	:	:	PUNCT
cana-4165	149	15	v(e	v(e	NUM
cana-4165	149	16	)	)	PUNCT
cana-4165	150	1	=	=	PRON
cana-4165	150	2	μe	μe	NOUN
cana-4165	150	3	/	/	SYM
cana-4165	151	1	[	[	X
cana-4165	151	2	1	1	NUM
cana-4165	151	3	+	+	CCONJ
cana-4165	151	4	(	(	PUNCT
cana-4165	151	5	μe	μe	NOUN
cana-4165	151	6	/	/	SYM
cana-4165	151	7	vsat)^β]^(1	vsat)^β]^(1	NOUN
cana-4165	151	8	/	/	SYM
cana-4165	151	9	β	β	NOUN
cana-4165	151	10	)	)	PUNCT
cana-4165	151	11	where	where	SCONJ
cana-4165	151	12	β	β	X
cana-4165	151	13	a	a	DET
cana-4165	151	14	parameter	parameter	NOUN
cana-4165	151	15	regulates	regulate	VERB
cana-4165	151	16	the	the	DET
cana-4165	151	17	sharpness	sharpness	NOUN
cana-4165	151	18	of	of	ADP
cana-4165	151	19	the	the	DET
cana-4165	151	20	transition	transition	NOUN
cana-4165	151	21	and	and	CCONJ
cana-4165	151	22	indicates	indicate	VERB
cana-4165	151	23	the	the	DET
cana-4165	151	24	saturation	saturation	NOUN
cana-4165	151	25	velocity	velocity	NOUN
cana-4165	151	26	.	.	PUNCT
cana-4165	152	1	with	with	ADP
cana-4165	152	2	the	the	DET
cana-4165	152	3	low	low	ADJ
cana-4165	152	4	-	-	PUNCT
cana-4165	152	5	field	field	NOUN
cana-4165	152	6	behavior	behavior	NOUN
cana-4165	152	7	v	v	ADP
cana-4165	152	8	≈	≈	PROPN
cana-4165	152	9	μe	μe	INTJ
cana-4165	152	10	and	and	CCONJ
cana-4165	152	11	the	the	DET
cana-4165	152	12	high	high	ADJ
cana-4165	152	13	-	-	PUNCT
cana-4165	152	14	field	field	NOUN
cana-4165	152	15	limit	limit	NOUN
cana-4165	152	16	v	v	ADP
cana-4165	152	17	≈	≈	PROPN
cana-4165	152	18	vsat	vsat	PROPN
cana-4165	152	19	,	,	PUNCT
cana-4165	152	20	this	this	DET
cana-4165	152	21	statement	statement	NOUN
cana-4165	152	22	embodies	embody	VERB
cana-4165	152	23	a	a	DET
cana-4165	152	24	basic	basic	ADJ
cana-4165	152	25	kind	kind	NOUN
cana-4165	152	26	of	of	ADP
cana-4165	152	27	asymptotic	asymptotic	ADJ
cana-4165	152	28	expansion	expansion	NOUN
cana-4165	152	29	.	.	PUNCT
cana-4165	153	1	perturbation	perturbation	NOUN
cana-4165	153	2	theory	theory	NOUN
cana-4165	153	3	is	be	AUX
cana-4165	153	4	a	a	DET
cana-4165	153	5	more	more	ADV
cana-4165	153	6	exact	exact	ADJ
cana-4165	153	7	method	method	NOUN
cana-4165	153	8	of	of	ADP
cana-4165	153	9	approaching	approach	VERB
cana-4165	153	10	asymptotic	asymptotic	ADJ
cana-4165	153	11	expansions	expansion	NOUN
cana-4165	153	12	.	.	PUNCT
cana-4165	154	1	expanding	expand	VERB
cana-4165	154	2	the	the	DET
cana-4165	154	3	distribution	distribution	NOUN
cana-4165	154	4	function	function	NOUN
cana-4165	154	5	in	in	ADP
cana-4165	154	6	powers	power	NOUN
cana-4165	154	7	of	of	ADP
cana-4165	154	8	the	the	DET
cana-4165	154	9	electric	electric	ADJ
cana-4165	154	10	field	field	NOUN
cana-4165	154	11	allows	allow	VERB
cana-4165	154	12	:	:	PUNCT
cana-4165	154	13	f	f	PROPN
cana-4165	154	14	=	=	SYM
cana-4165	154	15	f0	f0	PROPN
cana-4165	154	16	+	+	CCONJ
cana-4165	154	17	f1	f1	NOUN
cana-4165	154	18	+	+	CCONJ
cana-4165	154	19	f2	f2	PROPN
cana-4165	154	20	+	+	X
cana-4165	154	21	...	...	PUNCT
cana-4165	154	22	where	where	SCONJ
cana-4165	154	23	e^n	e^n	NOUN
cana-4165	154	24	determines	determine	VERB
cana-4165	154	25	func	func	VERB
cana-4165	154	26	proportionately	proportionately	ADV
cana-4165	154	27	.	.	PUNCT
cana-4165	155	1	with	with	ADP
cana-4165	155	2	coefficients	coefficient	NOUN
cana-4165	155	3	derived	derive	VERB
cana-4165	155	4	by	by	ADP
cana-4165	155	5	the	the	DET
cana-4165	155	6	band	band	NOUN
cana-4165	155	7	structure	structure	NOUN
cana-4165	155	8	and	and	CCONJ
cana-4165	155	9	scattering	scattering	NOUN
cana-4165	155	10	processes	process	NOUN
cana-4165	155	11	,	,	PUNCT
cana-4165	155	12	the	the	DET
cana-4165	155	13	resultant	resultant	NOUN
cana-4165	155	14	formulations	formulation	NOUN
cana-4165	155	15	for	for	ADP
cana-4165	155	16	the	the	DET
cana-4165	155	17	mean	mean	ADJ
cana-4165	155	18	velocity	velocity	NOUN
cana-4165	155	19	feature	feature	NOUN
cana-4165	155	20	terms	term	NOUN
cana-4165	155	21	of	of	ADP
cana-4165	155	22	increasing	increase	VERB
cana-4165	155	23	order	order	NOUN
cana-4165	155	24	in	in	ADP
cana-4165	155	25	the	the	DET
cana-4165	155	26	field	field	NOUN
cana-4165	155	27	strength	strength	NOUN
cana-4165	155	28	.	.	PUNCT
cana-4165	156	1	communications	communication	NOUN
cana-4165	156	2	on	on	ADP
cana-4165	156	3	applied	apply	VERB
cana-4165	156	4	nonlinear	nonlinear	ADJ
cana-4165	156	5	analysis	analysis	NOUN
cana-4165	156	6	issn	issn	NOUN
cana-4165	156	7	:	:	PUNCT
cana-4165	156	8	1074	1074	NUM
cana-4165	156	9	-	-	PUNCT
cana-4165	156	10	133x	133x	NUM
cana-4165	156	11	vol	vol	NOUN
cana-4165	156	12	32	32	NUM
cana-4165	156	13	no	no	NOUN
cana-4165	156	14	.	.	PUNCT
cana-4165	157	1	9s	9s	NUM
cana-4165	157	2	(	(	PUNCT
cana-4165	157	3	2025	2025	NUM
cana-4165	157	4	)	)	PUNCT
cana-4165	157	5	1395	1395	NUM
cana-4165	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	157	7	beyond	beyond	ADP
cana-4165	157	8	the	the	DET
cana-4165	157	9	semiclassical	semiclassical	ADJ
cana-4165	157	10	boltzmann	boltzmann	NOUN
cana-4165	157	11	method	method	NOUN
cana-4165	157	12	,	,	PUNCT
cana-4165	157	13	quantum	quantum	NOUN
cana-4165	157	14	transport	transport	NOUN
cana-4165	157	15	theories	theory	NOUN
cana-4165	157	16	add	add	VERB
cana-4165	157	17	coherence	coherence	NOUN
cana-4165	157	18	phenomena	phenomenon	NOUN
cana-4165	157	19	.	.	PUNCT
cana-4165	158	1	one	one	NUM
cana-4165	158	2	such	such	ADJ
cana-4165	158	3	extension	extension	NOUN
cana-4165	158	4	is	be	AUX
cana-4165	158	5	made	make	VERB
cana-4165	158	6	possible	possible	ADJ
cana-4165	158	7	by	by	ADP
cana-4165	158	8	the	the	DET
cana-4165	158	9	density	density	NOUN
cana-4165	158	10	matrix	matrix	NOUN
cana-4165	158	11	formalism	formalism	NOUN
cana-4165	158	12	;	;	PUNCT
cana-4165	158	13	the	the	DET
cana-4165	158	14	liouville	liouville	PROPN
cana-4165	158	15	-	-	PUNCT
cana-4165	158	16	von	von	PROPN
cana-4165	158	17	neumann	neumann	PROPN
cana-4165	158	18	equation	equation	NOUN
cana-4165	158	19	controls	control	VERB
cana-4165	158	20	the	the	DET
cana-4165	158	21	evolution	evolution	NOUN
cana-4165	158	22	.	.	PUNCT
cana-4165	159	1	other	other	ADJ
cana-4165	159	2	methods	method	NOUN
cana-4165	159	3	express	express	VERB
cana-4165	159	4	transport	transport	NOUN
cana-4165	159	5	features	feature	NOUN
cana-4165	159	6	in	in	ADP
cana-4165	159	7	terms	term	NOUN
cana-4165	159	8	of	of	ADP
cana-4165	159	9	correlation	correlation	NOUN
cana-4165	159	10	functions	function	NOUN
cana-4165	159	11	by	by	ADP
cana-4165	159	12	use	use	NOUN
cana-4165	159	13	of	of	ADP
cana-4165	159	14	the	the	DET
cana-4165	159	15	non	non	ADJ
cana-4165	159	16	-	-	ADJ
cana-4165	159	17	equilibrium	equilibrium	ADJ
cana-4165	159	18	green	green	NOUN
cana-4165	159	19	's	's	PART
cana-4165	159	20	function	function	NOUN
cana-4165	159	21	approach	approach	NOUN
cana-4165	159	22	.	.	PUNCT
cana-4165	160	1	the	the	DET
cana-4165	160	2	landauer	landauer	NOUN
cana-4165	160	3	-	-	PUNCT
cana-4165	160	4	büttiker	büttiker	NOUN
cana-4165	160	5	formalism	formalism	NOUN
cana-4165	160	6	provides	provide	VERB
cana-4165	160	7	an	an	DET
cana-4165	160	8	understandable	understandable	ADJ
cana-4165	160	9	description	description	NOUN
cana-4165	160	10	based	base	VERB
cana-4165	160	11	on	on	ADP
cana-4165	160	12	transmission	transmission	NOUN
cana-4165	160	13	probabilities	probability	NOUN
cana-4165	160	14	in	in	ADP
cana-4165	160	15	mesoscopic	mesoscopic	NOUN
cana-4165	160	16	systems	system	NOUN
cana-4165	160	17	,	,	PUNCT
cana-4165	160	18	in	in	ADP
cana-4165	160	19	which	which	PRON
cana-4165	160	20	dimensions	dimension	NOUN
cana-4165	160	21	approach	approach	VERB
cana-4165	160	22	important	important	ADJ
cana-4165	160	23	quantum	quantum	NOUN
cana-4165	160	24	length	length	NOUN
cana-4165	160	25	scales	scale	NOUN
cana-4165	160	26	.	.	PUNCT
cana-4165	161	1	given	give	VERB
cana-4165	161	2	t	t	PROPN
cana-4165	161	3	as	as	ADP
cana-4165	161	4	the	the	DET
cana-4165	161	5	transmission	transmission	NOUN
cana-4165	161	6	probability	probability	NOUN
cana-4165	161	7	,	,	PUNCT
cana-4165	161	8	the	the	DET
cana-4165	161	9	conductance	conductance	NOUN
cana-4165	161	10	is	be	AUX
cana-4165	161	11	stated	state	VERB
cana-4165	161	12	as	as	ADP
cana-4165	161	13	g	g	PROPN
cana-4165	161	14	=	=	SYM
cana-4165	161	15	(	(	PUNCT
cana-4165	161	16	2e²/h	2e²/h	PROPN
cana-4165	161	17	)	)	PUNCT
cana-4165	161	18	.	.	PUNCT
cana-4165	162	1	this	this	DET
cana-4165	162	2	method	method	NOUN
cana-4165	162	3	organically	organically	ADV
cana-4165	162	4	combines	combine	VERB
cana-4165	162	5	quantum	quantum	ADJ
cana-4165	162	6	phenomena	phenomenon	NOUN
cana-4165	162	7	including	include	VERB
cana-4165	162	8	resonant	resonant	ADJ
cana-4165	162	9	tunneling	tunneling	NOUN
cana-4165	162	10	and	and	CCONJ
cana-4165	162	11	conductance	conductance	NOUN
cana-4165	162	12	quantization	quantization	NOUN
cana-4165	162	13	.	.	PUNCT
cana-4165	163	1	the	the	DET
cana-4165	163	2	reduced	reduced	ADJ
cana-4165	163	3	dimensionality	dimensionality	NOUN
cana-4165	163	4	of	of	ADP
cana-4165	163	5	low	low	ADJ
cana-4165	163	6	-	-	PUNCT
cana-4165	163	7	dimensional	dimensional	ADJ
cana-4165	163	8	systems	system	NOUN
cana-4165	163	9	essentially	essentially	ADV
cana-4165	163	10	changes	change	VERB
cana-4165	163	11	the	the	DET
cana-4165	163	12	transport	transport	NOUN
cana-4165	163	13	characteristics	characteristic	NOUN
cana-4165	163	14	.	.	PUNCT
cana-4165	164	1	the	the	DET
cana-4165	164	2	density	density	NOUN
cana-4165	164	3	of	of	ADP
cana-4165	164	4	states	state	NOUN
cana-4165	164	5	becomes	become	VERB
cana-4165	164	6	independent	independent	ADJ
cana-4165	164	7	of	of	ADP
cana-4165	164	8	energy	energy	NOUN
cana-4165	164	9	in	in	ADP
cana-4165	164	10	two	two	NUM
cana-4165	164	11	-	-	PUNCT
cana-4165	164	12	dimensional	dimensional	ADJ
cana-4165	164	13	electron	electron	NOUN
cana-4165	164	14	vapors	vapor	NOUN
cana-4165	164	15	,	,	PUNCT
cana-4165	164	16	inside	inside	ADP
cana-4165	164	17	each	each	DET
cana-4165	164	18	subband	subband	NOUN
cana-4165	164	19	,	,	PUNCT
cana-4165	164	20	resulting	result	VERB
cana-4165	164	21	in	in	ADP
cana-4165	164	22	unique	unique	ADJ
cana-4165	164	23	characteristics	characteristic	NOUN
cana-4165	164	24	in	in	ADP
cana-4165	164	25	the	the	DET
cana-4165	164	26	transport	transport	NOUN
cana-4165	164	27	coefficients	coefficient	NOUN
cana-4165	164	28	.	.	PUNCT
cana-4165	165	1	the	the	DET
cana-4165	165	2	density	density	NOUN
cana-4165	165	3	of	of	ADP
cana-4165	165	4	states	state	NOUN
cana-4165	165	5	shows	show	VERB
cana-4165	165	6	van	van	PROPN
cana-4165	165	7	hove	hove	PROPN
cana-4165	165	8	singularities	singularity	NOUN
cana-4165	165	9	in	in	ADP
cana-4165	165	10	one	one	NUM
cana-4165	165	11	-	-	PUNCT
cana-4165	165	12	dimensional	dimensional	ADJ
cana-4165	165	13	systems	system	NOUN
cana-4165	165	14	;	;	PUNCT
cana-4165	165	15	hence	hence	ADV
cana-4165	165	16	,	,	PUNCT
cana-4165	165	17	electron	electron	NOUN
cana-4165	165	18	-	-	PUNCT
cana-4165	165	19	electron	electron	NOUN
cana-4165	165	20	interactions	interaction	NOUN
cana-4165	165	21	produce	produce	VERB
cana-4165	165	22	luttinger	lutting	ADJ
cana-4165	165	23	liquid	liquid	ADJ
cana-4165	165	24	behavior	behavior	NOUN
cana-4165	165	25	instead	instead	ADV
cana-4165	165	26	of	of	ADP
cana-4165	165	27	the	the	DET
cana-4165	165	28	standard	standard	ADJ
cana-4165	165	29	fermi	fermi	NOUN
cana-4165	165	30	liquid	liquid	ADJ
cana-4165	165	31	model	model	NOUN
cana-4165	165	32	.	.	PUNCT
cana-4165	166	1	temperature	temperature	NOUN
cana-4165	166	2	dependence	dependence	NOUN
cana-4165	166	3	adds	add	VERB
cana-4165	166	4	still	still	ADV
cana-4165	166	5	another	another	DET
cana-4165	166	6	level	level	NOUN
cana-4165	166	7	of	of	ADP
cana-4165	166	8	complication	complication	NOUN
cana-4165	166	9	.	.	PUNCT
cana-4165	167	1	usually	usually	ADV
cana-4165	167	2	dominated	dominate	VERB
cana-4165	167	3	at	at	ADP
cana-4165	167	4	high	high	ADJ
cana-4165	167	5	temperatures	temperature	NOUN
cana-4165	167	6	by	by	ADP
cana-4165	167	7	inelastic	inelastic	ADJ
cana-4165	167	8	scattering	scattering	NOUN
cana-4165	167	9	with	with	ADP
cana-4165	167	10	phonons	phonon	NOUN
cana-4165	167	11	,	,	PUNCT
cana-4165	167	12	this	this	PRON
cana-4165	167	13	causes	cause	VERB
cana-4165	167	14	a	a	DET
cana-4165	167	15	power	power	NOUN
cana-4165	167	16	-	-	PUNCT
cana-4165	167	17	law	law	NOUN
cana-4165	167	18	drop	drop	NOUN
cana-4165	167	19	in	in	ADP
cana-4165	167	20	mobility	mobility	NOUN
cana-4165	167	21	:	:	PUNCT
cana-4165	167	22	μ	μ	PROPN
cana-4165	167	23	∝	∝	PROPN
cana-4165	167	24	t^(α	t^(α	PRON
cana-4165	167	25	)	)	PUNCT
cana-4165	167	26	,	,	PUNCT
cana-4165	167	27	where	where	SCONJ
cana-4165	167	28	the	the	DET
cana-4165	167	29	exponent	exponent	NOUN
cana-4165	167	30	α	α	PROPN
cana-4165	167	31	depends	depend	VERB
cana-4165	167	32	on	on	ADP
cana-4165	167	33	the	the	DET
cana-4165	167	34	particular	particular	ADJ
cana-4165	167	35	scattering	scattering	NOUN
cana-4165	167	36	mechanism	mechanism	NOUN
cana-4165	167	37	.	.	PUNCT
cana-4165	168	1	under	under	ADP
cana-4165	168	2	low	low	ADJ
cana-4165	168	3	temperatures	temperature	NOUN
cana-4165	168	4	,	,	PUNCT
cana-4165	168	5	impurity	impurity	NOUN
cana-4165	168	6	scattering	scattering	NOUN
cana-4165	168	7	usually	usually	ADV
cana-4165	168	8	becomes	become	VERB
cana-4165	168	9	the	the	DET
cana-4165	168	10	limiting	limit	VERB
cana-4165	168	11	factor	factor	NOUN
cana-4165	168	12	,	,	PUNCT
cana-4165	168	13	producing	produce	VERB
cana-4165	168	14	in	in	ADP
cana-4165	168	15	the	the	DET
cana-4165	168	16	simplest	simple	ADJ
cana-4165	168	17	models	model	NOUN
cana-4165	168	18	a	a	DET
cana-4165	168	19	temperature	temperature	NOUN
cana-4165	168	20	-	-	PUNCT
cana-4165	168	21	independent	independent	ADJ
cana-4165	168	22	mobility	mobility	NOUN
cana-4165	168	23	.	.	PUNCT
cana-4165	169	1	still	still	ADV
cana-4165	169	2	in	in	ADP
cana-4165	169	3	this	this	DET
cana-4165	169	4	domain	domain	NOUN
cana-4165	169	5	,	,	PUNCT
cana-4165	169	6	quantum	quantum	ADJ
cana-4165	169	7	corrections	correction	NOUN
cana-4165	169	8	can	can	AUX
cana-4165	169	9	nevertheless	nevertheless	ADV
cana-4165	169	10	bring	bring	VERB
cana-4165	169	11	logarithmic	logarithmic	ADJ
cana-4165	169	12	or	or	CCONJ
cana-4165	169	13	power	power	NOUN
cana-4165	169	14	-	-	PUNCT
cana-4165	169	15	law	law	NOUN
cana-4165	169	16	temperature	temperature	NOUN
cana-4165	169	17	dependencies	dependency	NOUN
cana-4165	169	18	.	.	PUNCT
cana-4165	170	1	distinct	distinct	ADJ
cana-4165	170	2	dominating	dominating	NOUN
cana-4165	170	3	transport	transport	NOUN
cana-4165	170	4	mechanism	mechanism	NOUN
cana-4165	170	5	results	result	NOUN
cana-4165	170	6	in	in	ADP
cana-4165	170	7	distinct	distinct	ADJ
cana-4165	170	8	asymptotic	asymptotic	ADJ
cana-4165	170	9	behavior	behavior	NOUN
cana-4165	170	10	of	of	ADP
cana-4165	170	11	electron	electron	NOUN
cana-4165	170	12	mean	mean	NOUN
cana-4165	170	13	velocities	velocity	NOUN
cana-4165	170	14	.	.	PUNCT
cana-4165	171	1	the	the	DET
cana-4165	171	2	standard	standard	ADJ
cana-4165	171	3	drift	drift	NOUN
cana-4165	171	4	-	-	PUNCT
cana-4165	171	5	diffusion	diffusion	NOUN
cana-4165	171	6	model	model	NOUN
cana-4165	171	7	fits	fit	VERB
cana-4165	171	8	in	in	ADP
cana-4165	171	9	the	the	DET
cana-4165	171	10	diffusive	diffusive	ADJ
cana-4165	171	11	domain	domain	NOUN
cana-4165	171	12	,	,	PUNCT
cana-4165	171	13	in	in	ADP
cana-4165	171	14	which	which	PRON
cana-4165	171	15	the	the	DET
cana-4165	171	16	mean	mean	ADJ
cana-4165	171	17	free	free	ADJ
cana-4165	171	18	route	route	NOUN
cana-4165	171	19	is	be	AUX
cana-4165	171	20	far	far	ADV
cana-4165	171	21	shorter	short	ADJ
cana-4165	171	22	than	than	ADP
cana-4165	171	23	the	the	DET
cana-4165	171	24	system	system	NOUN
cana-4165	171	25	size	size	NOUN
cana-4165	171	26	,	,	PUNCT
cana-4165	171	27	where	where	SCONJ
cana-4165	171	28	velocity	velocity	NOUN
cana-4165	171	29	scales	scale	VERB
cana-4165	171	30	linearly	linearly	ADV
cana-4165	171	31	with	with	ADP
cana-4165	171	32	field	field	NOUN
cana-4165	171	33	at	at	ADP
cana-4165	171	34	low	low	ADJ
cana-4165	171	35	fields	field	NOUN
cana-4165	171	36	.	.	PUNCT
cana-4165	172	1	under	under	ADP
cana-4165	172	2	the	the	DET
cana-4165	172	3	ballistic	ballistic	ADJ
cana-4165	172	4	regime	regime	NOUN
cana-4165	172	5	,	,	PUNCT
cana-4165	172	6	in	in	ADP
cana-4165	172	7	which	which	PRON
cana-4165	172	8	electrons	electron	NOUN
cana-4165	172	9	move	move	VERB
cana-4165	172	10	the	the	DET
cana-4165	172	11	system	system	NOUN
cana-4165	172	12	without	without	ADP
cana-4165	172	13	dispersing	dispersing	NOUN
cana-4165	172	14	,	,	PUNCT
cana-4165	172	15	the	the	DET
cana-4165	172	16	velocity	velocity	NOUN
cana-4165	172	17	approaches	approach	VERB
cana-4165	172	18	the	the	DET
cana-4165	172	19	band	band	NOUN
cana-4165	172	20	-	-	PUNCT
cana-4165	172	21	structure	structure	NOUN
cana-4165	172	22	-	-	PUNCT
cana-4165	172	23	limited	limit	VERB
cana-4165	172	24	group	group	NOUN
cana-4165	172	25	velocity	velocity	NOUN
cana-4165	172	26	.	.	PUNCT
cana-4165	173	1	the	the	DET
cana-4165	173	2	knudsen	knudsen	PROPN
cana-4165	173	3	number	number	NOUN
cana-4165	173	4	kn	kn	PROPN
cana-4165	173	5	=	=	PUNCT
cana-4165	173	6	λ	λ	PROPN
cana-4165	173	7	/	/	SYM
cana-4165	173	8	l	l	NOUN
cana-4165	173	9	allows	allow	VERB
cana-4165	173	10	one	one	NUM
cana-4165	173	11	to	to	PART
cana-4165	173	12	define	define	VERB
cana-4165	173	13	the	the	DET
cana-4165	173	14	change	change	NOUN
cana-4165	173	15	between	between	ADP
cana-4165	173	16	these	these	DET
cana-4165	173	17	regimes	regime	NOUN
cana-4165	173	18	by	by	ADP
cana-4165	173	19	means	mean	NOUN
cana-4165	173	20	of	of	ADP
cana-4165	173	21	the	the	DET
cana-4165	173	22	mean	mean	ADJ
cana-4165	173	23	free	free	ADJ
cana-4165	173	24	path	path	NOUN
cana-4165	173	25	and	and	CCONJ
cana-4165	173	26	the	the	DET
cana-4165	173	27	characteristic	characteristic	ADJ
cana-4165	173	28	system	system	NOUN
cana-4165	173	29	size	size	NOUN
cana-4165	173	30	.	.	PUNCT
cana-4165	174	1	transport	transport	NOUN
cana-4165	174	2	is	be	AUX
cana-4165	174	3	diffused	diffuse	VERB
cana-4165	174	4	for	for	ADP
cana-4165	174	5	kn	kn	PROPN
cana-4165	174	6	<	<	X
cana-4165	174	7	<	<	X
cana-4165	174	8	1	1	NUM
cana-4165	174	9	and	and	CCONJ
cana-4165	174	10	ballistic	ballistic	ADJ
cana-4165	174	11	for	for	ADP
cana-4165	174	12	kn	kn	PROPN
cana-4165	174	13	>	>	X
cana-4165	174	14	>	>	X
cana-4165	175	1	1	1	X
cana-4165	175	2	.	.	PUNCT
cana-4165	175	3	often	often	ADV
cana-4165	175	4	by	by	ADP
cana-4165	175	5	numerical	numerical	ADJ
cana-4165	175	6	solution	solution	NOUN
cana-4165	175	7	of	of	ADP
cana-4165	175	8	the	the	DET
cana-4165	175	9	boltzmann	boltzmann	PROPN
cana-4165	175	10	equation	equation	NOUN
cana-4165	175	11	or	or	CCONJ
cana-4165	175	12	monte	monte	PROPN
cana-4165	175	13	carlo	carlo	PROPN
cana-4165	175	14	simulations	simulation	NOUN
cana-4165	175	15	,	,	PUNCT
cana-4165	175	16	the	the	DET
cana-4165	175	17	intermediate	intermediate	ADJ
cana-4165	175	18	zone	zone	NOUN
cana-4165	175	19	demands	demand	VERB
cana-4165	175	20	careful	careful	ADJ
cana-4165	175	21	study	study	NOUN
cana-4165	175	22	.	.	PUNCT
cana-4165	176	1	different	different	ADJ
cana-4165	176	2	scattering	scattering	NOUN
cana-4165	176	3	processes	process	NOUN
cana-4165	176	4	help	help	VERB
cana-4165	176	5	to	to	PART
cana-4165	176	6	control	control	VERB
cana-4165	176	7	the	the	DET
cana-4165	176	8	electron	electron	NOUN
cana-4165	176	9	velocity	velocity	NOUN
cana-4165	176	10	.	.	PUNCT
cana-4165	177	1	in	in	ADP
cana-4165	177	2	pure	pure	ADJ
cana-4165	177	3	semiconductors	semiconductor	NOUN
cana-4165	177	4	,	,	PUNCT
cana-4165	177	5	acoustic	acoustic	ADJ
cana-4165	177	6	phonon	phonon	NOUN
cana-4165	177	7	scattering	scattering	NOUN
cana-4165	177	8	usually	usually	ADV
cana-4165	177	9	rules	rule	VERB
cana-4165	177	10	low	low	ADJ
cana-4165	177	11	fields	field	NOUN
cana-4165	177	12	and	and	CCONJ
cana-4165	177	13	mild	mild	ADJ
cana-4165	177	14	temperatures	temperature	NOUN
cana-4165	177	15	.	.	PUNCT
cana-4165	178	1	at	at	ADP
cana-4165	178	2	higher	high	ADJ
cana-4165	178	3	fields	field	NOUN
cana-4165	178	4	,	,	PUNCT
cana-4165	178	5	optical	optical	ADJ
cana-4165	178	6	phonon	phonon	NOUN
cana-4165	178	7	emission	emission	NOUN
cana-4165	178	8	becomes	become	VERB
cana-4165	178	9	important	important	ADJ
cana-4165	178	10	when	when	SCONJ
cana-4165	178	11	electrons	electron	NOUN
cana-4165	178	12	acquire	acquire	VERB
cana-4165	178	13	enough	enough	ADJ
cana-4165	178	14	energy	energy	NOUN
cana-4165	178	15	to	to	PART
cana-4165	178	16	excite	excite	VERB
cana-4165	178	17	these	these	DET
cana-4165	178	18	modes	mode	NOUN
cana-4165	178	19	,	,	PUNCT
cana-4165	178	20	hence	hence	ADV
cana-4165	178	21	producing	produce	VERB
cana-4165	178	22	velocity	velocity	NOUN
cana-4165	178	23	saturation	saturation	NOUN
cana-4165	178	24	.	.	PUNCT
cana-4165	179	1	while	while	SCONJ
cana-4165	179	2	surface	surface	NOUN
cana-4165	179	3	or	or	CCONJ
cana-4165	179	4	interface	interface	NOUN
cana-4165	179	5	scattering	scattering	NOUN
cana-4165	179	6	becomes	become	VERB
cana-4165	179	7	more	more	ADV
cana-4165	179	8	critical	critical	ADJ
cana-4165	179	9	as	as	SCONJ
cana-4165	179	10	dimensions	dimension	NOUN
cana-4165	179	11	shrink	shrink	VERB
cana-4165	179	12	,	,	PUNCT
cana-4165	179	13	impurity	impurity	NOUN
cana-4165	179	14	scattering	scattering	NOUN
cana-4165	179	15	is	be	AUX
cana-4165	179	16	essential	essential	ADJ
cana-4165	179	17	in	in	ADP
cana-4165	179	18	doped	doped	ADJ
cana-4165	179	19	semiconductors	semiconductor	NOUN
cana-4165	179	20	and	and	CCONJ
cana-4165	179	21	at	at	ADP
cana-4165	179	22	low	low	ADJ
cana-4165	179	23	temperatures	temperature	NOUN
cana-4165	179	24	.	.	PUNCT
cana-4165	180	1	the	the	DET
cana-4165	180	2	identification	identification	NOUN
cana-4165	180	3	of	of	ADP
cana-4165	180	4	pertinent	pertinent	ADJ
cana-4165	180	5	dimensionless	dimensionless	NOUN
cana-4165	180	6	parameters	parameter	NOUN
cana-4165	180	7	and	and	CCONJ
cana-4165	180	8	the	the	DET
cana-4165	180	9	computation	computation	NOUN
cana-4165	180	10	of	of	ADP
cana-4165	180	11	suitable	suitable	ADJ
cana-4165	180	12	expansions	expansion	NOUN
cana-4165	180	13	in	in	ADP
cana-4165	180	14	several	several	ADJ
cana-4165	180	15	limiting	limit	VERB
cana-4165	180	16	conditions	condition	NOUN
cana-4165	180	17	are	be	AUX
cana-4165	180	18	prerequisites	prerequisite	NOUN
cana-4165	180	19	for	for	ADP
cana-4165	180	20	the	the	DET
cana-4165	180	21	construction	construction	NOUN
cana-4165	180	22	of	of	ADP
cana-4165	180	23	a	a	DET
cana-4165	180	24	complete	complete	ADJ
cana-4165	180	25	asymptotic	asymptotic	ADJ
cana-4165	180	26	expansion	expansion	NOUN
cana-4165	180	27	.	.	PUNCT
cana-4165	181	1	we	we	PRON
cana-4165	181	2	combine	combine	VERB
cana-4165	181	3	saddle	saddle	NOUN
cana-4165	181	4	-	-	PUNCT
cana-4165	181	5	point	point	NOUN
cana-4165	181	6	approximations	approximation	NOUN
cana-4165	181	7	and	and	CCONJ
cana-4165	181	8	variational	variational	ADJ
cana-4165	181	9	techniques	technique	NOUN
cana-4165	181	10	for	for	ADP
cana-4165	181	11	high	high	ADJ
cana-4165	181	12	-	-	PUNCT
cana-4165	181	13	field	field	NOUN
cana-4165	181	14	circumstances	circumstance	NOUN
cana-4165	181	15	with	with	ADP
cana-4165	181	16	perturbative	perturbative	ADJ
cana-4165	181	17	techniques	technique	NOUN
cana-4165	181	18	for	for	ADP
cana-4165	181	19	the	the	DET
cana-4165	181	20	low	low	ADJ
cana-4165	181	21	-	-	PUNCT
cana-4165	181	22	field	field	NOUN
cana-4165	181	23	realm	realm	NOUN
cana-4165	181	24	.	.	PUNCT
cana-4165	182	1	the	the	DET
cana-4165	182	2	generated	generate	VERB
cana-4165	182	3	expressions	expression	NOUN
cana-4165	182	4	are	be	AUX
cana-4165	182	5	then	then	ADV
cana-4165	182	6	matched	match	VERB
cana-4165	182	7	in	in	ADP
cana-4165	182	8	the	the	DET
cana-4165	182	9	intermediate	intermediate	ADJ
cana-4165	182	10	area	area	NOUN
cana-4165	182	11	to	to	PART
cana-4165	182	12	provide	provide	VERB
cana-4165	182	13	a	a	DET
cana-4165	182	14	seamless	seamless	ADJ
cana-4165	182	15	change	change	NOUN
cana-4165	182	16	between	between	ADP
cana-4165	182	17	regimes	regime	NOUN
cana-4165	182	18	.	.	PUNCT
cana-4165	183	1	communications	communication	NOUN
cana-4165	183	2	on	on	ADP
cana-4165	183	3	applied	apply	VERB
cana-4165	183	4	nonlinear	nonlinear	ADJ
cana-4165	183	5	analysis	analysis	NOUN
cana-4165	183	6	issn	issn	NOUN
cana-4165	183	7	:	:	PUNCT
cana-4165	183	8	1074	1074	NUM
cana-4165	183	9	-	-	PUNCT
cana-4165	183	10	133x	133x	NUM
cana-4165	183	11	vol	vol	NOUN
cana-4165	183	12	32	32	NUM
cana-4165	183	13	no	no	NOUN
cana-4165	183	14	.	.	PUNCT
cana-4165	184	1	9s	9s	NUM
cana-4165	184	2	(	(	PUNCT
cana-4165	184	3	2025	2025	NUM
cana-4165	184	4	)	)	PUNCT
cana-4165	184	5	1396	1396	NUM
cana-4165	184	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	184	7	table	table	NOUN
cana-4165	184	8	1	1	NUM
cana-4165	184	9	:	:	PUNCT
cana-4165	184	10	key	key	ADJ
cana-4165	184	11	dimensionless	dimensionless	NOUN
cana-4165	184	12	parameters	parameter	NOUN
cana-4165	184	13	in	in	ADP
cana-4165	184	14	electron	electron	NOUN
cana-4165	184	15	transport	transport	NOUN
cana-4165	184	16	parameter	parameter	PROPN
cana-4165	184	17	definition	definition	NOUN
cana-4165	184	18	physical	physical	ADJ
cana-4165	184	19	significance	significance	NOUN
cana-4165	184	20	e	e	PROPN
cana-4165	184	21	/	/	SYM
cana-4165	184	22	ec	ec	PROPN
cana-4165	184	23	ratio	ratio	NOUN
cana-4165	184	24	of	of	ADP
cana-4165	184	25	applied	applied	ADJ
cana-4165	184	26	field	field	NOUN
cana-4165	184	27	to	to	ADP
cana-4165	184	28	critical	critical	ADJ
cana-4165	184	29	field	field	NOUN
cana-4165	184	30	determines	determine	VERB
cana-4165	184	31	transition	transition	NOUN
cana-4165	184	32	to	to	ADP
cana-4165	184	33	non	non	ADJ
cana-4165	184	34	-	-	ADJ
cana-4165	184	35	linear	linear	ADJ
cana-4165	184	36	transport	transport	NOUN
cana-4165	184	37	kbt	kbt	PROPN
cana-4165	184	38	/	/	SYM
cana-4165	184	39	ef	ef	PROPN
cana-4165	184	40	ratio	ratio	NOUN
cana-4165	184	41	of	of	ADP
cana-4165	184	42	thermal	thermal	ADJ
cana-4165	184	43	energy	energy	NOUN
cana-4165	184	44	to	to	ADP
cana-4165	184	45	fermi	fermi	NOUN
cana-4165	184	46	energy	energy	NOUN
cana-4165	184	47	controls	control	NOUN
cana-4165	184	48	degeneracy	degeneracy	NOUN
cana-4165	184	49	of	of	ADP
cana-4165	184	50	electron	electron	NOUN
cana-4165	184	51	gas	gas	NOUN
cana-4165	184	52	λ	λ	PROPN
cana-4165	184	53	/	/	SYM
cana-4165	184	54	l	l	NOUN
cana-4165	184	55	ratio	ratio	NOUN
cana-4165	184	56	of	of	ADP
cana-4165	184	57	mean	mean	ADJ
cana-4165	184	58	free	free	ADJ
cana-4165	184	59	path	path	NOUN
cana-4165	184	60	to	to	ADP
cana-4165	184	61	system	system	NOUN
cana-4165	184	62	size	size	NOUN
cana-4165	184	63	knudsen	knudsen	PROPN
cana-4165	184	64	number	number	NOUN
cana-4165	184	65	for	for	ADP
cana-4165	184	66	diffusive	diffusive	ADJ
cana-4165	184	67	-	-	PUNCT
cana-4165	184	68	ballistic	ballistic	ADJ
cana-4165	184	69	transition	transition	NOUN
cana-4165	184	70	ℏ/τef	ℏ/τef	NOUN
cana-4165	184	71	ratio	ratio	NOUN
cana-4165	184	72	of	of	ADP
cana-4165	184	73	quantum	quantum	ADJ
cana-4165	184	74	lifetime	lifetime	NOUN
cana-4165	184	75	to	to	ADP
cana-4165	184	76	energy	energy	NOUN
cana-4165	184	77	scale	scale	NOUN
cana-4165	184	78	importance	importance	NOUN
cana-4165	184	79	of	of	ADP
cana-4165	184	80	quantum	quantum	ADJ
cana-4165	184	81	coherence	coherence	NOUN
cana-4165	184	82	effects	effect	NOUN
cana-4165	184	83	ωcτ	ωcτ	PROPN
cana-4165	184	84	product	product	NOUN
cana-4165	184	85	of	of	ADP
cana-4165	184	86	cyclotron	cyclotron	NOUN
cana-4165	184	87	frequency	frequency	NOUN
cana-4165	184	88	and	and	CCONJ
cana-4165	184	89	scattering	scatter	VERB
cana-4165	184	90	time	time	NOUN
cana-4165	184	91	strength	strength	NOUN
cana-4165	184	92	of	of	ADP
cana-4165	184	93	magnetotransport	magnetotransport	NOUN
cana-4165	184	94	effects	effect	VERB
cana-4165	184	95	our	our	PRON
cana-4165	184	96	thorough	thorough	ADJ
cana-4165	184	97	analytical	analytical	ADJ
cana-4165	184	98	derivations	derivation	NOUN
cana-4165	184	99	in	in	ADP
cana-4165	184	100	later	late	ADJ
cana-4165	184	101	sections	section	NOUN
cana-4165	184	102	find	find	VERB
cana-4165	184	103	their	their	PRON
cana-4165	184	104	basis	basis	NOUN
cana-4165	184	105	in	in	ADP
cana-4165	184	106	the	the	DET
cana-4165	184	107	conceptual	conceptual	ADJ
cana-4165	184	108	framework	framework	NOUN
cana-4165	184	109	already	already	ADV
cana-4165	184	110	described	describe	VERB
cana-4165	184	111	.	.	PUNCT
cana-4165	185	1	we	we	PRON
cana-4165	185	2	derive	derive	VERB
cana-4165	185	3	asymptotic	asymptotic	ADJ
cana-4165	185	4	expansions	expansion	NOUN
cana-4165	185	5	that	that	PRON
cana-4165	185	6	precisely	precisely	ADV
cana-4165	185	7	explain	explain	VERB
cana-4165	185	8	electron	electron	NOUN
cana-4165	185	9	mean	mean	NOUN
cana-4165	185	10	velocities	velocity	NOUN
cana-4165	185	11	over	over	ADP
cana-4165	185	12	several	several	ADJ
cana-4165	185	13	transport	transport	NOUN
cana-4165	185	14	regimes	regime	NOUN
cana-4165	185	15	by	by	ADP
cana-4165	185	16	methodically	methodically	ADV
cana-4165	185	17	accounting	account	VERB
cana-4165	185	18	for	for	ADP
cana-4165	185	19	quantum	quantum	ADJ
cana-4165	185	20	effects	effect	NOUN
cana-4165	185	21	,	,	PUNCT
cana-4165	185	22	many	many	ADJ
cana-4165	185	23	-	-	PUNCT
cana-4165	185	24	body	body	NOUN
cana-4165	185	25	interactions	interaction	NOUN
cana-4165	185	26	,	,	PUNCT
cana-4165	185	27	dimensional	dimensional	ADJ
cana-4165	185	28	limitations	limitation	NOUN
cana-4165	185	29	,	,	PUNCT
cana-4165	185	30	and	and	CCONJ
cana-4165	185	31	several	several	ADJ
cana-4165	185	32	scattering	scatter	VERB
cana-4165	185	33	mechanisms	mechanism	NOUN
cana-4165	185	34	.	.	PUNCT
cana-4165	186	1	research	research	NOUN
cana-4165	186	2	methodology	methodology	NOUN
cana-4165	186	3	using	use	VERB
cana-4165	186	4	a	a	DET
cana-4165	186	5	multifarious	multifarious	ADJ
cana-4165	186	6	approach	approach	NOUN
cana-4165	186	7	integrating	integrate	VERB
cana-4165	186	8	analytical	analytical	ADJ
cana-4165	186	9	theory	theory	NOUN
cana-4165	186	10	,	,	PUNCT
cana-4165	186	11	numerical	numerical	ADJ
cana-4165	186	12	modeling	modeling	NOUN
cana-4165	186	13	,	,	PUNCT
cana-4165	186	14	and	and	CCONJ
cana-4165	186	15	comparison	comparison	NOUN
cana-4165	186	16	with	with	ADP
cana-4165	186	17	actual	actual	ADJ
cana-4165	186	18	data	datum	NOUN
cana-4165	186	19	,	,	PUNCT
cana-4165	186	20	our	our	PRON
cana-4165	186	21	analysis	analysis	NOUN
cana-4165	186	22	of	of	ADP
cana-4165	186	23	the	the	DET
cana-4165	186	24	asymptotic	asymptotic	ADJ
cana-4165	186	25	behavior	behavior	NOUN
cana-4165	186	26	of	of	ADP
cana-4165	186	27	electron	electron	NOUN
cana-4165	186	28	mean	mean	NOUN
cana-4165	186	29	velocities	velocity	NOUN
cana-4165	186	30	this	this	DET
cana-4165	186	31	all	all	ADV
cana-4165	186	32	-	-	PUNCT
cana-4165	186	33	encompassing	encompass	VERB
cana-4165	186	34	methodology	methodology	NOUN
cana-4165	186	35	helps	help	VERB
cana-4165	186	36	us	we	PRON
cana-4165	186	37	to	to	PART
cana-4165	186	38	build	build	VERB
cana-4165	186	39	and	and	CCONJ
cana-4165	186	40	evaluate	evaluate	VERB
cana-4165	186	41	asymptotic	asymptotic	ADJ
cana-4165	186	42	expansions	expansion	NOUN
cana-4165	186	43	throughout	throughout	ADP
cana-4165	186	44	several	several	ADJ
cana-4165	186	45	material	material	NOUN
cana-4165	186	46	systems	system	NOUN
cana-4165	186	47	and	and	CCONJ
cana-4165	186	48	transportation	transportation	NOUN
cana-4165	186	49	regimes	regime	NOUN
cana-4165	186	50	.	.	PUNCT
cana-4165	187	1	analytical	analytical	ADJ
cana-4165	187	2	methods	method	NOUN
cana-4165	187	3	our	our	PRON
cana-4165	187	4	approach	approach	NOUN
cana-4165	187	5	starts	start	VERB
cana-4165	187	6	with	with	ADP
cana-4165	187	7	the	the	DET
cana-4165	187	8	construction	construction	NOUN
cana-4165	187	9	of	of	ADP
cana-4165	187	10	suitable	suitable	ADJ
cana-4165	187	11	transport	transport	NOUN
cana-4165	187	12	equations	equation	NOUN
cana-4165	187	13	depending	depend	VERB
cana-4165	187	14	on	on	ADP
cana-4165	187	15	the	the	DET
cana-4165	187	16	physical	physical	ADJ
cana-4165	187	17	properties	property	NOUN
cana-4165	187	18	of	of	ADP
cana-4165	187	19	the	the	DET
cana-4165	187	20	system	system	NOUN
cana-4165	187	21	under	under	ADP
cana-4165	187	22	analysis	analysis	NOUN
cana-4165	187	23	,	,	PUNCT
cana-4165	187	24	therefore	therefore	ADV
cana-4165	187	25	addressing	address	VERB
cana-4165	187	26	the	the	DET
cana-4165	187	27	analytical	analytical	ADJ
cana-4165	187	28	component	component	NOUN
cana-4165	187	29	of	of	ADP
cana-4165	187	30	it	it	PRON
cana-4165	187	31	.	.	PUNCT
cana-4165	188	1	we	we	PRON
cana-4165	188	2	apply	apply	VERB
cana-4165	188	3	boltzmann	boltzmann	PROPN
cana-4165	188	4	transport	transport	NOUN
cana-4165	188	5	equation	equation	NOUN
cana-4165	188	6	(	(	PUNCT
cana-4165	188	7	bte	bte	PROPN
cana-4165	188	8	)	)	PUNCT
cana-4165	188	9	with	with	ADP
cana-4165	188	10	several	several	ADJ
cana-4165	188	11	approximations	approximation	NOUN
cana-4165	188	12	for	for	ADP
cana-4165	188	13	the	the	DET
cana-4165	188	14	collision	collision	NOUN
cana-4165	188	15	integral	integral	ADJ
cana-4165	188	16	in	in	ADP
cana-4165	188	17	semiclassical	semiclassical	ADJ
cana-4165	188	18	transport	transport	NOUN
cana-4165	188	19	in	in	ADP
cana-4165	188	20	the	the	DET
cana-4165	188	21	diffusive	diffusive	ADJ
cana-4165	188	22	regime	regime	NOUN
cana-4165	188	23	.	.	PUNCT
cana-4165	189	1	starting	start	VERB
cana-4165	189	2	from	from	ADP
cana-4165	189	3	the	the	DET
cana-4165	189	4	relaxation	relaxation	NOUN
cana-4165	189	5	time	time	NOUN
cana-4165	189	6	approximation	approximation	NOUN
cana-4165	189	7	,	,	PUNCT
cana-4165	189	8	more	more	ADV
cana-4165	189	9	advanced	advanced	ADJ
cana-4165	189	10	approaches	approach	NOUN
cana-4165	189	11	include	include	VERB
cana-4165	189	12	explicit	explicit	ADJ
cana-4165	189	13	models	model	NOUN
cana-4165	189	14	for	for	ADP
cana-4165	189	15	several	several	ADJ
cana-4165	189	16	scattering	scatter	VERB
cana-4165	189	17	mechanisms	mechanism	NOUN
cana-4165	189	18	.	.	PUNCT
cana-4165	190	1	we	we	PRON
cana-4165	190	2	solve	solve	VERB
cana-4165	190	3	the	the	DET
cana-4165	190	4	bte	bte	NOUN
cana-4165	190	5	perturbatively	perturbatively	ADV
cana-4165	190	6	to	to	PART
cana-4165	190	7	get	get	VERB
cana-4165	190	8	asymptotic	asymptotic	ADJ
cana-4165	190	9	expansions	expansion	NOUN
cana-4165	190	10	in	in	ADP
cana-4165	190	11	the	the	DET
cana-4165	190	12	weak	weak	ADJ
cana-4165	190	13	-	-	PUNCT
cana-4165	190	14	field	field	NOUN
cana-4165	190	15	limit	limit	NOUN
cana-4165	190	16	.	.	PUNCT
cana-4165	191	1	the	the	DET
cana-4165	191	2	distribution	distribution	NOUN
cana-4165	191	3	function	function	NOUN
cana-4165	191	4	is	be	AUX
cana-4165	191	5	extended	extend	VERB
cana-4165	191	6	as	as	ADP
cana-4165	191	7	f	f	PROPN
cana-4165	191	8	=	=	PROPN
cana-4165	191	9	f₀	f₀	PROPN
cana-4165	191	10	+	+	CCONJ
cana-4165	191	11	f₁	f₁	ADJ
cana-4165	191	12	+	+	CCONJ
cana-4165	191	13	f₂	f₂	NOUN
cana-4165	191	14	+	+	X
cana-4165	191	15	...	...	PUNCT
cana-4165	191	16	,	,	PUNCT
cana-4165	191	17	where	where	SCONJ
cana-4165	191	18	f₀	f₀	PROPN
cana-4165	191	19	is	be	AUX
cana-4165	191	20	the	the	DET
cana-4165	191	21	equilibrium	equilibrium	NOUN
cana-4165	191	22	distribution	distribution	NOUN
cana-4165	191	23	and	and	CCONJ
cana-4165	191	24	later	later	ADJ
cana-4165	191	25	terms	term	NOUN
cana-4165	191	26	reflect	reflect	VERB
cana-4165	191	27	deviations	deviation	NOUN
cana-4165	191	28	of	of	ADP
cana-4165	191	29	increasing	increase	VERB
cana-4165	191	30	order	order	NOUN
cana-4165	191	31	in	in	ADP
cana-4165	191	32	the	the	DET
cana-4165	191	33	electric	electric	ADJ
cana-4165	191	34	field	field	NOUN
cana-4165	191	35	.	.	PUNCT
cana-4165	192	1	the	the	DET
cana-4165	192	2	mean	mean	ADJ
cana-4165	192	3	velocity	velocity	NOUN
cana-4165	192	4	is	be	AUX
cana-4165	192	5	subsequently	subsequently	ADV
cana-4165	192	6	computed	compute	VERB
cana-4165	192	7	as	as	ADP
cana-4165	192	8	:	:	PUNCT
cana-4165	192	9	v	v	NUM
cana-4165	192	10	=	=	SYM
cana-4165	192	11	∫	∫	PROPN
cana-4165	192	12	v(k	v(k	PROPN
cana-4165	192	13	)	)	PUNCT
cana-4165	192	14	f(k	f(k	PUNCT
cana-4165	192	15	)	)	PUNCT
cana-4165	192	16	dk	dk	PROPN
cana-4165	192	17	/	/	SYM
cana-4165	192	18	∫	∫	PROPN
cana-4165	192	19	f(k	f(k	PROPN
cana-4165	192	20	)	)	PUNCT
cana-4165	192	21	dk	dk	NOUN
cana-4165	192	22	communications	communication	NOUN
cana-4165	192	23	on	on	ADP
cana-4165	192	24	applied	apply	VERB
cana-4165	192	25	nonlinear	nonlinear	ADJ
cana-4165	192	26	analysis	analysis	NOUN
cana-4165	192	27	issn	issn	NOUN
cana-4165	192	28	:	:	PUNCT
cana-4165	192	29	1074	1074	NUM
cana-4165	192	30	-	-	PUNCT
cana-4165	192	31	133x	133x	NUM
cana-4165	192	32	vol	vol	NOUN
cana-4165	192	33	32	32	NUM
cana-4165	192	34	no	no	NOUN
cana-4165	192	35	.	.	PUNCT
cana-4165	193	1	9s	9s	NUM
cana-4165	193	2	(	(	PUNCT
cana-4165	193	3	2025	2025	NUM
cana-4165	193	4	)	)	PUNCT
cana-4165	193	5	1397	1397	NUM
cana-4165	193	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	193	7	with	with	ADP
cana-4165	193	8	coefficients	coefficient	NOUN
cana-4165	193	9	found	find	VERB
cana-4165	193	10	by	by	ADP
cana-4165	193	11	the	the	DET
cana-4165	193	12	band	band	NOUN
cana-4165	193	13	structure	structure	NOUN
cana-4165	193	14	and	and	CCONJ
cana-4165	193	15	scattering	scatter	VERB
cana-4165	193	16	parameters	parameter	NOUN
cana-4165	193	17	,	,	PUNCT
cana-4165	193	18	this	this	DET
cana-4165	193	19	method	method	NOUN
cana-4165	193	20	produces	produce	VERB
cana-4165	193	21	an	an	DET
cana-4165	193	22	electric	electric	ADJ
cana-4165	193	23	field	field	NOUN
cana-4165	193	24	power	power	NOUN
cana-4165	193	25	series	series	NOUN
cana-4165	193	26	.	.	PUNCT
cana-4165	194	1	we	we	PRON
cana-4165	194	2	use	use	VERB
cana-4165	194	3	the	the	DET
cana-4165	194	4	non	non	ADJ
cana-4165	194	5	-	-	ADJ
cana-4165	194	6	equilibrium	equilibrium	ADJ
cana-4165	194	7	green	green	NOUN
cana-4165	194	8	's	's	PART
cana-4165	194	9	function	function	NOUN
cana-4165	194	10	(	(	PUNCT
cana-4165	194	11	negf	negf	NOUN
cana-4165	194	12	)	)	PUNCT
cana-4165	194	13	formalism	formalism	NOUN
cana-4165	194	14	for	for	ADP
cana-4165	194	15	quantum	quantum	ADJ
cana-4165	194	16	transport	transport	NOUN
cana-4165	194	17	to	to	PART
cana-4165	194	18	give	give	VERB
cana-4165	194	19	a	a	DET
cana-4165	194	20	more	more	ADV
cana-4165	194	21	exact	exact	ADJ
cana-4165	194	22	characterization	characterization	NOUN
cana-4165	194	23	of	of	ADP
cana-4165	194	24	coherence	coherence	NOUN
cana-4165	194	25	effects	effect	NOUN
cana-4165	194	26	.	.	PUNCT
cana-4165	195	1	from	from	ADP
cana-4165	195	2	the	the	DET
cana-4165	195	3	dyson	dyson	PROPN
cana-4165	195	4	and	and	CCONJ
cana-4165	195	5	keldysh	keldysh	ADJ
cana-4165	195	6	equations	equation	NOUN
cana-4165	195	7	respectively	respectively	ADV
cana-4165	195	8	,	,	PUNCT
cana-4165	195	9	one	one	PRON
cana-4165	195	10	finds	find	VERB
cana-4165	195	11	the	the	DET
cana-4165	195	12	retarded	retarded	ADJ
cana-4165	195	13	green	green	NOUN
cana-4165	195	14	's	's	PART
cana-4165	195	15	function	function	NOUN
cana-4165	195	16	g^r	g^r	PROPN
cana-4165	195	17	and	and	CCONJ
cana-4165	195	18	the	the	DET
cana-4165	195	19	lesser	less	ADJ
cana-4165	195	20	green	green	NOUN
cana-4165	195	21	's	's	PART
cana-4165	195	22	function	function	NOUN
cana-4165	195	23	g^.	g^.	NOUN
cana-4165	195	24	the	the	DET
cana-4165	195	25	mean	mean	ADJ
cana-4165	195	26	speed	speed	NOUN
cana-4165	195	27	then	then	ADV
cana-4165	195	28	is	be	AUX
cana-4165	195	29	computed	compute	VERB
cana-4165	195	30	from	from	ADP
cana-4165	195	31	:	:	PUNCT
cana-4165	195	32	v	v	NOUN
cana-4165	195	33	=	=	SYM
cana-4165	195	34	-i∫	-i∫	ADJ
cana-4165	195	35	tr[v(k	tr[v(k	PROPN
cana-4165	195	36	)	)	PUNCT
cana-4165	195	37	g^<(k	g^<(k	PROPN
cana-4165	195	38	,	,	PUNCT
cana-4165	195	39	k	k	PROPN
cana-4165	195	40	,	,	PUNCT
cana-4165	195	41	e	e	NOUN
cana-4165	195	42	)	)	PUNCT
cana-4165	195	43	]	]	PUNCT
cana-4165	195	44	de	de	X
cana-4165	195	45	/	/	SYM
cana-4165	195	46	(	(	PUNCT
cana-4165	195	47	2π	2π	NOUN
cana-4165	195	48	)	)	PUNCT
cana-4165	195	49	where	where	SCONJ
cana-4165	195	50	v(k	v(k	NOUN
cana-4165	195	51	)	)	PUNCT
cana-4165	195	52	represents	represent	VERB
cana-4165	195	53	the	the	DET
cana-4165	195	54	velocity	velocity	NOUN
cana-4165	195	55	operator	operator	NOUN
cana-4165	195	56	.	.	PUNCT
cana-4165	196	1	we	we	PRON
cana-4165	196	2	apply	apply	VERB
cana-4165	196	3	variational	variational	ADJ
cana-4165	196	4	methods	method	NOUN
cana-4165	196	5	and	and	CCONJ
cana-4165	196	6	saddle	saddle	NOUN
cana-4165	196	7	-	-	PUNCT
cana-4165	196	8	point	point	NOUN
cana-4165	196	9	approximations	approximation	NOUN
cana-4165	196	10	in	in	ADP
cana-4165	196	11	the	the	DET
cana-4165	196	12	high	high	ADJ
cana-4165	196	13	-	-	PUNCT
cana-4165	196	14	field	field	NOUN
cana-4165	196	15	regime	regime	NOUN
cana-4165	196	16	,	,	PUNCT
cana-4165	196	17	when	when	SCONJ
cana-4165	196	18	perturbative	perturbative	ADJ
cana-4165	196	19	techniques	technique	NOUN
cana-4165	196	20	become	become	VERB
cana-4165	196	21	insufficient	insufficient	ADJ
cana-4165	196	22	.	.	PUNCT
cana-4165	197	1	appropriate	appropriate	ADJ
cana-4165	197	2	functional	functional	ADJ
cana-4165	197	3	forms	form	NOUN
cana-4165	197	4	define	define	VERB
cana-4165	197	5	the	the	DET
cana-4165	197	6	distribution	distribution	NOUN
cana-4165	197	7	function	function	NOUN
cana-4165	197	8	;	;	PUNCT
cana-4165	197	9	variational	variational	ADJ
cana-4165	197	10	concepts	concept	NOUN
cana-4165	197	11	are	be	AUX
cana-4165	197	12	used	use	VERB
cana-4165	197	13	to	to	PART
cana-4165	197	14	find	find	VERB
cana-4165	197	15	the	the	DET
cana-4165	197	16	ideal	ideal	ADJ
cana-4165	197	17	values	value	NOUN
cana-4165	197	18	.	.	PUNCT
cana-4165	198	1	this	this	DET
cana-4165	198	2	method	method	NOUN
cana-4165	198	3	remains	remain	VERB
cana-4165	198	4	analytically	analytically	ADV
cana-4165	198	5	tractable	tractable	ADJ
cana-4165	198	6	and	and	CCONJ
cana-4165	198	7	catches	catch	VERB
cana-4165	198	8	the	the	DET
cana-4165	198	9	fundamental	fundamental	ADJ
cana-4165	198	10	physics	physics	NOUN
cana-4165	198	11	of	of	ADP
cana-4165	198	12	velocity	velocity	NOUN
cana-4165	198	13	saturation	saturation	NOUN
cana-4165	198	14	.	.	PUNCT
cana-4165	199	1	we	we	PRON
cana-4165	199	2	build	build	VERB
cana-4165	199	3	dimension	dimension	NOUN
cana-4165	199	4	-	-	PUNCT
cana-4165	199	5	specific	specific	ADJ
cana-4165	199	6	models	model	NOUN
cana-4165	199	7	considering	consider	VERB
cana-4165	199	8	the	the	DET
cana-4165	199	9	changed	change	VERB
cana-4165	199	10	density	density	NOUN
cana-4165	199	11	of	of	ADP
cana-4165	199	12	states	state	NOUN
cana-4165	199	13	and	and	CCONJ
cana-4165	199	14	scattering	scatter	VERB
cana-4165	199	15	mechanisms	mechanism	NOUN
cana-4165	199	16	for	for	ADP
cana-4165	199	17	low	low	ADJ
cana-4165	199	18	-	-	PUNCT
cana-4165	199	19	dimensional	dimensional	ADJ
cana-4165	199	20	systems	system	NOUN
cana-4165	199	21	.	.	PUNCT
cana-4165	200	1	in	in	ADP
cana-4165	200	2	two	two	NUM
cana-4165	200	3	-	-	PUNCT
cana-4165	200	4	dimensional	dimensional	ADJ
cana-4165	200	5	systems	system	NOUN
cana-4165	200	6	,	,	PUNCT
cana-4165	200	7	for	for	ADP
cana-4165	200	8	example	example	NOUN
cana-4165	200	9	,	,	PUNCT
cana-4165	200	10	the	the	DET
cana-4165	200	11	screening	screening	NOUN
cana-4165	200	12	of	of	ADP
cana-4165	200	13	charged	charge	VERB
cana-4165	200	14	impurities	impurity	NOUN
cana-4165	200	15	follows	follow	VERB
cana-4165	200	16	a	a	DET
cana-4165	200	17	different	different	ADJ
cana-4165	200	18	functional	functional	ADJ
cana-4165	200	19	dependence	dependence	NOUN
cana-4165	200	20	than	than	ADP
cana-4165	200	21	in	in	ADP
cana-4165	200	22	bulk	bulk	ADJ
cana-4165	200	23	materials	material	NOUN
cana-4165	200	24	,	,	PUNCT
cana-4165	200	25	hence	hence	ADV
cana-4165	200	26	influencing	influence	VERB
cana-4165	200	27	the	the	DET
cana-4165	200	28	resultant	resultant	NOUN
cana-4165	200	29	mobility	mobility	NOUN
cana-4165	200	30	and	and	CCONJ
cana-4165	200	31	field	field	NOUN
cana-4165	200	32	-	-	PUNCT
cana-4165	200	33	dependent	dependent	ADJ
cana-4165	200	34	velocity	velocity	NOUN
cana-4165	200	35	.	.	PUNCT
cana-4165	201	1	asymptotic	asymptotic	ADJ
cana-4165	201	2	matching	matching	NOUN
cana-4165	201	3	methods	method	NOUN
cana-4165	201	4	solve	solve	VERB
cana-4165	201	5	the	the	DET
cana-4165	201	6	change	change	NOUN
cana-4165	201	7	between	between	ADP
cana-4165	201	8	diffusive	diffusive	ADJ
cana-4165	201	9	and	and	CCONJ
cana-4165	201	10	ballistic	ballistic	ADJ
cana-4165	201	11	transport	transport	NOUN
cana-4165	201	12	.	.	PUNCT
cana-4165	202	1	we	we	PRON
cana-4165	202	2	build	build	VERB
cana-4165	202	3	intermediary	intermediary	ADJ
cana-4165	202	4	expressions	expression	NOUN
cana-4165	202	5	that	that	PRON
cana-4165	202	6	smoothly	smoothly	ADV
cana-4165	202	7	connect	connect	VERB
cana-4165	202	8	the	the	DET
cana-4165	202	9	limiting	limit	VERB
cana-4165	202	10	instances	instance	NOUN
cana-4165	202	11	kn	kn	PROPN
cana-4165	202	12	<	<	X
cana-4165	202	13	<	<	X
cana-4165	202	14	1	1	NUM
cana-4165	202	15	(	(	PUNCT
cana-4165	202	16	diffusive	diffusive	ADJ
cana-4165	202	17	)	)	PUNCT
cana-4165	202	18	and	and	CCONJ
cana-4165	202	19	kn	kn	PROPN
cana-4165	202	20	>	>	X
cana-4165	202	21	>	>	X
cana-4165	202	22	1	1	NUM
cana-4165	202	23	(	(	PUNCT
cana-4165	202	24	ballistic	ballistic	ADJ
cana-4165	202	25	)	)	PUNCT
cana-4165	202	26	,	,	PUNCT
cana-4165	202	27	then	then	ADV
cana-4165	202	28	separate	separate	VERB
cana-4165	202	29	expansions	expansion	NOUN
cana-4165	202	30	for	for	ADP
cana-4165	202	31	these	these	DET
cana-4165	202	32	regimes	regime	NOUN
cana-4165	202	33	.	.	PUNCT
cana-4165	203	1	this	this	DET
cana-4165	203	2	method	method	NOUN
cana-4165	203	3	guarantees	guarantee	VERB
cana-4165	203	4	that	that	SCONJ
cana-4165	203	5	our	our	PRON
cana-4165	203	6	asymptotic	asymptotic	ADJ
cana-4165	203	7	expansions	expansion	NOUN
cana-4165	203	8	keep	keep	VERB
cana-4165	203	9	validity	validity	NOUN
cana-4165	203	10	over	over	ADP
cana-4165	203	11	the	the	DET
cana-4165	203	12	whole	whole	ADJ
cana-4165	203	13	knudsen	knudsen	PROPN
cana-4165	203	14	number	number	NOUN
cana-4165	203	15	range	range	PROPN
cana-4165	203	16	.	.	PUNCT
cana-4165	204	1	numerical	numerical	ADJ
cana-4165	204	2	simulations	simulation	NOUN
cana-4165	204	3	we	we	PRON
cana-4165	204	4	investigate	investigate	VERB
cana-4165	204	5	regimes	regime	NOUN
cana-4165	204	6	where	where	SCONJ
cana-4165	204	7	analytical	analytical	ADJ
cana-4165	204	8	solutions	solution	NOUN
cana-4165	204	9	become	become	VERB
cana-4165	204	10	intractable	intractable	ADJ
cana-4165	204	11	and	and	CCONJ
cana-4165	204	12	complement	complement	VERB
cana-4165	204	13	our	our	PRON
cana-4165	204	14	analytical	analytical	ADJ
cana-4165	204	15	work	work	NOUN
cana-4165	204	16	by	by	ADP
cana-4165	204	17	means	mean	NOUN
cana-4165	204	18	of	of	ADP
cana-4165	204	19	comprehensive	comprehensive	ADJ
cana-4165	204	20	numerical	numerical	ADJ
cana-4165	204	21	simulations	simulation	NOUN
cana-4165	204	22	validating	validate	VERB
cana-4165	204	23	the	the	DET
cana-4165	204	24	derived	derive	VERB
cana-4165	204	25	asymptotic	asymptotic	ADJ
cana-4165	204	26	expansions	expansion	NOUN
cana-4165	204	27	.	.	PUNCT
cana-4165	205	1	our	our	PRON
cana-4165	205	2	numerical	numerical	ADJ
cana-4165	205	3	method	method	NOUN
cana-4165	205	4	consists	consist	VERB
cana-4165	205	5	of	of	ADP
cana-4165	205	6	multiple	multiple	ADJ
cana-4165	205	7	separate	separate	ADJ
cana-4165	205	8	techniques	technique	NOUN
cana-4165	205	9	catered	cater	VERB
cana-4165	205	10	for	for	ADP
cana-4165	205	11	various	various	ADJ
cana-4165	205	12	transport	transport	NOUN
cana-4165	205	13	regimes	regime	NOUN
cana-4165	205	14	.	.	PUNCT
cana-4165	206	1	we	we	PRON
cana-4165	206	2	consider	consider	VERB
cana-4165	206	3	both	both	CCONJ
cana-4165	206	4	deterministic	deterministic	ADJ
cana-4165	206	5	and	and	CCONJ
cana-4165	206	6	stochastic	stochastic	ADJ
cana-4165	206	7	solutions	solution	NOUN
cana-4165	206	8	of	of	ADP
cana-4165	206	9	the	the	DET
cana-4165	206	10	boltzmann	boltzmann	PROPN
cana-4165	206	11	equation	equation	NOUN
cana-4165	206	12	for	for	ADP
cana-4165	206	13	semiclassical	semiclassical	ADJ
cana-4165	206	14	transport	transport	NOUN
cana-4165	206	15	.	.	PUNCT
cana-4165	207	1	the	the	DET
cana-4165	207	2	deterministic	deterministic	ADJ
cana-4165	207	3	method	method	NOUN
cana-4165	207	4	uses	use	VERB
cana-4165	207	5	spectral	spectral	ADJ
cana-4165	207	6	or	or	CCONJ
cana-4165	207	7	finite	finite	ADJ
cana-4165	207	8	-	-	PUNCT
cana-4165	207	9	difference	difference	NOUN
cana-4165	207	10	techniques	technique	NOUN
cana-4165	207	11	to	to	PART
cana-4165	207	12	directly	directly	ADV
cana-4165	207	13	numerical	numerical	PROPN
cana-4165	207	14	integrate	integrate	VERB
cana-4165	207	15	the	the	DET
cana-4165	207	16	bte	bte	NOUN
cana-4165	207	17	.	.	PUNCT
cana-4165	208	1	when	when	SCONJ
cana-4165	208	2	the	the	DET
cana-4165	208	3	distribution	distribution	NOUN
cana-4165	208	4	function	function	NOUN
cana-4165	208	5	somewhat	somewhat	ADV
cana-4165	208	6	deviates	deviate	VERB
cana-4165	208	7	from	from	ADP
cana-4165	208	8	the	the	DET
cana-4165	208	9	fermi	fermi	NOUN
cana-4165	208	10	-	-	PUNCT
cana-4165	208	11	dirac	dirac	NOUN
cana-4165	208	12	form	form	NOUN
cana-4165	208	13	,	,	PUNCT
cana-4165	208	14	this	this	DET
cana-4165	208	15	method	method	NOUN
cana-4165	208	16	shows	show	VERB
cana-4165	208	17	to	to	PART
cana-4165	208	18	be	be	AUX
cana-4165	208	19	most	most	ADV
cana-4165	208	20	successful	successful	ADJ
cana-4165	208	21	for	for	ADP
cana-4165	208	22	near	near	ADJ
cana-4165	208	23	-	-	PUNCT
cana-4165	208	24	equilibrium	equilibrium	NOUN
cana-4165	208	25	situations	situation	NOUN
cana-4165	208	26	.	.	PUNCT
cana-4165	209	1	particularly	particularly	ADV
cana-4165	209	2	for	for	ADP
cana-4165	209	3	very	very	ADJ
cana-4165	209	4	non	non	ADJ
cana-4165	209	5	-	-	ADJ
cana-4165	209	6	equilibrium	equilibrium	ADJ
cana-4165	209	7	settings	setting	NOUN
cana-4165	209	8	,	,	PUNCT
cana-4165	209	9	stochastic	stochastic	ADJ
cana-4165	209	10	simulations	simulation	NOUN
cana-4165	209	11	based	base	VERB
cana-4165	209	12	on	on	ADP
cana-4165	209	13	the	the	DET
cana-4165	209	14	ensemble	ensemble	ADJ
cana-4165	209	15	monte	monte	PROPN
cana-4165	209	16	carlo	carlo	PROPN
cana-4165	209	17	technique	technique	NOUN
cana-4165	209	18	offer	offer	VERB
cana-4165	209	19	a	a	DET
cana-4165	209	20	more	more	ADV
cana-4165	209	21	flexible	flexible	ADJ
cana-4165	209	22	substitute	substitute	NOUN
cana-4165	209	23	.	.	PUNCT
cana-4165	210	1	under	under	ADP
cana-4165	210	2	the	the	DET
cana-4165	210	3	impact	impact	NOUN
cana-4165	210	4	of	of	ADP
cana-4165	210	5	the	the	DET
cana-4165	210	6	applied	apply	VERB
cana-4165	210	7	field	field	NOUN
cana-4165	210	8	and	and	CCONJ
cana-4165	210	9	random	random	ADJ
cana-4165	210	10	scattering	scatter	VERB
cana-4165	210	11	events	event	NOUN
cana-4165	210	12	,	,	PUNCT
cana-4165	210	13	this	this	DET
cana-4165	210	14	method	method	NOUN
cana-4165	210	15	simulates	simulate	VERB
cana-4165	210	16	the	the	DET
cana-4165	210	17	paths	path	NOUN
cana-4165	210	18	of	of	ADP
cana-4165	210	19	representative	representative	ADJ
cana-4165	210	20	particles	particle	NOUN
cana-4165	210	21	.	.	PUNCT
cana-4165	211	1	after	after	ADP
cana-4165	211	2	that	that	PRON
cana-4165	211	3	,	,	PUNCT
cana-4165	211	4	averaging	average	VERB
cana-4165	211	5	over	over	ADP
cana-4165	211	6	the	the	DET
cana-4165	211	7	ensemble	ensemble	ADJ
cana-4165	211	8	determines	determine	NOUN
cana-4165	211	9	the	the	DET
cana-4165	211	10	mean	mean	ADJ
cana-4165	211	11	speed	speed	NOUN
cana-4165	211	12	.	.	PUNCT
cana-4165	212	1	our	our	PRON
cana-4165	212	2	system	system	NOUN
cana-4165	212	3	includes	include	VERB
cana-4165	212	4	thorough	thorough	ADJ
cana-4165	212	5	models	model	NOUN
cana-4165	212	6	for	for	ADP
cana-4165	212	7	several	several	ADJ
cana-4165	212	8	scattering	scatter	VERB
cana-4165	212	9	mechanisms	mechanism	NOUN
cana-4165	212	10	together	together	ADV
cana-4165	212	11	with	with	ADP
cana-4165	212	12	reasonable	reasonable	ADJ
cana-4165	212	13	band	band	NOUN
cana-4165	212	14	structures	structure	NOUN
cana-4165	212	15	derived	derive	VERB
cana-4165	212	16	from	from	ADP
cana-4165	212	17	empirical	empirical	ADJ
cana-4165	212	18	pseudopotential	pseudopotential	ADJ
cana-4165	212	19	computations	computation	NOUN
cana-4165	212	20	or	or	CCONJ
cana-4165	212	21	k·p	k·p	NOUN
cana-4165	212	22	theory	theory	NOUN
cana-4165	212	23	.	.	PUNCT
cana-4165	213	1	we	we	PRON
cana-4165	213	2	apply	apply	VERB
cana-4165	213	3	numerical	numerical	ADJ
cana-4165	213	4	implementations	implementation	NOUN
cana-4165	213	5	of	of	ADP
cana-4165	213	6	the	the	DET
cana-4165	213	7	negf	negf	NOUN
cana-4165	213	8	framework	framework	NOUN
cana-4165	213	9	for	for	ADP
cana-4165	213	10	quantum	quantum	ADJ
cana-4165	213	11	transportation	transportation	NOUN
cana-4165	213	12	in	in	ADP
cana-4165	213	13	mesoscopic	mesoscopic	NOUN
cana-4165	213	14	systems	system	NOUN
cana-4165	213	15	.	.	PUNCT
cana-4165	214	1	the	the	DET
cana-4165	214	2	system	system	NOUN
cana-4165	214	3	is	be	AUX
cana-4165	214	4	discretized	discretize	VERB
cana-4165	214	5	into	into	ADP
cana-4165	214	6	a	a	DET
cana-4165	214	7	tight	tight	ADV
cana-4165	214	8	-	-	PUNCT
cana-4165	214	9	binding	bind	VERB
cana-4165	214	10	representation	representation	NOUN
cana-4165	214	11	,	,	PUNCT
cana-4165	214	12	and	and	CCONJ
cana-4165	214	13	recursive	recursive	ADJ
cana-4165	214	14	methods	method	NOUN
cana-4165	214	15	handle	handle	VERB
cana-4165	214	16	huge	huge	ADJ
cana-4165	214	17	systems	system	NOUN
cana-4165	214	18	effectively	effectively	ADV
cana-4165	214	19	to	to	PART
cana-4165	214	20	compute	compute	VERB
cana-4165	214	21	the	the	DET
cana-4165	214	22	green	green	NOUN
cana-4165	214	23	's	's	PART
cana-4165	214	24	functions	function	NOUN
cana-4165	214	25	.	.	PUNCT
cana-4165	215	1	this	this	DET
cana-4165	215	2	method	method	NOUN
cana-4165	215	3	inherently	inherently	ADV
cana-4165	215	4	communications	communication	NOUN
cana-4165	215	5	on	on	ADP
cana-4165	215	6	applied	apply	VERB
cana-4165	215	7	nonlinear	nonlinear	ADJ
cana-4165	215	8	analysis	analysis	NOUN
cana-4165	215	9	issn	issn	NOUN
cana-4165	215	10	:	:	PUNCT
cana-4165	215	11	1074	1074	NUM
cana-4165	215	12	-	-	PUNCT
cana-4165	215	13	133x	133x	NUM
cana-4165	215	14	vol	vol	NOUN
cana-4165	215	15	32	32	NUM
cana-4165	215	16	no	no	NOUN
cana-4165	215	17	.	.	PUNCT
cana-4165	216	1	9s	9s	NUM
cana-4165	216	2	(	(	PUNCT
cana-4165	216	3	2025	2025	NUM
cana-4165	216	4	)	)	PUNCT
cana-4165	216	5	1398	1398	NUM
cana-4165	216	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	216	7	combines	combine	VERB
cana-4165	216	8	quantum	quantum	NOUN
cana-4165	216	9	processes	process	NOUN
cana-4165	216	10	including	include	VERB
cana-4165	216	11	tunneling	tunneling	NOUN
cana-4165	216	12	and	and	CCONJ
cana-4165	216	13	interference	interference	NOUN
cana-4165	216	14	,	,	PUNCT
cana-4165	216	15	which	which	PRON
cana-4165	216	16	are	be	AUX
cana-4165	216	17	necessary	necessary	ADJ
cana-4165	216	18	for	for	ADP
cana-4165	216	19	a	a	DET
cana-4165	216	20	realistic	realistic	ADJ
cana-4165	216	21	understanding	understanding	NOUN
cana-4165	216	22	of	of	ADP
cana-4165	216	23	nanoscale	nanoscale	NOUN
cana-4165	216	24	electronics	electronic	NOUN
cana-4165	216	25	.	.	PUNCT
cana-4165	217	1	in	in	ADP
cana-4165	217	2	all	all	DET
cana-4165	217	3	numerical	numerical	ADJ
cana-4165	217	4	simulations	simulation	NOUN
cana-4165	217	5	,	,	PUNCT
cana-4165	217	6	especially	especially	ADV
cana-4165	217	7	convergence	convergence	NOUN
cana-4165	217	8	problems	problem	NOUN
cana-4165	217	9	and	and	CCONJ
cana-4165	217	10	error	error	NOUN
cana-4165	217	11	estimate	estimate	NOUN
cana-4165	217	12	receive	receive	VERB
cana-4165	217	13	special	special	ADJ
cana-4165	217	14	focus	focus	NOUN
cana-4165	217	15	.	.	PUNCT
cana-4165	218	1	the	the	DET
cana-4165	218	2	same	same	ADJ
cana-4165	218	3	physical	physical	ADJ
cana-4165	218	4	problem	problem	NOUN
cana-4165	218	5	is	be	AUX
cana-4165	218	6	solved	solve	VERB
cana-4165	218	7	using	use	VERB
cana-4165	218	8	several	several	ADJ
cana-4165	218	9	numerical	numerical	ADJ
cana-4165	218	10	techniques	technique	NOUN
cana-4165	218	11	in	in	ADP
cana-4165	218	12	order	order	NOUN
cana-4165	218	13	to	to	PART
cana-4165	218	14	cross	cross	VERB
cana-4165	218	15	-	-	VERB
cana-4165	218	16	valuate	valuate	VERB
cana-4165	218	17	the	the	DET
cana-4165	218	18	outputs	output	NOUN
cana-4165	218	19	and	and	CCONJ
cana-4165	218	20	provide	provide	VERB
cana-4165	218	21	robustness	robustness	NOUN
cana-4165	218	22	against	against	ADP
cana-4165	218	23	methodological	methodological	ADJ
cana-4165	218	24	artifacts	artifact	NOUN
cana-4165	218	25	.	.	PUNCT
cana-4165	219	1	figure	figure	NOUN
cana-4165	219	2	1	1	NUM
cana-4165	219	3	:	:	PUNCT
cana-4165	219	4	flowchart	flowchart	NOUN
cana-4165	219	5	of	of	ADP
cana-4165	219	6	the	the	DET
cana-4165	219	7	numerical	numerical	PROPN
cana-4165	219	8	simulation	simulation	PROPN
cana-4165	219	9	methodology	methodology	PROPN
cana-4165	219	10	experimental	experimental	ADJ
cana-4165	219	11	comparison	comparison	NOUN
cana-4165	219	12	we	we	PRON
cana-4165	219	13	validate	validate	VERB
cana-4165	219	14	our	our	PRON
cana-4165	219	15	theoretical	theoretical	ADJ
cana-4165	219	16	framework	framework	NOUN
cana-4165	219	17	by	by	ADP
cana-4165	219	18	matching	match	VERB
cana-4165	219	19	our	our	PRON
cana-4165	219	20	predictions	prediction	NOUN
cana-4165	219	21	with	with	ADP
cana-4165	219	22	experimental	experimental	ADJ
cana-4165	219	23	data	datum	NOUN
cana-4165	219	24	from	from	ADP
cana-4165	219	25	several	several	ADJ
cana-4165	219	26	material	material	NOUN
cana-4165	219	27	systems	system	NOUN
cana-4165	219	28	.	.	PUNCT
cana-4165	220	1	including	include	VERB
cana-4165	220	2	a	a	DET
cana-4165	220	3	broad	broad	ADJ
cana-4165	220	4	spectrum	spectrum	NOUN
cana-4165	220	5	of	of	ADP
cana-4165	220	6	materials	material	NOUN
cana-4165	220	7	,	,	PUNCT
cana-4165	220	8	temperature	temperature	NOUN
cana-4165	220	9	settings	setting	NOUN
cana-4165	220	10	,	,	PUNCT
cana-4165	220	11	and	and	CCONJ
cana-4165	220	12	field	field	NOUN
cana-4165	220	13	intensities	intensity	NOUN
cana-4165	220	14	,	,	PUNCT
cana-4165	220	15	the	the	DET
cana-4165	220	16	experimental	experimental	ADJ
cana-4165	220	17	data	datum	NOUN
cana-4165	220	18	come	come	VERB
cana-4165	220	19	from	from	ADP
cana-4165	220	20	both	both	CCONJ
cana-4165	220	21	our	our	PRON
cana-4165	220	22	own	own	ADJ
cana-4165	220	23	experiments	experiment	NOUN
cana-4165	220	24	and	and	CCONJ
cana-4165	220	25	the	the	DET
cana-4165	220	26	published	publish	VERB
cana-4165	220	27	literature	literature	NOUN
cana-4165	220	28	.	.	PUNCT
cana-4165	221	1	for	for	ADP
cana-4165	221	2	bulk	bulk	ADJ
cana-4165	221	3	semiconductors	semiconductor	NOUN
cana-4165	221	4	like	like	ADP
cana-4165	221	5	gallium	gallium	NOUN
cana-4165	221	6	arsenicide	arsenicide	NOUN
cana-4165	221	7	and	and	CCONJ
cana-4165	221	8	silicon	silicon	NOUN
cana-4165	221	9	,	,	PUNCT
cana-4165	221	10	we	we	PRON
cana-4165	221	11	derive	derive	VERB
cana-4165	221	12	standard	standard	ADJ
cana-4165	221	13	velocity	velocity	NOUN
cana-4165	221	14	-	-	PUNCT
cana-4165	221	15	field	field	NOUN
cana-4165	221	16	properties	property	NOUN
cana-4165	221	17	either	either	CCONJ
cana-4165	221	18	from	from	ADP
cana-4165	221	19	device	device	NOUN
cana-4165	221	20	characteristics	characteristic	NOUN
cana-4165	221	21	or	or	CCONJ
cana-4165	221	22	determined	determine	VERB
cana-4165	221	23	by	by	ADP
cana-4165	221	24	time	time	NOUN
cana-4165	221	25	-	-	PUNCT
cana-4165	221	26	offlight	offlight	VERB
cana-4165	221	27	studies	study	NOUN
cana-4165	221	28	.	.	PUNCT
cana-4165	222	1	before	before	ADP
cana-4165	222	2	moving	move	VERB
cana-4165	222	3	on	on	ADV
cana-4165	222	4	to	to	ADP
cana-4165	222	5	more	more	ADV
cana-4165	222	6	difficult	difficult	ADJ
cana-4165	222	7	systems	system	NOUN
cana-4165	222	8	,	,	PUNCT
cana-4165	222	9	these	these	DET
cana-4165	222	10	materials	material	NOUN
cana-4165	222	11	offer	offer	VERB
cana-4165	222	12	reliable	reliable	ADJ
cana-4165	222	13	sources	source	NOUN
cana-4165	222	14	for	for	ADP
cana-4165	222	15	verifying	verify	VERB
cana-4165	222	16	our	our	PRON
cana-4165	222	17	fundamental	fundamental	ADJ
cana-4165	222	18	theoretical	theoretical	ADJ
cana-4165	222	19	foundation	foundation	NOUN
cana-4165	222	20	.	.	PUNCT
cana-4165	223	1	we	we	PRON
cana-4165	223	2	address	address	VERB
cana-4165	223	3	semiconductor	semiconductor	NOUN
cana-4165	223	4	heterostructures	heterostructure	NOUN
cana-4165	223	5	(	(	PUNCT
cana-4165	223	6	especially	especially	ADV
cana-4165	223	7	gaas	gaas	VERB
cana-4165	223	8	/	/	SYM
cana-4165	223	9	algaas	algaas	NOUN
cana-4165	223	10	quantum	quantum	ADJ
cana-4165	223	11	wells	well	NOUN
cana-4165	223	12	)	)	PUNCT
cana-4165	223	13	and	and	CCONJ
cana-4165	223	14	graphene	graphene	VERB
cana-4165	223	15	for	for	ADP
cana-4165	223	16	two	two	NUM
cana-4165	223	17	-	-	PUNCT
cana-4165	223	18	dimensional	dimensional	ADJ
cana-4165	223	19	systems	system	NOUN
cana-4165	223	20	.	.	PUNCT
cana-4165	224	1	while	while	SCONJ
cana-4165	224	2	the	the	DET
cana-4165	224	3	latter	latter	NOUN
cana-4165	224	4	provides	provide	VERB
cana-4165	224	5	special	special	ADJ
cana-4165	224	6	difficulties	difficulty	NOUN
cana-4165	224	7	because	because	SCONJ
cana-4165	224	8	of	of	ADP
cana-4165	224	9	its	its	PRON
cana-4165	224	10	linear	linear	ADJ
cana-4165	224	11	communications	communication	NOUN
cana-4165	224	12	on	on	ADP
cana-4165	224	13	applied	apply	VERB
cana-4165	224	14	nonlinear	nonlinear	ADJ
cana-4165	224	15	analysis	analysis	NOUN
cana-4165	224	16	issn	issn	NOUN
cana-4165	224	17	:	:	PUNCT
cana-4165	224	18	1074	1074	NUM
cana-4165	224	19	-	-	PUNCT
cana-4165	224	20	133x	133x	NUM
cana-4165	224	21	vol	vol	NOUN
cana-4165	224	22	32	32	NUM
cana-4165	224	23	no	no	NOUN
cana-4165	224	24	.	.	PUNCT
cana-4165	225	1	9s	9s	NUM
cana-4165	225	2	(	(	PUNCT
cana-4165	225	3	2025	2025	NUM
cana-4165	225	4	)	)	PUNCT
cana-4165	225	5	1399	1399	NUM
cana-4165	225	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	225	7	dispersion	dispersion	NOUN
cana-4165	225	8	relation	relation	NOUN
cana-4165	225	9	and	and	CCONJ
cana-4165	225	10	chiral	chiral	ADJ
cana-4165	225	11	nature	nature	NOUN
cana-4165	225	12	of	of	ADP
cana-4165	225	13	carriers	carrier	NOUN
cana-4165	225	14	,	,	PUNCT
cana-4165	225	15	the	the	DET
cana-4165	225	16	former	former	ADJ
cana-4165	225	17	offers	offer	VERB
cana-4165	225	18	quite	quite	ADV
cana-4165	225	19	high	high	ADJ
cana-4165	225	20	mobility	mobility	NOUN
cana-4165	225	21	and	and	CCONJ
cana-4165	225	22	wellcharacterized	wellcharacterize	VERB
cana-4165	225	23	band	band	NOUN
cana-4165	225	24	structure	structure	NOUN
cana-4165	225	25	.	.	PUNCT
cana-4165	226	1	for	for	ADP
cana-4165	226	2	these	these	DET
cana-4165	226	3	systems	system	NOUN
cana-4165	226	4	,	,	PUNCT
cana-4165	226	5	experimental	experimental	ADJ
cana-4165	226	6	data	datum	NOUN
cana-4165	226	7	comes	come	VERB
cana-4165	226	8	from	from	ADP
cana-4165	226	9	direct	direct	ADJ
cana-4165	226	10	microwave	microwave	NOUN
cana-4165	226	11	approaches	approach	NOUN
cana-4165	226	12	for	for	ADP
cana-4165	226	13	velocity	velocity	NOUN
cana-4165	226	14	determination	determination	NOUN
cana-4165	226	15	,	,	PUNCT
cana-4165	226	16	magnetoresistance	magnetoresistance	NOUN
cana-4165	226	17	studies	study	NOUN
cana-4165	226	18	,	,	PUNCT
cana-4165	226	19	and	and	CCONJ
cana-4165	226	20	hall	hall	NOUN
cana-4165	226	21	measurements	measurement	NOUN
cana-4165	226	22	.	.	PUNCT
cana-4165	227	1	investigated	investigate	VERB
cana-4165	227	2	in	in	ADP
cana-4165	227	3	semiconductor	semiconductor	NOUN
cana-4165	227	4	nanowires	nanowire	NOUN
cana-4165	227	5	and	and	CCONJ
cana-4165	227	6	carbon	carbon	NOUN
cana-4165	227	7	nanotubes	nanotube	NOUN
cana-4165	227	8	where	where	SCONJ
cana-4165	227	9	quantum	quantum	NOUN
cana-4165	227	10	confinement	confinement	NOUN
cana-4165	227	11	significantly	significantly	ADV
cana-4165	227	12	alters	alter	VERB
cana-4165	227	13	the	the	DET
cana-4165	227	14	transport	transport	NOUN
cana-4165	227	15	properties	property	NOUN
cana-4165	227	16	is	be	AUX
cana-4165	227	17	one	one	NUM
cana-4165	227	18	-	-	PUNCT
cana-4165	227	19	dimensional	dimensional	ADJ
cana-4165	227	20	transport	transport	NOUN
cana-4165	227	21	.	.	PUNCT
cana-4165	228	1	although	although	SCONJ
cana-4165	228	2	these	these	DET
cana-4165	228	3	systems	system	NOUN
cana-4165	228	4	present	present	VERB
cana-4165	228	5	significant	significant	ADJ
cana-4165	228	6	experimental	experimental	ADJ
cana-4165	228	7	difficulties	difficulty	NOUN
cana-4165	228	8	,	,	PUNCT
cana-4165	228	9	new	new	ADJ
cana-4165	228	10	developments	development	NOUN
cana-4165	228	11	in	in	ADP
cana-4165	228	12	nanofabrication	nanofabrication	NOUN
cana-4165	228	13	and	and	CCONJ
cana-4165	228	14	measuring	measure	VERB
cana-4165	228	15	methods	method	NOUN
cana-4165	228	16	have	have	AUX
cana-4165	228	17	given	give	VERB
cana-4165	228	18	consistent	consistent	ADJ
cana-4165	228	19	data	datum	NOUN
cana-4165	228	20	for	for	ADP
cana-4165	228	21	validation	validation	NOUN
cana-4165	228	22	needs	need	NOUN
cana-4165	228	23	.	.	PUNCT
cana-4165	229	1	we	we	PRON
cana-4165	229	2	consider	consider	VERB
cana-4165	229	3	experimental	experimental	ADJ
cana-4165	229	4	uncertainties	uncertainty	NOUN
cana-4165	229	5	and	and	CCONJ
cana-4165	229	6	possible	possible	ADJ
cana-4165	229	7	systematic	systematic	ADJ
cana-4165	229	8	flaws	flaw	NOUN
cana-4165	229	9	when	when	SCONJ
cana-4165	229	10	we	we	PRON
cana-4165	229	11	compare	compare	VERB
cana-4165	229	12	theoretical	theoretical	ADJ
cana-4165	229	13	forecasts	forecast	NOUN
cana-4165	229	14	with	with	ADP
cana-4165	229	15	actual	actual	ADJ
cana-4165	229	16	data	datum	NOUN
cana-4165	229	17	.	.	PUNCT
cana-4165	230	1	where	where	SCONJ
cana-4165	230	2	differences	difference	NOUN
cana-4165	230	3	exist	exist	VERB
cana-4165	230	4	,	,	PUNCT
cana-4165	230	5	we	we	PRON
cana-4165	230	6	investigate	investigate	VERB
cana-4165	230	7	possible	possible	ADJ
cana-4165	230	8	causes	cause	NOUN
cana-4165	230	9	including	include	VERB
cana-4165	230	10	limits	limit	NOUN
cana-4165	230	11	in	in	ADP
cana-4165	230	12	our	our	PRON
cana-4165	230	13	theoretical	theoretical	ADJ
cana-4165	230	14	models	model	NOUN
cana-4165	230	15	,	,	PUNCT
cana-4165	230	16	simplifying	simplify	VERB
cana-4165	230	17	assumptions	assumption	NOUN
cana-4165	230	18	,	,	PUNCT
cana-4165	230	19	or	or	CCONJ
cana-4165	230	20	experimental	experimental	ADJ
cana-4165	230	21	artifacts	artifact	NOUN
cana-4165	230	22	.	.	PUNCT
cana-4165	231	1	this	this	DET
cana-4165	231	2	iterative	iterative	NOUN
cana-4165	231	3	process	process	NOUN
cana-4165	231	4	of	of	ADP
cana-4165	231	5	comparison	comparison	NOUN
cana-4165	231	6	and	and	CCONJ
cana-4165	231	7	improvement	improvement	NOUN
cana-4165	231	8	guarantees	guarantee	NOUN
cana-4165	231	9	that	that	SCONJ
cana-4165	231	10	our	our	PRON
cana-4165	231	11	asymptotic	asymptotic	ADJ
cana-4165	231	12	expansions	expansion	NOUN
cana-4165	231	13	at	at	ADP
cana-4165	231	14	last	last	ADJ
cana-4165	231	15	fairly	fairly	ADV
cana-4165	231	16	represent	represent	VERB
cana-4165	231	17	actual	actual	ADJ
cana-4165	231	18	physical	physical	ADJ
cana-4165	231	19	systems	system	NOUN
cana-4165	231	20	.	.	PUNCT
cana-4165	232	1	data	datum	NOUN
cana-4165	232	2	analysis	analysis	NOUN
cana-4165	232	3	and	and	CCONJ
cana-4165	232	4	parameter	parameter	NOUN
cana-4165	232	5	extraction	extraction	NOUN
cana-4165	232	6	to	to	PART
cana-4165	232	7	extract	extract	VERB
cana-4165	232	8	the	the	DET
cana-4165	232	9	pertinent	pertinent	ADJ
cana-4165	232	10	parameters	parameter	NOUN
cana-4165	232	11	for	for	ADP
cana-4165	232	12	our	our	PRON
cana-4165	232	13	asymptotic	asymptotic	ADJ
cana-4165	232	14	expansions	expansion	NOUN
cana-4165	232	15	from	from	ADP
cana-4165	232	16	raw	raw	ADJ
cana-4165	232	17	experimental	experimental	ADJ
cana-4165	232	18	data	datum	NOUN
cana-4165	232	19	and	and	CCONJ
cana-4165	232	20	numerical	numerical	PROPN
cana-4165	232	21	simulation	simulation	NOUN
cana-4165	232	22	results	result	NOUN
cana-4165	232	23	,	,	PUNCT
cana-4165	232	24	one	one	PRON
cana-4165	232	25	must	must	AUX
cana-4165	232	26	exercise	exercise	VERB
cana-4165	232	27	great	great	ADJ
cana-4165	232	28	attention	attention	NOUN
cana-4165	232	29	.	.	PUNCT
cana-4165	233	1	we	we	PRON
cana-4165	233	2	find	find	VERB
cana-4165	233	3	the	the	DET
cana-4165	233	4	coefficients	coefficient	NOUN
cana-4165	233	5	in	in	ADP
cana-4165	233	6	our	our	PRON
cana-4165	233	7	theoretical	theoretical	ADJ
cana-4165	233	8	statements	statement	NOUN
cana-4165	233	9	using	use	VERB
cana-4165	233	10	several	several	ADJ
cana-4165	233	11	appropriate	appropriate	ADJ
cana-4165	233	12	techniques	technique	NOUN
cana-4165	233	13	including	include	VERB
cana-4165	233	14	bayesian	bayesian	NOUN
cana-4165	233	15	approaches	approach	NOUN
cana-4165	233	16	and	and	CCONJ
cana-4165	233	17	nonlinear	nonlinear	ADJ
cana-4165	233	18	least	least	ADJ
cana-4165	233	19	squares	square	NOUN
cana-4165	233	20	.	.	PUNCT
cana-4165	234	1	we	we	PRON
cana-4165	234	2	apply	apply	VERB
cana-4165	234	3	linear	linear	ADJ
cana-4165	234	4	regression	regression	NOUN
cana-4165	234	5	in	in	ADP
cana-4165	234	6	the	the	DET
cana-4165	234	7	suitable	suitable	ADJ
cana-4165	234	8	region	region	NOUN
cana-4165	234	9	on	on	ADP
cana-4165	234	10	the	the	DET
cana-4165	234	11	velocity	velocity	NOUN
cana-4165	234	12	-	-	PUNCT
cana-4165	234	13	field	field	NOUN
cana-4165	234	14	data	datum	NOUN
cana-4165	234	15	for	for	ADP
cana-4165	234	16	the	the	DET
cana-4165	234	17	low	low	ADJ
cana-4165	234	18	-	-	PUNCT
cana-4165	234	19	field	field	NOUN
cana-4165	234	20	mobility	mobility	NOUN
cana-4165	234	21	.	.	PUNCT
cana-4165	235	1	from	from	ADP
cana-4165	235	2	the	the	DET
cana-4165	235	3	junction	junction	NOUN
cana-4165	235	4	of	of	ADP
cana-4165	235	5	the	the	DET
cana-4165	235	6	linear	linear	ADJ
cana-4165	235	7	extrapolation	extrapolation	NOUN
cana-4165	235	8	with	with	ADP
cana-4165	235	9	an	an	DET
cana-4165	235	10	appropriate	appropriate	ADJ
cana-4165	235	11	high	high	ADJ
cana-4165	235	12	-	-	PUNCT
cana-4165	235	13	field	field	NOUN
cana-4165	235	14	asymptotic	asymptotic	ADJ
cana-4165	235	15	form	form	NOUN
cana-4165	235	16	,	,	PUNCT
cana-4165	235	17	one	one	PRON
cana-4165	235	18	finds	find	VERB
cana-4165	235	19	the	the	DET
cana-4165	235	20	critical	critical	ADJ
cana-4165	235	21	field	field	NOUN
cana-4165	235	22	signaling	signal	VERB
cana-4165	235	23	the	the	DET
cana-4165	235	24	shift	shift	NOUN
cana-4165	235	25	to	to	ADP
cana-4165	235	26	nonlinear	nonlinear	ADJ
cana-4165	235	27	behavior	behavior	NOUN
cana-4165	235	28	.	.	PUNCT
cana-4165	236	1	the	the	DET
cana-4165	236	2	high	high	ADJ
cana-4165	236	3	-	-	PUNCT
cana-4165	236	4	field	field	NOUN
cana-4165	236	5	plateaus	plateaus	NOUN
cana-4165	236	6	seen	see	VERB
cana-4165	236	7	in	in	ADP
cana-4165	236	8	the	the	DET
cana-4165	236	9	velocityfield	velocityfield	NOUN
cana-4165	236	10	characteristics	characteristic	NOUN
cana-4165	236	11	allow	allow	VERB
cana-4165	236	12	one	one	PRON
cana-4165	236	13	to	to	PART
cana-4165	236	14	obtain	obtain	VERB
cana-4165	236	15	saturation	saturation	NOUN
cana-4165	236	16	velocities	velocity	NOUN
cana-4165	236	17	.	.	PUNCT
cana-4165	237	1	analyzed	analyze	VERB
cana-4165	237	2	by	by	ADP
cana-4165	237	3	power	power	NOUN
cana-4165	237	4	-	-	PUNCT
cana-4165	237	5	law	law	NOUN
cana-4165	237	6	fits	fit	VERB
cana-4165	237	7	v	v	NUM
cana-4165	237	8	∝	∝	NOUN
cana-4165	237	9	t^α	t^α	NOUN
cana-4165	237	10	or	or	CCONJ
cana-4165	237	11	more	more	ADV
cana-4165	237	12	complicated	complicated	ADJ
cana-4165	237	13	functional	functional	ADJ
cana-4165	237	14	forms	form	NOUN
cana-4165	237	15	as	as	ADP
cana-4165	237	16	suitable	suitable	ADJ
cana-4165	237	17	are	be	AUX
cana-4165	237	18	temperature	temperature	NOUN
cana-4165	237	19	relationships	relationship	NOUN
cana-4165	237	20	.	.	PUNCT
cana-4165	238	1	reflecting	reflect	VERB
cana-4165	238	2	the	the	DET
cana-4165	238	3	fundamental	fundamental	ADJ
cana-4165	238	4	scattering	scattering	ADJ
cana-4165	238	5	mechanisms	mechanism	NOUN
cana-4165	238	6	controlling	control	VERB
cana-4165	238	7	at	at	ADP
cana-4165	238	8	various	various	ADJ
cana-4165	238	9	temperature	temperature	NOUN
cana-4165	238	10	regimes	regime	NOUN
cana-4165	238	11	,	,	PUNCT
cana-4165	238	12	the	the	DET
cana-4165	238	13	derived	derive	VERB
cana-4165	238	14	exponents	exponent	NOUN
cana-4165	238	15	offer	offer	VERB
cana-4165	238	16	essential	essential	ADJ
cana-4165	238	17	assessments	assessment	NOUN
cana-4165	238	18	of	of	ADP
cana-4165	238	19	our	our	PRON
cana-4165	238	20	theoretical	theoretical	ADJ
cana-4165	238	21	theories	theory	NOUN
cana-4165	238	22	.	.	PUNCT
cana-4165	239	1	dimensional	dimensional	ADJ
cana-4165	239	2	effects	effect	NOUN
cana-4165	239	3	are	be	AUX
cana-4165	239	4	measured	measure	VERB
cana-4165	239	5	by	by	ADP
cana-4165	239	6	means	mean	NOUN
cana-4165	239	7	of	of	ADP
cana-4165	239	8	systems	system	NOUN
cana-4165	239	9	with	with	ADP
cana-4165	239	10	varying	vary	VERB
cana-4165	239	11	degrees	degree	NOUN
cana-4165	239	12	of	of	ADP
cana-4165	239	13	confinement	confinement	NOUN
cana-4165	239	14	but	but	CCONJ
cana-4165	239	15	otherwise	otherwise	ADV
cana-4165	239	16	equivalent	equivalent	ADJ
cana-4165	239	17	material	material	NOUN
cana-4165	239	18	properties	property	NOUN
cana-4165	239	19	.	.	PUNCT
cana-4165	240	1	essential	essential	ADJ
cana-4165	240	2	understanding	understanding	NOUN
cana-4165	240	3	of	of	ADP
cana-4165	240	4	the	the	DET
cana-4165	240	5	validity	validity	NOUN
cana-4165	240	6	of	of	ADP
cana-4165	240	7	our	our	PRON
cana-4165	240	8	dimensional	dimensional	ADJ
cana-4165	240	9	analysis	analysis	NOUN
cana-4165	240	10	comes	come	VERB
cana-4165	240	11	from	from	ADP
cana-4165	240	12	the	the	DET
cana-4165	240	13	scaling	scale	VERB
cana-4165	240	14	behaviors	behavior	NOUN
cana-4165	240	15	with	with	ADP
cana-4165	240	16	regard	regard	NOUN
cana-4165	240	17	to	to	ADP
cana-4165	240	18	system	system	NOUN
cana-4165	240	19	size	size	NOUN
cana-4165	240	20	,	,	PUNCT
cana-4165	240	21	carrier	carrier	NOUN
cana-4165	240	22	concentration	concentration	NOUN
cana-4165	240	23	,	,	PUNCT
cana-4165	240	24	and	and	CCONJ
cana-4165	240	25	other	other	ADJ
cana-4165	240	26	parameters	parameter	NOUN
cana-4165	240	27	.	.	PUNCT
cana-4165	241	1	bootstrapping	bootstrappe	VERB
cana-4165	241	2	and	and	CCONJ
cana-4165	241	3	cross	cross	NOUN
cana-4165	241	4	-	-	ADJ
cana-4165	241	5	validation	validation	NOUN
cana-4165	241	6	are	be	AUX
cana-4165	241	7	used	use	VERB
cana-4165	241	8	throughout	throughout	ADP
cana-4165	241	9	this	this	DET
cana-4165	241	10	procedure	procedure	NOUN
cana-4165	241	11	to	to	PART
cana-4165	241	12	evaluate	evaluate	VERB
cana-4165	241	13	the	the	DET
cana-4165	241	14	robustness	robustness	NOUN
cana-4165	241	15	of	of	ADP
cana-4165	241	16	the	the	DET
cana-4165	241	17	obtained	obtain	VERB
cana-4165	241	18	parameters	parameter	NOUN
cana-4165	241	19	and	and	CCONJ
cana-4165	241	20	generate	generate	VERB
cana-4165	241	21	significant	significant	ADJ
cana-4165	241	22	error	error	NOUN
cana-4165	241	23	estimates	estimate	NOUN
cana-4165	241	24	.	.	PUNCT
cana-4165	242	1	these	these	DET
cana-4165	242	2	statistical	statistical	ADJ
cana-4165	242	3	methods	method	NOUN
cana-4165	242	4	guarantee	guarantee	VERB
cana-4165	242	5	that	that	SCONJ
cana-4165	242	6	,	,	PUNCT
cana-4165	242	7	in	in	ADP
cana-4165	242	8	spite	spite	NOUN
cana-4165	242	9	of	of	ADP
cana-4165	242	10	natural	natural	ADJ
cana-4165	242	11	variability	variability	NOUN
cana-4165	242	12	in	in	ADP
cana-4165	242	13	experimental	experimental	ADJ
cana-4165	242	14	data	datum	NOUN
cana-4165	242	15	,	,	PUNCT
cana-4165	242	16	our	our	PRON
cana-4165	242	17	results	result	NOUN
cana-4165	242	18	are	be	AUX
cana-4165	242	19	firmly	firmly	ADV
cana-4165	242	20	based	base	VERB
cana-4165	242	21	.	.	PUNCT
cana-4165	243	1	analysis	analysis	NOUN
cana-4165	243	2	of	of	ADP
cana-4165	243	3	primary	primary	ADJ
cana-4165	243	4	data	datum	NOUN
cana-4165	243	5	we	we	PRON
cana-4165	243	6	investigated	investigate	VERB
cana-4165	243	7	electron	electron	NOUN
cana-4165	243	8	mean	mean	NOUN
cana-4165	243	9	velocities	velocity	NOUN
cana-4165	243	10	under	under	ADP
cana-4165	243	11	several	several	ADJ
cana-4165	243	12	conditions	condition	NOUN
cana-4165	243	13	—	—	PUNCT
cana-4165	243	14	including	include	VERB
cana-4165	243	15	different	different	ADJ
cana-4165	243	16	materials	material	NOUN
cana-4165	243	17	,	,	PUNCT
cana-4165	243	18	dimensional	dimensional	ADJ
cana-4165	243	19	confinements	confinement	NOUN
cana-4165	243	20	,	,	PUNCT
cana-4165	243	21	temperature	temperature	NOUN
cana-4165	243	22	ranges	range	NOUN
cana-4165	243	23	,	,	PUNCT
cana-4165	243	24	and	and	CCONJ
cana-4165	243	25	field	field	NOUN
cana-4165	243	26	strengths	strength	NOUN
cana-4165	243	27	—	—	PUNCT
cana-4165	243	28	producing	produce	VERB
cana-4165	243	29	a	a	DET
cana-4165	243	30	lot	lot	NOUN
cana-4165	243	31	of	of	ADP
cana-4165	243	32	data	datum	NOUN
cana-4165	243	33	.	.	PUNCT
cana-4165	244	1	focusing	focus	VERB
cana-4165	244	2	on	on	ADP
cana-4165	244	3	the	the	DET
cana-4165	244	4	validation	validation	NOUN
cana-4165	244	5	of	of	ADP
cana-4165	244	6	our	our	PRON
cana-4165	244	7	asymptotic	asymptotic	ADJ
cana-4165	244	8	expansions	expansion	NOUN
cana-4165	244	9	and	and	CCONJ
cana-4165	244	10	the	the	DET
cana-4165	244	11	extraction	extraction	NOUN
cana-4165	244	12	of	of	ADP
cana-4165	244	13	important	important	ADJ
cana-4165	244	14	physical	physical	ADJ
cana-4165	244	15	parameters	parameter	NOUN
cana-4165	244	16	,	,	PUNCT
cana-4165	244	17	this	this	DET
cana-4165	244	18	part	part	NOUN
cana-4165	244	19	offers	offer	VERB
cana-4165	244	20	a	a	DET
cana-4165	244	21	methodical	methodical	ADJ
cana-4165	244	22	study	study	NOUN
cana-4165	244	23	of	of	ADP
cana-4165	244	24	these	these	DET
cana-4165	244	25	results	result	NOUN
cana-4165	244	26	.	.	PUNCT
cana-4165	245	1	bulk	bulk	ADJ
cana-4165	245	2	semiconductors	semiconductor	NOUN
cana-4165	245	3	:	:	PUNCT
cana-4165	245	4	silicon	silicon	NOUN
cana-4165	245	5	and	and	CCONJ
cana-4165	245	6	gallium	gallium	PROPN
cana-4165	245	7	arsenide	arsenide	NOUN
cana-4165	245	8	communications	communication	NOUN
cana-4165	245	9	on	on	ADP
cana-4165	245	10	applied	apply	VERB
cana-4165	245	11	nonlinear	nonlinear	ADJ
cana-4165	245	12	analysis	analysis	NOUN
cana-4165	245	13	issn	issn	NOUN
cana-4165	245	14	:	:	PUNCT
cana-4165	245	15	1074	1074	NUM
cana-4165	245	16	-	-	PUNCT
cana-4165	245	17	133x	133x	NUM
cana-4165	245	18	vol	vol	NOUN
cana-4165	245	19	32	32	NUM
cana-4165	245	20	no	no	NOUN
cana-4165	245	21	.	.	PUNCT
cana-4165	246	1	9s	9s	NUM
cana-4165	246	2	(	(	PUNCT
cana-4165	246	3	2025	2025	NUM
cana-4165	246	4	)	)	PUNCT
cana-4165	246	5	1400	1400	NUM
cana-4165	246	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	247	1	both	both	CCONJ
cana-4165	247	2	silicon	silicon	NOUN
cana-4165	247	3	and	and	CCONJ
cana-4165	247	4	gallium	gallium	PROPN
cana-4165	247	5	arsenicide	arsenicide	NOUN
cana-4165	247	6	provide	provide	VERB
cana-4165	247	7	opposing	oppose	VERB
cana-4165	247	8	test	test	NOUN
cana-4165	247	9	cases	case	NOUN
cana-4165	247	10	for	for	ADP
cana-4165	247	11	our	our	PRON
cana-4165	247	12	theoretical	theoretical	ADJ
cana-4165	247	13	framework	framework	NOUN
cana-4165	247	14	and	and	CCONJ
cana-4165	247	15	act	act	VERB
cana-4165	247	16	as	as	ADP
cana-4165	247	17	canonical	canonical	ADJ
cana-4165	247	18	models	model	NOUN
cana-4165	247	19	of	of	ADP
cana-4165	247	20	indirect	indirect	ADJ
cana-4165	247	21	and	and	CCONJ
cana-4165	247	22	direct	direct	ADJ
cana-4165	247	23	bandgap	bandgap	NOUN
cana-4165	247	24	semiconductors	semiconductor	NOUN
cana-4165	247	25	respectively	respectively	ADV
cana-4165	247	26	.	.	PUNCT
cana-4165	248	1	together	together	ADV
cana-4165	248	2	with	with	ADP
cana-4165	248	3	curves	curve	NOUN
cana-4165	248	4	computed	compute	VERB
cana-4165	248	5	from	from	ADP
cana-4165	248	6	our	our	PRON
cana-4165	248	7	asymptotic	asymptotic	ADJ
cana-4165	248	8	expansion	expansion	NOUN
cana-4165	248	9	,	,	PUNCT
cana-4165	248	10	figure	figure	NOUN
cana-4165	248	11	2	2	NUM
cana-4165	248	12	shows	show	VERB
cana-4165	248	13	the	the	DET
cana-4165	248	14	measured	measured	ADJ
cana-4165	248	15	velocity	velocity	NOUN
cana-4165	248	16	-	-	PUNCT
cana-4165	248	17	field	field	NOUN
cana-4165	248	18	characteristics	characteristic	NOUN
cana-4165	248	19	for	for	ADP
cana-4165	248	20	n	n	CCONJ
cana-4165	248	21	-	-	PUNCT
cana-4165	248	22	type	type	NOUN
cana-4165	248	23	silicon	silicon	NOUN
cana-4165	248	24	at	at	ADP
cana-4165	248	25	various	various	ADJ
cana-4165	248	26	temperatures	temperature	NOUN
cana-4165	248	27	.	.	PUNCT
cana-4165	249	1	figure	figure	VERB
cana-4165	249	2	2	2	NUM
cana-4165	249	3	:	:	PUNCT
cana-4165	249	4	velocity	velocity	NOUN
cana-4165	249	5	-	-	PUNCT
cana-4165	249	6	field	field	NOUN
cana-4165	249	7	characteristics	characteristic	NOUN
cana-4165	249	8	of	of	ADP
cana-4165	249	9	n	n	CCONJ
cana-4165	249	10	-	-	PUNCT
cana-4165	249	11	type	type	NOUN
cana-4165	249	12	silicon	silicon	NOUN
cana-4165	249	13	the	the	DET
cana-4165	249	14	observed	observe	VERB
cana-4165	249	15	data	datum	NOUN
cana-4165	249	16	show	show	VERB
cana-4165	249	17	several	several	ADJ
cana-4165	249	18	interesting	interesting	ADJ
cana-4165	249	19	properties	property	NOUN
cana-4165	249	20	:	:	PUNCT
cana-4165	249	21	a	a	DET
cana-4165	249	22	linear	linear	ADJ
cana-4165	249	23	regime	regime	NOUN
cana-4165	249	24	at	at	ADP
cana-4165	249	25	low	low	ADJ
cana-4165	249	26	fields	field	NOUN
cana-4165	249	27	,	,	PUNCT
cana-4165	249	28	then	then	ADV
cana-4165	249	29	sublinear	sublinear	VERB
cana-4165	249	30	behavior	behavior	NOUN
cana-4165	249	31	and	and	CCONJ
cana-4165	249	32	finally	finally	ADV
cana-4165	249	33	saturation	saturation	NOUN
cana-4165	249	34	at	at	ADP
cana-4165	249	35	high	high	ADJ
cana-4165	249	36	fields	field	NOUN
cana-4165	249	37	.	.	PUNCT
cana-4165	250	1	by	by	ADP
cana-4165	250	2	means	mean	NOUN
cana-4165	250	3	of	of	ADP
cana-4165	250	4	the	the	DET
cana-4165	250	5	formula	formula	NOUN
cana-4165	250	6	,	,	PUNCT
cana-4165	250	7	our	our	PRON
cana-4165	250	8	asymptotic	asymptotic	ADJ
cana-4165	250	9	expansion	expansion	NOUN
cana-4165	250	10	precisely	precisely	ADV
cana-4165	250	11	reflects	reflect	VERB
cana-4165	250	12	this	this	DET
cana-4165	250	13	behavior	behavior	NOUN
cana-4165	250	14	:	:	PUNCT
cana-4165	250	15	v(e	v(e	NUM
cana-4165	250	16	)	)	PUNCT
cana-4165	250	17	=	=	PUNCT
cana-4165	251	1	μ₀e	μ₀e	NUM
cana-4165	251	2	/	/	PUNCT
cana-4165	252	1	[	[	X
cana-4165	252	2	1	1	NUM
cana-4165	252	3	+	+	CCONJ
cana-4165	252	4	(	(	PUNCT
cana-4165	252	5	e	e	NOUN
cana-4165	252	6	/	/	SYM
cana-4165	252	7	ec)^α]^(1	ec)^α]^(1	NOUN
cana-4165	252	8	/	/	SYM
cana-4165	252	9	β	β	NOUN
cana-4165	252	10	)	)	PUNCT
cana-4165	252	11	μ₀	μ₀	NOUN
cana-4165	252	12	is	be	AUX
cana-4165	252	13	the	the	DET
cana-4165	252	14	low	low	ADJ
cana-4165	252	15	-	-	PUNCT
cana-4165	252	16	field	field	NOUN
cana-4165	252	17	mobility	mobility	NOUN
cana-4165	252	18	;	;	PUNCT
cana-4165	252	19	ec	ec	PROPN
cana-4165	252	20	marks	mark	VERB
cana-4165	252	21	the	the	DET
cana-4165	252	22	beginning	beginning	NOUN
cana-4165	252	23	of	of	ADP
cana-4165	252	24	nonlinear	nonlinear	ADJ
cana-4165	252	25	behavior	behavior	NOUN
cana-4165	252	26	;	;	PUNCT
cana-4165	252	27	α	α	PROPN
cana-4165	252	28	and	and	CCONJ
cana-4165	252	29	β	β	PROPN
cana-4165	252	30	are	be	AUX
cana-4165	252	31	parameters	parameter	NOUN
cana-4165	252	32	regulating	regulate	VERB
cana-4165	252	33	the	the	DET
cana-4165	252	34	sharpness	sharpness	NOUN
cana-4165	252	35	of	of	ADP
cana-4165	252	36	the	the	DET
cana-4165	252	37	transition	transition	NOUN
cana-4165	252	38	and	and	CCONJ
cana-4165	252	39	the	the	DET
cana-4165	252	40	high	high	ADJ
cana-4165	252	41	-	-	PUNCT
cana-4165	252	42	field	field	NOUN
cana-4165	252	43	asymptotic	asymptotic	ADJ
cana-4165	252	44	behavior	behavior	NOUN
cana-4165	252	45	correspondingly	correspondingly	ADV
cana-4165	252	46	.	.	PUNCT
cana-4165	253	1	table	table	NOUN
cana-4165	253	2	2	2	NUM
cana-4165	253	3	shows	show	VERB
cana-4165	253	4	the	the	DET
cana-4165	253	5	fitted	fit	VERB
cana-4165	253	6	silicon	silicon	NOUN
cana-4165	253	7	properties	property	NOUN
cana-4165	253	8	at	at	ADP
cana-4165	253	9	many	many	ADJ
cana-4165	253	10	temperatures	temperature	NOUN
cana-4165	253	11	.	.	PUNCT
cana-4165	254	1	following	follow	VERB
cana-4165	254	2	almost	almost	ADV
cana-4165	254	3	a	a	DET
cana-4165	254	4	t^(-2.4	t^(-2.4	NOUN
cana-4165	254	5	)	)	PUNCT
cana-4165	254	6	dependency	dependency	NOUN
cana-4165	254	7	,	,	PUNCT
cana-4165	254	8	the	the	DET
cana-4165	254	9	low	low	ADJ
cana-4165	254	10	-	-	PUNCT
cana-4165	254	11	field	field	NOUN
cana-4165	254	12	mobility	mobility	NOUN
cana-4165	254	13	shows	show	VERB
cana-4165	254	14	the	the	DET
cana-4165	254	15	predicted	predict	VERB
cana-4165	254	16	reduction	reduction	NOUN
cana-4165	254	17	with	with	ADP
cana-4165	254	18	increasing	increase	VERB
cana-4165	254	19	temperature	temperature	NOUN
cana-4165	254	20	,	,	PUNCT
cana-4165	254	21	compatible	compatible	ADJ
cana-4165	254	22	with	with	ADP
cana-4165	254	23	phonon	phonon	NOUN
cana-4165	254	24	scattering	scatter	VERB
cana-4165	254	25	as	as	ADP
cana-4165	254	26	the	the	DET
cana-4165	254	27	main	main	ADJ
cana-4165	254	28	cause	cause	NOUN
cana-4165	254	29	.	.	PUNCT
cana-4165	255	1	reflecting	reflect	VERB
cana-4165	255	2	the	the	DET
cana-4165	255	3	increased	increase	VERB
cana-4165	255	4	energy	energy	NOUN
cana-4165	255	5	needed	need	VERB
cana-4165	255	6	for	for	ADP
cana-4165	255	7	major	major	ADJ
cana-4165	255	8	optical	optical	ADJ
cana-4165	255	9	phonon	phonon	NOUN
cana-4165	255	10	emission	emission	NOUN
cana-4165	255	11	at	at	ADP
cana-4165	255	12	increasing	increase	VERB
cana-4165	255	13	temperatures	temperature	NOUN
cana-4165	255	14	,	,	PUNCT
cana-4165	255	15	the	the	DET
cana-4165	255	16	critical	critical	ADJ
cana-4165	255	17	field	field	NOUN
cana-4165	255	18	rises	rise	VERB
cana-4165	255	19	with	with	ADP
cana-4165	255	20	temperature	temperature	NOUN
cana-4165	255	21	.	.	PUNCT
cana-4165	256	1	table	table	NOUN
cana-4165	256	2	2	2	NUM
cana-4165	256	3	:	:	PUNCT
cana-4165	256	4	fitted	fit	VERB
cana-4165	256	5	parameters	parameter	NOUN
cana-4165	256	6	for	for	ADP
cana-4165	256	7	n	n	CCONJ
cana-4165	256	8	-	-	PUNCT
cana-4165	256	9	type	type	NOUN
cana-4165	256	10	silicon	silicon	NOUN
cana-4165	256	11	temperature	temperature	NOUN
cana-4165	256	12	(	(	PUNCT
cana-4165	256	13	k	k	NOUN
cana-4165	256	14	)	)	PUNCT
cana-4165	256	15	μ₀	μ₀	NOUN
cana-4165	256	16	(	(	PUNCT
cana-4165	256	17	cm²/vs	cm²/vs	NOUN
cana-4165	256	18	)	)	PUNCT
cana-4165	256	19	ec	ec	PROPN
cana-4165	256	20	(	(	PUNCT
cana-4165	256	21	kv	kv	PROPN
cana-4165	256	22	/	/	SYM
cana-4165	256	23	cm	cm	NOUN
cana-4165	256	24	)	)	PUNCT
cana-4165	257	1	α	α	PROPN
cana-4165	257	2	β	β	X
cana-4165	257	3	vsat	vsat	NOUN
cana-4165	257	4	(	(	PUNCT
cana-4165	257	5	10⁷	10⁷	NUM
cana-4165	257	6	cm	cm	NOUN
cana-4165	257	7	/	/	SYM
cana-4165	257	8	s	s	PROPN
cana-4165	257	9	)	)	PUNCT
cana-4165	257	10	77	77	NUM
cana-4165	257	11	24,300	24,300	NUM
cana-4165	257	12	2.1	2.1	NUM
cana-4165	257	13	1.92	1.92	NUM
cana-4165	257	14	1.85	1.85	NUM
cana-4165	257	15	1.02	1.02	NUM
cana-4165	257	16	150	150	NUM
cana-4165	257	17	8,650	8,650	NUM
cana-4165	257	18	3.8	3.8	NUM
cana-4165	257	19	1.88	1.88	NUM
cana-4165	257	20	1.82	1.82	NUM
cana-4165	257	21	0.97	0.97	NUM
cana-4165	257	22	300	300	NUM
cana-4165	257	23	1,450	1,450	NUM
cana-4165	257	24	6.5	6.5	NUM
cana-4165	257	25	1.75	1.75	NUM
cana-4165	257	26	1.76	1.76	NUM
cana-4165	257	27	0.92	0.92	NUM
cana-4165	257	28	400	400	NUM
cana-4165	257	29	850	850	NUM
cana-4165	257	30	8.2	8.2	NUM
cana-4165	257	31	1.71	1.71	NUM
cana-4165	257	32	1.72	1.72	NUM
cana-4165	257	33	0.89	0.89	NUM
cana-4165	257	34	communications	communication	NOUN
cana-4165	257	35	on	on	ADP
cana-4165	257	36	applied	apply	VERB
cana-4165	257	37	nonlinear	nonlinear	ADJ
cana-4165	257	38	analysis	analysis	NOUN
cana-4165	257	39	issn	issn	NOUN
cana-4165	257	40	:	:	PUNCT
cana-4165	257	41	1074	1074	NUM
cana-4165	257	42	-	-	PUNCT
cana-4165	257	43	133x	133x	NUM
cana-4165	257	44	vol	vol	NOUN
cana-4165	257	45	32	32	NUM
cana-4165	257	46	no	no	NOUN
cana-4165	257	47	.	.	PUNCT
cana-4165	258	1	9s	9s	NUM
cana-4165	258	2	(	(	PUNCT
cana-4165	258	3	2025	2025	NUM
cana-4165	258	4	)	)	PUNCT
cana-4165	258	5	1401	1401	NUM
cana-4165	259	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	259	2	similar	similar	ADJ
cana-4165	259	3	experiments	experiment	NOUN
cana-4165	259	4	for	for	ADP
cana-4165	259	5	gallium	gallium	NOUN
cana-4165	259	6	arsenicide	arsenicide	NOUN
cana-4165	259	7	expose	expose	VERB
cana-4165	259	8	different	different	ADJ
cana-4165	259	9	transport	transport	NOUN
cana-4165	259	10	properties	property	NOUN
cana-4165	259	11	because	because	SCONJ
cana-4165	259	12	of	of	ADP
cana-4165	259	13	the	the	DET
cana-4165	259	14	differing	differ	VERB
cana-4165	259	15	band	band	NOUN
cana-4165	259	16	structure	structure	NOUN
cana-4165	259	17	.	.	PUNCT
cana-4165	260	1	the	the	DET
cana-4165	260	2	velocity	velocity	NOUN
cana-4165	260	3	-	-	PUNCT
cana-4165	260	4	field	field	NOUN
cana-4165	260	5	relationship	relationship	NOUN
cana-4165	260	6	for	for	ADP
cana-4165	260	7	n	n	CCONJ
cana-4165	260	8	-	-	PUNCT
cana-4165	260	9	type	type	NOUN
cana-4165	260	10	gaas	gaas	NOUN
cana-4165	260	11	,	,	PUNCT
cana-4165	260	12	stressing	stress	VERB
cana-4165	260	13	the	the	DET
cana-4165	260	14	somewhat	somewhat	ADV
cana-4165	260	15	negative	negative	ADJ
cana-4165	260	16	differential	differential	ADJ
cana-4165	260	17	mobility	mobility	NOUN
cana-4165	260	18	at	at	ADP
cana-4165	260	19	high	high	ADJ
cana-4165	260	20	fields	field	NOUN
cana-4165	260	21	resulting	result	VERB
cana-4165	260	22	from	from	ADP
cana-4165	260	23	intervalley	intervalley	NOUN
cana-4165	260	24	transfer	transfer	NOUN
cana-4165	260	25	.	.	PUNCT
cana-4165	261	1	the	the	DET
cana-4165	261	2	standard	standard	ADJ
cana-4165	261	3	asymptotic	asymptotic	ADJ
cana-4165	261	4	expansion	expansion	NOUN
cana-4165	261	5	requires	require	VERB
cana-4165	261	6	modification	modification	NOUN
cana-4165	261	7	to	to	PART
cana-4165	261	8	account	account	VERB
cana-4165	261	9	for	for	ADP
cana-4165	261	10	this	this	DET
cana-4165	261	11	behavior	behavior	NOUN
cana-4165	261	12	.	.	PUNCT
cana-4165	262	1	we	we	PRON
cana-4165	262	2	incorporate	incorporate	VERB
cana-4165	262	3	an	an	DET
cana-4165	262	4	additional	additional	ADJ
cana-4165	262	5	term	term	NOUN
cana-4165	262	6	representing	represent	VERB
cana-4165	262	7	the	the	DET
cana-4165	262	8	high	high	ADJ
cana-4165	262	9	-	-	PUNCT
cana-4165	262	10	field	field	NOUN
cana-4165	262	11	decrease	decrease	NOUN
cana-4165	262	12	:	:	PUNCT
cana-4165	262	13	v(e	v(e	NUM
cana-4165	262	14	)	)	PUNCT
cana-4165	262	15	=	=	PRON
cana-4165	263	1	(	(	PUNCT
cana-4165	263	2	μ₀e	μ₀e	NUM
cana-4165	263	3	/	/	SYM
cana-4165	264	1	[	[	X
cana-4165	264	2	1	1	NUM
cana-4165	264	3	+	+	CCONJ
cana-4165	264	4	(	(	PUNCT
cana-4165	264	5	e	e	NOUN
cana-4165	264	6	/	/	SYM
cana-4165	264	7	ec₁)^α]^(1	ec₁)^α]^(1	NOUN
cana-4165	264	8	/	/	SYM
cana-4165	264	9	β	β	NOUN
cana-4165	264	10	)	)	PUNCT
cana-4165	264	11	)	)	PUNCT
cana-4165	264	12	·	·	PUNCT
cana-4165	265	1	[	[	X
cana-4165	265	2	1	1	NUM
cana-4165	265	3	γ(1	γ(1	PROPN
cana-4165	265	4	exp(-(e	exp(-(e	PROPN
cana-4165	265	5	-	-	PUNCT
cana-4165	265	6	et)/e₀	et)/e₀	NOUN
cana-4165	265	7	)	)	PUNCT
cana-4165	265	8	)	)	PUNCT
cana-4165	265	9	]	]	PUNCT
cana-4165	265	10	et	et	NOUN
cana-4165	265	11	shows	show	VERB
cana-4165	265	12	the	the	DET
cana-4165	265	13	threshold	threshold	NOUN
cana-4165	265	14	field	field	NOUN
cana-4165	265	15	for	for	ADP
cana-4165	265	16	intervalley	intervalley	NOUN
cana-4165	265	17	transfer	transfer	NOUN
cana-4165	265	18	;	;	PUNCT
cana-4165	265	19	γ	γ	X
cana-4165	265	20	and	and	CCONJ
cana-4165	265	21	e₀	e₀	ADJ
cana-4165	265	22	respectively	respectively	ADV
cana-4165	265	23	govern	govern	VERB
cana-4165	265	24	the	the	DET
cana-4165	265	25	amount	amount	NOUN
cana-4165	265	26	and	and	CCONJ
cana-4165	265	27	sharpness	sharpness	NOUN
cana-4165	265	28	of	of	ADP
cana-4165	265	29	the	the	DET
cana-4165	265	30	high	high	ADJ
cana-4165	265	31	-	-	PUNCT
cana-4165	265	32	field	field	NOUN
cana-4165	265	33	decline	decline	NOUN
cana-4165	265	34	.	.	PUNCT
cana-4165	266	1	consistent	consistent	ADJ
cana-4165	266	2	with	with	ADP
cana-4165	266	3	the	the	DET
cana-4165	266	4	reduced	reduce	VERB
cana-4165	266	5	effective	effective	ADJ
cana-4165	266	6	mass	mass	NOUN
cana-4165	266	7	in	in	ADP
cana-4165	266	8	the	the	DET
cana-4165	266	9	γ	γ	PROPN
cana-4165	266	10	valley	valley	NOUN
cana-4165	266	11	,	,	PUNCT
cana-4165	266	12	the	the	DET
cana-4165	266	13	fitted	fit	VERB
cana-4165	266	14	parameters	parameter	NOUN
cana-4165	266	15	for	for	ADP
cana-4165	266	16	gaas	gaas	PROPN
cana-4165	266	17	(	(	PUNCT
cana-4165	266	18	table	table	NOUN
cana-4165	266	19	3	3	NUM
cana-4165	266	20	)	)	PUNCT
cana-4165	266	21	expose	expose	VERB
cana-4165	266	22	notably	notably	ADV
cana-4165	266	23	better	well	ADJ
cana-4165	266	24	low	low	ADJ
cana-4165	266	25	-	-	PUNCT
cana-4165	266	26	field	field	NOUN
cana-4165	266	27	mobility	mobility	NOUN
cana-4165	266	28	than	than	ADP
cana-4165	266	29	those	those	PRON
cana-4165	266	30	for	for	ADP
cana-4165	266	31	silicon	silicon	NOUN
cana-4165	266	32	.	.	PUNCT
cana-4165	267	1	the	the	DET
cana-4165	267	2	altered	alter	VERB
cana-4165	267	3	phonon	phonon	NOUN
cana-4165	267	4	spectrum	spectrum	NOUN
cana-4165	267	5	causes	cause	VERB
cana-4165	267	6	mobility	mobility	NOUN
cana-4165	267	7	to	to	PART
cana-4165	267	8	follow	follow	VERB
cana-4165	267	9	about	about	ADP
cana-4165	267	10	a	a	DET
cana-4165	267	11	t^(-2.2	t^(-2.2	NOUN
cana-4165	267	12	)	)	PUNCT
cana-4165	267	13	curve	curve	NOUN
cana-4165	267	14	,	,	PUNCT
cana-4165	267	15	somewhat	somewhat	ADV
cana-4165	267	16	less	less	ADJ
cana-4165	267	17	than	than	ADP
cana-4165	267	18	in	in	ADP
cana-4165	267	19	silicon	silicon	NOUN
cana-4165	267	20	.	.	PUNCT
cana-4165	268	1	table	table	NOUN
cana-4165	268	2	3	3	NUM
cana-4165	268	3	:	:	PUNCT
cana-4165	268	4	fitted	fit	VERB
cana-4165	268	5	parameters	parameter	NOUN
cana-4165	268	6	for	for	ADP
cana-4165	268	7	n	n	CCONJ
cana-4165	268	8	-	-	PUNCT
cana-4165	268	9	type	type	NOUN
cana-4165	268	10	gallium	gallium	NOUN
cana-4165	268	11	arsenide	arsenide	NOUN
cana-4165	268	12	(	(	PUNCT
cana-4165	268	13	continued	continued	ADJ
cana-4165	268	14	)	)	PUNCT
cana-4165	268	15	temperature	temperature	NOUN
cana-4165	268	16	(	(	PUNCT
cana-4165	268	17	k	k	NOUN
cana-4165	268	18	)	)	PUNCT
cana-4165	268	19	μ₀	μ₀	NOUN
cana-4165	268	20	(	(	PUNCT
cana-4165	268	21	cm²/vs	cm²/vs	NOUN
cana-4165	268	22	)	)	PUNCT
cana-4165	268	23	ec₁	ec₁	NOUN
cana-4165	268	24	(	(	PUNCT
cana-4165	268	25	kv	kv	PROPN
cana-4165	268	26	/	/	SYM
cana-4165	268	27	cm	cm	NOUN
cana-4165	268	28	)	)	PUNCT
cana-4165	269	1	α	α	X
cana-4165	269	2	β	β	X
cana-4165	269	3	et	et	PROPN
cana-4165	269	4	(	(	PUNCT
cana-4165	269	5	kv	kv	PROPN
cana-4165	269	6	/	/	SYM
cana-4165	269	7	cm	cm	NOUN
cana-4165	269	8	)	)	PUNCT
cana-4165	269	9	γ	γ	PROPN
cana-4165	269	10	e₀	e₀	NOUN
cana-4165	269	11	(	(	PUNCT
cana-4165	269	12	kv	kv	PROPN
cana-4165	269	13	/	/	SYM
cana-4165	269	14	cm	cm	NOUN
cana-4165	269	15	)	)	PUNCT
cana-4165	269	16	77	77	NUM
cana-4165	269	17	145,000	145,000	NUM
cana-4165	269	18	0.8	0.8	NUM
cana-4165	269	19	1.95	1.95	NUM
cana-4165	269	20	1.90	1.90	NUM
cana-4165	269	21	3.2	3.2	NUM
cana-4165	269	22	0.35	0.35	NUM
cana-4165	269	23	1.2	1.2	NUM
cana-4165	269	24	200	200	NUM
cana-4165	269	25	12,000	12,000	NUM
cana-4165	269	26	1.5	1.5	NUM
cana-4165	269	27	1.85	1.85	NUM
cana-4165	269	28	1.86	1.86	NUM
cana-4165	269	29	3.5	3.5	NUM
cana-4165	269	30	0.32	0.32	NUM
cana-4165	269	31	1.4	1.4	NUM
cana-4165	269	32	300	300	NUM
cana-4165	269	33	8,500	8,500	NUM
cana-4165	269	34	2.2	2.2	NUM
cana-4165	269	35	1.78	1.78	NUM
cana-4165	269	36	1.82	1.82	NUM
cana-4165	269	37	3.8	3.8	NUM
cana-4165	269	38	0.30	0.30	NUM
cana-4165	269	39	1.5	1.5	NUM
cana-4165	269	40	for	for	ADP
cana-4165	269	41	verifying	verify	VERB
cana-4165	269	42	our	our	PRON
cana-4165	269	43	asymptotic	asymptotic	ADJ
cana-4165	269	44	expansion	expansion	NOUN
cana-4165	269	45	,	,	PUNCT
cana-4165	269	46	the	the	DET
cana-4165	269	47	behavior	behavior	NOUN
cana-4165	269	48	at	at	ADP
cana-4165	269	49	intermediate	intermediate	ADJ
cana-4165	269	50	fields	field	NOUN
cana-4165	269	51	is	be	AUX
cana-4165	269	52	quite	quite	ADV
cana-4165	269	53	instructive	instructive	ADJ
cana-4165	269	54	.	.	PUNCT
cana-4165	270	1	plotting	plot	VERB
cana-4165	270	2	the	the	DET
cana-4165	270	3	divergence	divergence	NOUN
cana-4165	270	4	from	from	ADP
cana-4165	270	5	linearity	linearity	NOUN
cana-4165	270	6	as	as	ADP
cana-4165	270	7	(	(	PUNCT
cana-4165	270	8	v	v	NOUN
cana-4165	270	9	/	/	SYM
cana-4165	270	10	e)/μ₀	e)/μ₀	NOUN
cana-4165	270	11	against	against	ADP
cana-4165	270	12	e	e	NOUN
cana-4165	270	13	,	,	PUNCT
cana-4165	270	14	for	for	ADP
cana-4165	270	15	both	both	CCONJ
cana-4165	270	16	silicon	silicon	NOUN
cana-4165	270	17	and	and	CCONJ
cana-4165	270	18	gallium	gallium	NOUN
cana-4165	270	19	arsenicide	arsenicide	NOUN
cana-4165	270	20	at	at	ADP
cana-4165	270	21	300k	300k	PROPN
cana-4165	270	22	.	.	PUNCT
cana-4165	271	1	this	this	DET
cana-4165	271	2	depiction	depiction	NOUN
cana-4165	271	3	emphasizes	emphasize	VERB
cana-4165	271	4	how	how	SCONJ
cana-4165	271	5	different	different	ADJ
cana-4165	271	6	our	our	PRON
cana-4165	271	7	growth	growth	NOUN
cana-4165	271	8	in	in	ADP
cana-4165	271	9	the	the	DET
cana-4165	271	10	transition	transition	NOUN
cana-4165	271	11	zone	zone	NOUN
cana-4165	271	12	is	be	AUX
cana-4165	271	13	from	from	ADP
cana-4165	271	14	ohm	ohm	NOUN
cana-4165	271	15	's	's	PART
cana-4165	271	16	law	law	NOUN
cana-4165	271	17	and	and	CCONJ
cana-4165	271	18	offers	offer	VERB
cana-4165	271	19	a	a	DET
cana-4165	271	20	strict	strict	ADJ
cana-4165	271	21	test	test	NOUN
cana-4165	271	22	of	of	ADP
cana-4165	271	23	it	it	PRON
cana-4165	271	24	.	.	PUNCT
cana-4165	272	1	the	the	DET
cana-4165	272	2	results	result	NOUN
cana-4165	272	3	quite	quite	ADV
cana-4165	272	4	closely	closely	ADV
cana-4165	272	5	match	match	VERB
cana-4165	272	6	our	our	PRON
cana-4165	272	7	expected	expect	VERB
cana-4165	272	8	curves	curve	NOUN
cana-4165	272	9	,	,	PUNCT
cana-4165	272	10	so	so	ADV
cana-4165	272	11	validating	validate	VERB
cana-4165	272	12	our	our	PRON
cana-4165	272	13	method	method	NOUN
cana-4165	272	14	.	.	PUNCT
cana-4165	273	1	with	with	ADP
cana-4165	273	2	an	an	DET
cana-4165	273	3	exponent	exponent	NOUN
cana-4165	273	4	connected	connect	VERB
cana-4165	273	5	to	to	ADP
cana-4165	273	6	the	the	DET
cana-4165	273	7	parameter	parameter	NOUN
cana-4165	273	8	α	α	PROPN
cana-4165	273	9	in	in	ADP
cana-4165	273	10	our	our	PRON
cana-4165	273	11	expansion	expansion	NOUN
cana-4165	273	12	,	,	PUNCT
cana-4165	273	13	the	the	DET
cana-4165	273	14	log	log	NOUN
cana-4165	273	15	-	-	PUNCT
cana-4165	273	16	log	log	NOUN
cana-4165	273	17	plot	plot	NOUN
cana-4165	273	18	exposes	expose	VERB
cana-4165	273	19	power	power	NOUN
cana-4165	273	20	-	-	PUNCT
cana-4165	273	21	law	law	NOUN
cana-4165	273	22	behavior	behavior	NOUN
cana-4165	273	23	in	in	ADP
cana-4165	273	24	this	this	DET
cana-4165	273	25	transition	transition	NOUN
cana-4165	273	26	zone	zone	NOUN
cana-4165	273	27	.	.	PUNCT
cana-4165	274	1	two	two	NUM
cana-4165	274	2	-	-	PUNCT
cana-4165	274	3	dimensional	dimensional	ADJ
cana-4165	274	4	electron	electron	NOUN
cana-4165	274	5	gas	gas	NOUN
cana-4165	274	6	:	:	PUNCT
cana-4165	274	7	gaas	gaas	NOUN
cana-4165	274	8	/	/	SYM
cana-4165	274	9	algaas	algaas	PROPN
cana-4165	274	10	heterostructures	heterostructure	NOUN
cana-4165	274	11	one	one	NUM
cana-4165	274	12	dimension	dimension	NOUN
cana-4165	274	13	of	of	ADP
cana-4165	274	14	quantum	quantum	ADJ
cana-4165	274	15	confinement	confinement	NOUN
cana-4165	274	16	generates	generate	VERB
cana-4165	274	17	a	a	DET
cana-4165	274	18	two	two	NUM
cana-4165	274	19	-	-	PUNCT
cana-4165	274	20	dimensional	dimensional	ADJ
cana-4165	274	21	electron	electron	NOUN
cana-4165	274	22	gas	gas	NOUN
cana-4165	274	23	(	(	PUNCT
cana-4165	274	24	2deg	2deg	NUM
cana-4165	274	25	)	)	PUNCT
cana-4165	274	26	with	with	ADP
cana-4165	274	27	changed	change	VERB
cana-4165	274	28	transport	transport	NOUN
cana-4165	274	29	characteristics	characteristic	NOUN
cana-4165	274	30	.	.	PUNCT
cana-4165	275	1	we	we	PRON
cana-4165	275	2	investigated	investigate	VERB
cana-4165	275	3	high	high	ADJ
cana-4165	275	4	-	-	PUNCT
cana-4165	275	5	mobility	mobility	NOUN
cana-4165	275	6	gaas	gaas	NOUN
cana-4165	275	7	/	/	SYM
cana-4165	275	8	algaas	algaas	NOUN
cana-4165	275	9	heterostructures	heterostructure	NOUN
cana-4165	275	10	with	with	ADP
cana-4165	275	11	carrier	carrier	NOUN
cana-4165	275	12	densities	density	NOUN
cana-4165	275	13	spanning	span	VERB
cana-4165	275	14	1	1	NUM
cana-4165	275	15	x	x	SYM
cana-4165	275	16	10¹¹	10¹¹	NUM
cana-4165	275	17	to	to	ADP
cana-4165	275	18	5	5	NUM
cana-4165	275	19	x	x	SYM
cana-4165	275	20	10¹⁻	10¹⁻	NUM
cana-4165	275	21	�	�	PROPN
cana-4165	275	22	cm⁻	cm⁻	PROPN
cana-4165	275	23	�	�	PROPN
cana-4165	275	24	.	.	PUNCT
cana-4165	276	1	particularly	particularly	ADV
cana-4165	276	2	at	at	ADP
cana-4165	276	3	cryogenic	cryogenic	ADJ
cana-4165	276	4	temperatures	temperature	NOUN
cana-4165	276	5	when	when	SCONJ
cana-4165	276	6	values	value	NOUN
cana-4165	276	7	above	above	ADP
cana-4165	276	8	10⁶	10⁶	NUM
cana-4165	276	9	cm²/vs	cm²/vs	NOUN
cana-4165	276	10	were	be	AUX
cana-4165	276	11	found	find	VERB
cana-4165	276	12	,	,	PUNCT
cana-4165	276	13	the	the	DET
cana-4165	276	14	2deg	2deg	NUM
cana-4165	276	15	shows	show	VERB
cana-4165	276	16	astonishingly	astonishingly	ADV
cana-4165	276	17	great	great	ADJ
cana-4165	276	18	low	low	ADJ
cana-4165	276	19	-	-	PUNCT
cana-4165	276	20	field	field	NOUN
cana-4165	276	21	mobility	mobility	NOUN
cana-4165	276	22	.	.	PUNCT
cana-4165	277	1	for	for	ADP
cana-4165	277	2	2d	2d	PROPN
cana-4165	277	3	systems	system	NOUN
cana-4165	277	4	,	,	PUNCT
cana-4165	277	5	our	our	PRON
cana-4165	277	6	asymptotic	asymptotic	ADJ
cana-4165	277	7	expansion	expansion	NOUN
cana-4165	277	8	consists	consist	VERB
cana-4165	277	9	in	in	ADP
cana-4165	277	10	:	:	PUNCT
cana-4165	277	11	v(e	v(e	NUM
cana-4165	277	12	)	)	PUNCT
cana-4165	277	13	=	=	PUNCT
cana-4165	278	1	μ₀e	μ₀e	NUM
cana-4165	278	2	/	/	PUNCT
cana-4165	279	1	[	[	X
cana-4165	279	2	1	1	NUM
cana-4165	279	3	+	+	NUM
cana-4165	279	4	(	(	PUNCT
cana-4165	279	5	(	(	PUNCT
cana-4165	279	6	μ₀e)/(vsat))^β]^(1	μ₀e)/(vsat))^β]^(1	X
cana-4165	279	7	/	/	SYM
cana-4165	279	8	β	β	NOUN
cana-4165	279	9	)	)	PUNCT
cana-4165	279	10	with	with	ADP
cana-4165	279	11	less	less	ADJ
cana-4165	279	12	variables	variable	NOUN
cana-4165	279	13	than	than	ADP
cana-4165	279	14	the	the	DET
cana-4165	279	15	general	general	ADJ
cana-4165	279	16	case	case	NOUN
cana-4165	279	17	,	,	PUNCT
cana-4165	279	18	this	this	DET
cana-4165	279	19	reduced	reduce	VERB
cana-4165	279	20	form	form	NOUN
cana-4165	279	21	sufficiently	sufficiently	ADV
cana-4165	279	22	explains	explain	VERB
cana-4165	279	23	the	the	DET
cana-4165	279	24	2deg	2deg	NUM
cana-4165	279	25	behavior	behavior	NOUN
cana-4165	279	26	.	.	PUNCT
cana-4165	280	1	the	the	DET
cana-4165	280	2	critical	critical	ADJ
cana-4165	280	3	field	field	NOUN
cana-4165	280	4	can	can	AUX
cana-4165	280	5	be	be	AUX
cana-4165	280	6	obtained	obtain	VERB
cana-4165	280	7	as	as	ADP
cana-4165	280	8	ec	ec	PROPN
cana-4165	280	9	=	=	SYM
cana-4165	280	10	vsat	vsat	PROPN
cana-4165	280	11	/	/	SYM
cana-4165	280	12	μ₀	μ₀	PROPN
cana-4165	280	13	rather	rather	ADV
cana-4165	280	14	than	than	ADP
cana-4165	280	15	explicitly	explicitly	ADV
cana-4165	280	16	.	.	PUNCT
cana-4165	281	1	communications	communication	NOUN
cana-4165	281	2	on	on	ADP
cana-4165	281	3	applied	apply	VERB
cana-4165	281	4	nonlinear	nonlinear	ADJ
cana-4165	281	5	analysis	analysis	NOUN
cana-4165	281	6	issn	issn	NOUN
cana-4165	281	7	:	:	PUNCT
cana-4165	281	8	1074	1074	NUM
cana-4165	281	9	-	-	PUNCT
cana-4165	281	10	133x	133x	NUM
cana-4165	281	11	vol	vol	NOUN
cana-4165	281	12	32	32	NUM
cana-4165	281	13	no	no	NOUN
cana-4165	281	14	.	.	PUNCT
cana-4165	282	1	9s	9s	NUM
cana-4165	282	2	(	(	PUNCT
cana-4165	282	3	2025	2025	NUM
cana-4165	282	4	)	)	PUNCT
cana-4165	282	5	1402	1402	NUM
cana-4165	282	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	282	7	table	table	NOUN
cana-4165	282	8	4	4	NUM
cana-4165	282	9	shows	show	VERB
cana-4165	282	10	the	the	DET
cana-4165	282	11	2deg	2deg	NUM
cana-4165	282	12	fitted	fit	VERB
cana-4165	282	13	parameters	parameter	NOUN
cana-4165	282	14	at	at	ADP
cana-4165	282	15	several	several	ADJ
cana-4165	282	16	temperatures	temperature	NOUN
cana-4165	282	17	and	and	CCONJ
cana-4165	282	18	carrier	carrier	NOUN
cana-4165	282	19	densities	density	NOUN
cana-4165	282	20	.	.	PUNCT
cana-4165	283	1	characteristic	characteristic	ADJ
cana-4165	283	2	of	of	ADP
cana-4165	283	3	remote	remote	ADJ
cana-4165	283	4	ionized	ionized	ADJ
cana-4165	283	5	impurity	impurity	NOUN
cana-4165	283	6	scattering	scattering	NOUN
cana-4165	283	7	,	,	PUNCT
cana-4165	283	8	the	the	DET
cana-4165	283	9	temperature	temperature	NOUN
cana-4165	283	10	dependence	dependence	NOUN
cana-4165	283	11	of	of	ADP
cana-4165	283	12	mobility	mobility	NOUN
cana-4165	283	13	reveals	reveal	VERB
cana-4165	283	14	a	a	DET
cana-4165	283	15	change	change	NOUN
cana-4165	283	16	from	from	ADP
cana-4165	283	17	t⁻¹	t⁻¹	DET
cana-4165	283	18	behavior	behavior	NOUN
cana-4165	283	19	at	at	ADP
cana-4165	283	20	low	low	ADJ
cana-4165	283	21	temperatures	temperature	NOUN
cana-4165	283	22	,	,	PUNCT
cana-4165	283	23	to	to	ADP
cana-4165	283	24	t⁻	t⁻	PROPN
cana-4165	283	25	�	�	NOUN
cana-4165	283	26	·⁵	·⁵	PROPN
cana-4165	283	27	at	at	ADP
cana-4165	283	28	higher	high	ADJ
cana-4165	283	29	temperatures	temperature	NOUN
cana-4165	283	30	when	when	SCONJ
cana-4165	283	31	phonon	phonon	NOUN
cana-4165	283	32	scattering	scatter	VERB
cana-4165	283	33	dominates	dominate	VERB
cana-4165	283	34	.	.	PUNCT
cana-4165	284	1	table	table	NOUN
cana-4165	284	2	4	4	NUM
cana-4165	284	3	:	:	PUNCT
cana-4165	284	4	fitted	fit	VERB
cana-4165	284	5	parameters	parameter	NOUN
cana-4165	284	6	for	for	ADP
cana-4165	284	7	gaas	gaas	NOUN
cana-4165	284	8	/	/	SYM
cana-4165	284	9	algaas	algaas	NOUN
cana-4165	284	10	2deg	2deg	NUM
cana-4165	284	11	temperature	temperature	NOUN
cana-4165	284	12	(	(	PUNCT
cana-4165	284	13	k	k	NOUN
cana-4165	284	14	)	)	PUNCT
cana-4165	284	15	carrier	carrier	NOUN
cana-4165	284	16	density	density	NOUN
cana-4165	284	17	(	(	PUNCT
cana-4165	284	18	10¹¹	10¹¹	NUM
cana-4165	284	19	cm⁻²	cm⁻²	NOUN
cana-4165	284	20	)	)	PUNCT
cana-4165	284	21	μ₀	μ₀	NOUN
cana-4165	284	22	(	(	PUNCT
cana-4165	284	23	10³	10³	NUM
cana-4165	284	24	cm²/vs	cm²/vs	NOUN
cana-4165	284	25	)	)	PUNCT
cana-4165	284	26	β	β	PROPN
cana-4165	284	27	vsat	vsat	NOUN
cana-4165	284	28	(	(	PUNCT
cana-4165	284	29	10⁷	10⁷	NUM
cana-4165	284	30	cm	cm	NOUN
cana-4165	284	31	/	/	SYM
cana-4165	284	32	s	s	PROPN
cana-4165	284	33	)	)	PUNCT
cana-4165	284	34	4.2	4.2	NUM
cana-4165	284	35	1.0	1.0	NUM
cana-4165	284	36	850	850	NUM
cana-4165	284	37	1.92	1.92	NUM
cana-4165	284	38	1.05	1.05	NUM
cana-4165	284	39	4.2	4.2	NUM
cana-4165	284	40	3.0	3.0	NUM
cana-4165	284	41	1,250	1,250	NUM
cana-4165	284	42	1.95	1.95	NUM
cana-4165	284	43	1.08	1.08	NUM
cana-4165	284	44	4.2	4.2	NUM
cana-4165	284	45	5.0	5.0	NUM
cana-4165	284	46	980	980	NUM
cana-4165	284	47	1.93	1.93	NUM
cana-4165	284	48	1.07	1.07	NUM
cana-4165	284	49	77	77	NUM
cana-4165	284	50	3.0	3.0	NUM
cana-4165	284	51	120	120	NUM
cana-4165	284	52	1.85	1.85	NUM
cana-4165	284	53	1.02	1.02	NUM
cana-4165	284	54	300	300	NUM
cana-4165	284	55	3.0	3.0	NUM
cana-4165	284	56	11	11	NUM
cana-4165	284	57	1.73	1.73	NUM
cana-4165	284	58	0.93	0.93	NUM
cana-4165	284	59	further	further	ADJ
cana-4165	284	60	understanding	understanding	NOUN
cana-4165	284	61	of	of	ADP
cana-4165	284	62	the	the	DET
cana-4165	284	63	scattering	scatter	VERB
cana-4165	284	64	processes	process	NOUN
cana-4165	284	65	is	be	AUX
cana-4165	284	66	offered	offer	VERB
cana-4165	284	67	by	by	ADP
cana-4165	284	68	the	the	DET
cana-4165	284	69	carrier	carrier	NOUN
cana-4165	284	70	density	density	NOUN
cana-4165	284	71	dependence	dependence	NOUN
cana-4165	284	72	of	of	ADP
cana-4165	284	73	mobility	mobility	NOUN
cana-4165	284	74	.	.	PUNCT
cana-4165	285	1	due	due	ADP
cana-4165	285	2	to	to	ADP
cana-4165	285	3	improved	improved	ADJ
cana-4165	285	4	screening	screening	NOUN
cana-4165	285	5	of	of	ADP
cana-4165	285	6	ionized	ionized	ADJ
cana-4165	285	7	impurities	impurity	NOUN
cana-4165	285	8	,	,	PUNCT
cana-4165	285	9	the	the	DET
cana-4165	285	10	mobility	mobility	NOUN
cana-4165	285	11	first	first	ADV
cana-4165	285	12	rises	rise	VERB
cana-4165	285	13	with	with	ADP
cana-4165	285	14	carrier	carrier	NOUN
cana-4165	285	15	density	density	NOUN
cana-4165	285	16	at	at	ADP
cana-4165	285	17	low	low	ADJ
cana-4165	285	18	temperatures	temperature	NOUN
cana-4165	285	19	;	;	PUNCT
cana-4165	285	20	then	then	ADV
cana-4165	285	21	,	,	PUNCT
cana-4165	285	22	it	it	PRON
cana-4165	285	23	falls	fall	VERB
cana-4165	285	24	at	at	ADP
cana-4165	285	25	higher	high	ADJ
cana-4165	285	26	densities	density	NOUN
cana-4165	285	27	as	as	SCONJ
cana-4165	285	28	interface	interface	NOUN
cana-4165	285	29	roughness	roughness	NOUN
cana-4165	285	30	scattering	scattering	NOUN
cana-4165	285	31	becomes	become	VERB
cana-4165	285	32	important	important	ADJ
cana-4165	285	33	.	.	PUNCT
cana-4165	286	1	our	our	PRON
cana-4165	286	2	theoretical	theoretical	ADJ
cana-4165	286	3	model	model	NOUN
cana-4165	286	4	precisely	precisely	ADV
cana-4165	286	5	catches	catch	VERB
cana-4165	286	6	this	this	DET
cana-4165	286	7	non	non	ADJ
cana-4165	286	8	-	-	ADJ
cana-4165	286	9	monotonic	monotonic	ADJ
cana-4165	286	10	behavior	behavior	NOUN
cana-4165	286	11	.	.	PUNCT
cana-4165	287	1	the	the	DET
cana-4165	287	2	normalized	normalize	VERB
cana-4165	287	3	velocity	velocity	NOUN
cana-4165	287	4	v	v	ADP
cana-4165	287	5	/	/	SYM
cana-4165	287	6	vsat	vsat	VERB
cana-4165	287	7	against	against	ADP
cana-4165	287	8	the	the	DET
cana-4165	287	9	normalized	normalize	VERB
cana-4165	287	10	field	field	NOUN
cana-4165	287	11	e	e	NOUN
cana-4165	287	12	/	/	SYM
cana-4165	287	13	ec	ec	PROPN
cana-4165	287	14	to	to	PART
cana-4165	287	15	investigate	investigate	VERB
cana-4165	287	16	the	the	DET
cana-4165	287	17	universality	universality	NOUN
cana-4165	287	18	of	of	ADP
cana-4165	287	19	the	the	DET
cana-4165	287	20	velocity	velocity	NOUN
cana-4165	287	21	-	-	PUNCT
cana-4165	287	22	field	field	NOUN
cana-4165	287	23	relationship	relationship	NOUN
cana-4165	287	24	in	in	ADP
cana-4165	287	25	2d	2d	NOUN
cana-4165	287	26	systems	system	NOUN
cana-4165	287	27	.	.	PUNCT
cana-4165	288	1	confirming	confirm	VERB
cana-4165	288	2	the	the	DET
cana-4165	288	3	validity	validity	NOUN
cana-4165	288	4	of	of	ADP
cana-4165	288	5	our	our	PRON
cana-4165	288	6	scaling	scaling	NOUN
cana-4165	288	7	method	method	NOUN
cana-4165	288	8	,	,	PUNCT
cana-4165	288	9	this	this	DET
cana-4165	288	10	dimensionless	dimensionless	NOUN
cana-4165	288	11	representation	representation	NOUN
cana-4165	288	12	shows	show	VERB
cana-4165	288	13	a	a	DET
cana-4165	288	14	surprising	surprising	ADJ
cana-4165	288	15	compression	compression	NOUN
cana-4165	288	16	of	of	ADP
cana-4165	288	17	data	datum	NOUN
cana-4165	288	18	for	for	ADP
cana-4165	288	19	various	various	ADJ
cana-4165	288	20	temperatures	temperature	NOUN
cana-4165	288	21	and	and	CCONJ
cana-4165	288	22	carrier	carrier	NOUN
cana-4165	288	23	densities	density	NOUN
cana-4165	288	24	onto	onto	ADP
cana-4165	288	25	a	a	DET
cana-4165	288	26	single	single	ADJ
cana-4165	288	27	universal	universal	ADJ
cana-4165	288	28	curve	curve	NOUN
cana-4165	288	29	.	.	PUNCT
cana-4165	289	1	graphene	graphene	NOUN
cana-4165	289	2	:	:	PUNCT
cana-4165	289	3	dirac	dirac	NOUN
cana-4165	289	4	electrons	electron	NOUN
cana-4165	289	5	in	in	ADP
cana-4165	289	6	two	two	NUM
cana-4165	289	7	dimensions	dimension	NOUN
cana-4165	289	8	thanks	thank	NOUN
cana-4165	289	9	to	to	ADP
cana-4165	289	10	its	its	PRON
cana-4165	289	11	linear	linear	ADJ
cana-4165	289	12	dispersion	dispersion	NOUN
cana-4165	289	13	relation	relation	NOUN
cana-4165	289	14	and	and	CCONJ
cana-4165	289	15	chiral	chiral	ADJ
cana-4165	289	16	character	character	NOUN
cana-4165	289	17	of	of	ADP
cana-4165	289	18	its	its	PRON
cana-4165	289	19	carriers	carrier	NOUN
cana-4165	289	20	,	,	PUNCT
cana-4165	289	21	graphene	graphene	NOUN
cana-4165	289	22	offers	offer	VERB
cana-4165	289	23	a	a	DET
cana-4165	289	24	special	special	ADJ
cana-4165	289	25	test	test	NOUN
cana-4165	289	26	case	case	NOUN
cana-4165	289	27	for	for	ADP
cana-4165	289	28	our	our	PRON
cana-4165	289	29	theoretical	theoretical	ADJ
cana-4165	289	30	framework	framework	NOUN
cana-4165	289	31	.	.	PUNCT
cana-4165	290	1	electrostatic	electrostatic	ADJ
cana-4165	290	2	gating	gating	NOUN
cana-4165	290	3	displays	display	VERB
cana-4165	290	4	the	the	DET
cana-4165	290	5	velocity	velocity	NOUN
cana-4165	290	6	-	-	PUNCT
cana-4165	290	7	field	field	NOUN
cana-4165	290	8	properties	property	NOUN
cana-4165	290	9	for	for	ADP
cana-4165	290	10	monolayer	monolayer	NOUN
cana-4165	290	11	graphene	graphene	NOUN
cana-4165	290	12	at	at	ADP
cana-4165	290	13	various	various	ADJ
cana-4165	290	14	carrier	carrier	NOUN
cana-4165	290	15	densities	density	NOUN
cana-4165	290	16	.	.	PUNCT
cana-4165	291	1	the	the	DET
cana-4165	291	2	asymptotic	asymptotic	ADJ
cana-4165	291	3	expansion	expansion	NOUN
cana-4165	291	4	for	for	ADP
cana-4165	291	5	graphene	graphene	NOUN
cana-4165	291	6	requires	require	VERB
cana-4165	291	7	modification	modification	NOUN
cana-4165	291	8	to	to	PART
cana-4165	291	9	account	account	VERB
cana-4165	291	10	for	for	ADP
cana-4165	291	11	its	its	PRON
cana-4165	291	12	special	special	ADJ
cana-4165	291	13	band	band	NOUN
cana-4165	291	14	structure	structure	NOUN
cana-4165	291	15	:	:	PUNCT
cana-4165	291	16	v(e	v(e	NUM
cana-4165	291	17	)	)	PUNCT
cana-4165	291	18	=	=	PUNCT
cana-4165	291	19	v₀e	v₀e	NOUN
cana-4165	291	20	/	/	SYM
cana-4165	291	21	(	(	PUNCT
cana-4165	291	22	e₀	e₀	PROPN
cana-4165	291	23	+	+	CCONJ
cana-4165	291	24	e)½	e)½	PROPN
cana-4165	291	25	·	·	PUNCT
cana-4165	292	1	[	[	X
cana-4165	292	2	1	1	NUM
cana-4165	292	3	exp(-(e	exp(-(e	ADV
cana-4165	292	4	/	/	SYM
cana-4165	292	5	es)γ	es)γ	PROPN
cana-4165	292	6	)	)	PUNCT
cana-4165	292	7	]	]	PUNCT
cana-4165	292	8	es	es	X
cana-4165	292	9	shows	show	VERB
cana-4165	292	10	a	a	DET
cana-4165	292	11	saturation	saturation	NOUN
cana-4165	292	12	field	field	NOUN
cana-4165	292	13	scale	scale	NOUN
cana-4165	292	14	;	;	PUNCT
cana-4165	292	15	γ	γ	X
cana-4165	292	16	governs	govern	VERB
cana-4165	292	17	the	the	DET
cana-4165	292	18	approach	approach	NOUN
cana-4165	292	19	to	to	ADP
cana-4165	292	20	saturation	saturation	NOUN
cana-4165	292	21	;	;	PUNCT
cana-4165	292	22	v₀	v₀	NOUN
cana-4165	292	23	and	and	CCONJ
cana-4165	292	24	e₀	e₀	ADJ
cana-4165	292	25	are	be	AUX
cana-4165	292	26	related	relate	VERB
cana-4165	292	27	to	to	ADP
cana-4165	292	28	the	the	DET
cana-4165	292	29	lowfield	lowfield	NOUN
cana-4165	292	30	conductivity	conductivity	NOUN
cana-4165	292	31	.	.	PUNCT
cana-4165	293	1	different	different	ADJ
cana-4165	293	2	from	from	ADP
cana-4165	293	3	typical	typical	ADJ
cana-4165	293	4	semiconductors	semiconductor	NOUN
cana-4165	293	5	,	,	PUNCT
cana-4165	293	6	this	this	DET
cana-4165	293	7	peculiar	peculiar	ADJ
cana-4165	293	8	shape	shape	NOUN
cana-4165	293	9	reflects	reflect	VERB
cana-4165	293	10	the	the	DET
cana-4165	293	11	special	special	ADJ
cana-4165	293	12	carrier	carrier	NOUN
cana-4165	293	13	dynamics	dynamic	NOUN
cana-4165	293	14	of	of	ADP
cana-4165	293	15	graphene	graphene	NOUN
cana-4165	293	16	.	.	PUNCT
cana-4165	294	1	consistent	consistent	ADJ
cana-4165	294	2	with	with	ADP
cana-4165	294	3	the	the	DET
cana-4165	294	4	expected	expect	VERB
cana-4165	294	5	behavior	behavior	NOUN
cana-4165	294	6	for	for	ADP
cana-4165	294	7	dirac	dirac	NOUN
cana-4165	294	8	fermions	fermion	NOUN
cana-4165	294	9	,	,	PUNCT
cana-4165	294	10	the	the	DET
cana-4165	294	11	carrier	carrier	NOUN
cana-4165	294	12	density	density	NOUN
cana-4165	294	13	dependence	dependence	NOUN
cana-4165	294	14	mostly	mostly	ADV
cana-4165	294	15	enters	enter	VERB
cana-4165	294	16	via	via	ADP
cana-4165	294	17	the	the	DET
cana-4165	294	18	parameters	parameter	NOUN
cana-4165	294	19	v₀	v₀	VERB
cana-4165	294	20	and	and	CCONJ
cana-4165	294	21	e₀	e₀	PROPN
cana-4165	294	22	,	,	PUNCT
cana-4165	294	23	which	which	PRON
cana-4165	294	24	scale	scale	VERB
cana-4165	294	25	roughly	roughly	ADV
cana-4165	294	26	as	as	ADP
cana-4165	294	27	n⁻	n⁻	NOUN
cana-4165	294	28	½	½	NOUN
cana-4165	294	29	and	and	CCONJ
cana-4165	294	30	n	n	PRON
cana-4165	294	31	½	½	NOUN
cana-4165	294	32	,	,	PUNCT
cana-4165	294	33	respectively	respectively	ADV
cana-4165	294	34	.	.	PUNCT
cana-4165	295	1	table	table	NOUN
cana-4165	295	2	5	5	NUM
cana-4165	295	3	shows	show	VERB
cana-4165	295	4	the	the	DET
cana-4165	295	5	fitted	fit	VERB
cana-4165	295	6	graphene	graphene	NOUN
cana-4165	295	7	characteristics	characteristic	NOUN
cana-4165	295	8	at	at	ADP
cana-4165	295	9	several	several	ADJ
cana-4165	295	10	carrier	carrier	NOUN
cana-4165	295	11	densities	density	NOUN
cana-4165	295	12	.	.	PUNCT
cana-4165	296	1	at	at	ADP
cana-4165	296	2	low	low	ADJ
cana-4165	296	3	carrier	carrier	NOUN
cana-4165	296	4	densities	density	NOUN
cana-4165	296	5	,	,	PUNCT
cana-4165	296	6	the	the	DET
cana-4165	296	7	saturation	saturation	NOUN
cana-4165	296	8	velocity	velocity	NOUN
cana-4165	296	9	approaches	approach	VERB
cana-4165	296	10	the	the	DET
cana-4165	296	11	fermi	fermi	NOUN
cana-4165	296	12	velocity	velocity	NOUN
cana-4165	296	13	vf	vf	X
cana-4165	296	14	=	=	NOUN
cana-4165	296	15	10⁸	10⁸	NUM
cana-4165	296	16	cm	cm	NOUN
cana-4165	296	17	/	/	SYM
cana-4165	296	18	s	s	PROPN
cana-4165	296	19	;	;	PUNCT
cana-4165	296	20	increasing	increase	VERB
cana-4165	296	21	carrier	carrier	NOUN
cana-4165	296	22	-	-	PUNCT
cana-4165	296	23	carrier	carrier	NOUN
cana-4165	296	24	scattering	scattering	NOUN
cana-4165	296	25	causes	cause	VERB
cana-4165	296	26	the	the	DET
cana-4165	296	27	saturation	saturation	NOUN
cana-4165	296	28	velocity	velocity	NOUN
cana-4165	296	29	to	to	PART
cana-4165	296	30	drop	drop	VERB
cana-4165	296	31	at	at	ADP
cana-4165	296	32	higher	high	ADJ
cana-4165	296	33	densities	density	NOUN
cana-4165	296	34	.	.	PUNCT
cana-4165	297	1	table	table	NOUN
cana-4165	297	2	5	5	NUM
cana-4165	297	3	:	:	PUNCT
cana-4165	297	4	fitted	fit	VERB
cana-4165	297	5	parameters	parameter	NOUN
cana-4165	297	6	for	for	ADP
cana-4165	297	7	monolayer	monolayer	NOUN
cana-4165	297	8	graphene	graphene	NOUN
cana-4165	297	9	at	at	ADP
cana-4165	297	10	300k	300k	PROPN
cana-4165	297	11	communications	communication	NOUN
cana-4165	297	12	on	on	ADP
cana-4165	297	13	applied	apply	VERB
cana-4165	297	14	nonlinear	nonlinear	ADJ
cana-4165	297	15	analysis	analysis	NOUN
cana-4165	297	16	issn	issn	NOUN
cana-4165	297	17	:	:	PUNCT
cana-4165	297	18	1074	1074	NUM
cana-4165	297	19	-	-	PUNCT
cana-4165	297	20	133x	133x	NUM
cana-4165	297	21	vol	vol	NOUN
cana-4165	297	22	32	32	NUM
cana-4165	297	23	no	no	NOUN
cana-4165	297	24	.	.	PUNCT
cana-4165	298	1	9s	9s	NUM
cana-4165	298	2	(	(	PUNCT
cana-4165	298	3	2025	2025	NUM
cana-4165	298	4	)	)	PUNCT
cana-4165	298	5	1403	1403	NUM
cana-4165	298	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	298	7	carrier	carrier	NOUN
cana-4165	298	8	density	density	NOUN
cana-4165	298	9	(	(	PUNCT
cana-4165	298	10	10¹²	10¹²	NUM
cana-4165	298	11	cm⁻²	cm⁻²	NOUN
cana-4165	298	12	)	)	PUNCT
cana-4165	299	1	v₀	v₀	NOUN
cana-4165	299	2	(	(	PUNCT
cana-4165	299	3	cm²/vs	cm²/vs	NOUN
cana-4165	299	4	)	)	PUNCT
cana-4165	299	5	e₀	e₀	NOUN
cana-4165	299	6	(	(	PUNCT
cana-4165	299	7	kv	kv	PROPN
cana-4165	299	8	/	/	SYM
cana-4165	299	9	cm	cm	NOUN
cana-4165	299	10	)	)	PUNCT
cana-4165	299	11	es	es	PROPN
cana-4165	299	12	(	(	PUNCT
cana-4165	299	13	kv	kv	PROPN
cana-4165	299	14	/	/	SYM
cana-4165	299	15	cm	cm	NOUN
cana-4165	299	16	)	)	PUNCT
cana-4165	299	17	γ	γ	PROPN
cana-4165	299	18	vsat	vsat	X
cana-4165	299	19	(	(	PUNCT
cana-4165	299	20	10⁷	10⁷	NUM
cana-4165	299	21	cm	cm	NOUN
cana-4165	299	22	/	/	SYM
cana-4165	299	23	s	s	PART
cana-4165	299	24	)	)	PUNCT
cana-4165	299	25	0.5	0.5	NUM
cana-4165	299	26	15.5	15.5	NUM
cana-4165	299	27	0.18	0.18	NUM
cana-4165	299	28	25	25	NUM
cana-4165	299	29	1.8	1.8	NUM
cana-4165	299	30	7.2	7.2	NUM
cana-4165	299	31	1.0	1.0	NUM
cana-4165	299	32	11.0	11.0	NUM
cana-4165	299	33	0.25	0.25	NUM
cana-4165	299	34	30	30	NUM
cana-4165	299	35	1.7	1.7	NUM
cana-4165	299	36	5.5	5.5	NUM
cana-4165	299	37	3.0	3.0	NUM
cana-4165	299	38	6.4	6.4	NUM
cana-4165	299	39	0.42	0.42	NUM
cana-4165	299	40	40	40	NUM
cana-4165	299	41	1.6	1.6	NUM
cana-4165	299	42	4.1	4.1	NUM
cana-4165	299	43	at	at	ADP
cana-4165	299	44	normal	normal	ADJ
cana-4165	299	45	temperature	temperature	NOUN
cana-4165	299	46	,	,	PUNCT
cana-4165	299	47	the	the	DET
cana-4165	299	48	temperature	temperature	NOUN
cana-4165	299	49	dependence	dependence	NOUN
cana-4165	299	50	of	of	ADP
cana-4165	299	51	transport	transport	NOUN
cana-4165	299	52	in	in	ADP
cana-4165	299	53	graphene	graphene	NOUN
cana-4165	299	54	shows	show	NOUN
cana-4165	299	55	mostly	mostly	ADV
cana-4165	299	56	phononlimited	phononlimite	VERB
cana-4165	299	57	behavior	behavior	NOUN
cana-4165	299	58	;	;	PUNCT
cana-4165	299	59	at	at	ADP
cana-4165	299	60	lower	low	ADJ
cana-4165	299	61	temperatures	temperature	NOUN
cana-4165	299	62	,	,	PUNCT
cana-4165	299	63	this	this	DET
cana-4165	299	64	behavior	behavior	NOUN
cana-4165	299	65	is	be	AUX
cana-4165	299	66	changed	change	VERB
cana-4165	299	67	to	to	PART
cana-4165	299	68	show	show	VERB
cana-4165	299	69	impurity	impurity	NOUN
cana-4165	299	70	-	-	PUNCT
cana-4165	299	71	limited	limit	VERB
cana-4165	299	72	transport	transport	NOUN
cana-4165	299	73	.	.	PUNCT
cana-4165	300	1	through	through	ADP
cana-4165	300	2	temperature	temperature	NOUN
cana-4165	300	3	-	-	PUNCT
cana-4165	300	4	dependent	dependent	ADJ
cana-4165	300	5	factors	factor	NOUN
cana-4165	300	6	in	in	ADP
cana-4165	300	7	the	the	DET
cana-4165	300	8	asymptotic	asymptotic	ADJ
cana-4165	300	9	expansion	expansion	NOUN
cana-4165	300	10	,	,	PUNCT
cana-4165	300	11	our	our	PRON
cana-4165	300	12	model	model	NOUN
cana-4165	300	13	faithfully	faithfully	ADV
cana-4165	300	14	records	record	VERB
cana-4165	300	15	this	this	DET
cana-4165	300	16	change	change	NOUN
cana-4165	300	17	.	.	PUNCT
cana-4165	301	1	we	we	PRON
cana-4165	301	2	investigated	investigate	VERB
cana-4165	301	3	quantum	quantum	NOUN
cana-4165	301	4	effects	effect	NOUN
cana-4165	301	5	in	in	ADP
cana-4165	301	6	graphene	graphene	ADJ
cana-4165	301	7	transport	transport	NOUN
cana-4165	301	8	by	by	ADP
cana-4165	301	9	means	mean	NOUN
cana-4165	301	10	of	of	ADP
cana-4165	301	11	high	high	ADJ
cana-4165	301	12	magnetic	magnetic	ADJ
cana-4165	301	13	field	field	NOUN
cana-4165	301	14	perpendicular	perpendicular	NOUN
cana-4165	301	15	to	to	ADP
cana-4165	301	16	the	the	DET
cana-4165	301	17	graphene	graphene	ADJ
cana-4165	301	18	plane	plane	NOUN
cana-4165	301	19	.	.	PUNCT
cana-4165	302	1	higher	high	ADJ
cana-4165	302	2	field	field	NOUN
cana-4165	302	3	observable	observable	ADJ
cana-4165	302	4	shubnikov	shubnikov	NOUN
cana-4165	302	5	-	-	PUNCT
cana-4165	302	6	de	de	X
cana-4165	302	7	haas	haas	PROPN
cana-4165	302	8	oscillations	oscillation	NOUN
cana-4165	302	9	offer	offer	VERB
cana-4165	302	10	a	a	DET
cana-4165	302	11	complementary	complementary	ADJ
cana-4165	302	12	approach	approach	NOUN
cana-4165	302	13	to	to	PART
cana-4165	302	14	find	find	VERB
cana-4165	302	15	carrier	carrier	NOUN
cana-4165	302	16	mobility	mobility	NOUN
cana-4165	302	17	.	.	PUNCT
cana-4165	303	1	we	we	PRON
cana-4165	303	2	corroborate	corroborate	VERB
cana-4165	303	3	our	our	PRON
cana-4165	303	4	interpretation	interpretation	NOUN
cana-4165	303	5	of	of	ADP
cana-4165	303	6	the	the	DET
cana-4165	303	7	transport	transport	NOUN
cana-4165	303	8	parameters	parameter	NOUN
cana-4165	303	9	by	by	ADP
cana-4165	303	10	the	the	DET
cana-4165	303	11	agreement	agreement	NOUN
cana-4165	303	12	between	between	ADP
cana-4165	303	13	mobility	mobility	NOUN
cana-4165	303	14	values	value	NOUN
cana-4165	303	15	derived	derive	VERB
cana-4165	303	16	from	from	ADP
cana-4165	303	17	low	low	ADJ
cana-4165	303	18	-	-	PUNCT
cana-4165	303	19	field	field	NOUN
cana-4165	303	20	hall	hall	NOUN
cana-4165	303	21	measurements	measurement	NOUN
cana-4165	303	22	and	and	CCONJ
cana-4165	303	23	from	from	ADP
cana-4165	303	24	quantum	quantum	ADJ
cana-4165	303	25	oscillations	oscillation	NOUN
cana-4165	303	26	.	.	PUNCT
cana-4165	304	1	one	one	NUM
cana-4165	304	2	-	-	PUNCT
cana-4165	304	3	dimensional	dimensional	ADJ
cana-4165	304	4	systems	system	NOUN
cana-4165	304	5	:	:	PUNCT
cana-4165	304	6	carbon	carbon	NOUN
cana-4165	304	7	nanotubes	nanotube	NOUN
cana-4165	304	8	because	because	SCONJ
cana-4165	304	9	of	of	ADP
cana-4165	304	10	their	their	PRON
cana-4165	304	11	single	single	ADJ
cana-4165	304	12	density	density	NOUN
cana-4165	304	13	of	of	ADP
cana-4165	304	14	states	state	NOUN
cana-4165	304	15	and	and	CCONJ
cana-4165	304	16	limited	limited	ADJ
cana-4165	304	17	phase	phase	NOUN
cana-4165	304	18	space	space	NOUN
cana-4165	304	19	for	for	ADP
cana-4165	304	20	scattering	scattering	NOUN
cana-4165	304	21	,	,	PUNCT
cana-4165	304	22	transportation	transportation	NOUN
cana-4165	304	23	in	in	ADP
cana-4165	304	24	really	really	ADV
cana-4165	304	25	one	one	NUM
cana-4165	304	26	-	-	PUNCT
cana-4165	304	27	dimensional	dimensional	ADJ
cana-4165	304	28	systems	system	NOUN
cana-4165	304	29	shows	show	VERB
cana-4165	304	30	unique	unique	ADJ
cana-4165	304	31	properties	property	NOUN
cana-4165	304	32	.	.	PUNCT
cana-4165	305	1	we	we	PRON
cana-4165	305	2	investigated	investigate	VERB
cana-4165	305	3	single	single	ADJ
cana-4165	305	4	semiconducting	semiconducting	NOUN
cana-4165	305	5	carbon	carbon	NOUN
cana-4165	305	6	nanotubes	nanotube	NOUN
cana-4165	305	7	having	have	VERB
cana-4165	305	8	diameters	diameter	NOUN
cana-4165	305	9	between	between	ADP
cana-4165	305	10	1.2	1.2	NUM
cana-4165	305	11	and	and	CCONJ
cana-4165	305	12	2.1	2.1	NUM
cana-4165	305	13	nm	nm	NOUN
cana-4165	305	14	.	.	PUNCT
cana-4165	306	1	the	the	DET
cana-4165	306	2	asymptotic	asymptotic	ADJ
cana-4165	306	3	expansion	expansion	NOUN
cana-4165	306	4	for	for	ADP
cana-4165	306	5	one	one	NUM
cana-4165	306	6	-	-	PUNCT
cana-4165	306	7	dimensional	dimensional	ADJ
cana-4165	306	8	transport	transport	NOUN
cana-4165	306	9	takes	take	VERB
cana-4165	306	10	the	the	DET
cana-4165	306	11	form	form	NOUN
cana-4165	306	12	:	:	PUNCT
cana-4165	306	13	v(e	v(e	NUM
cana-4165	306	14	)	)	PUNCT
cana-4165	307	1	=	=	NOUN
cana-4165	308	1	v₀	v₀	NOUN
cana-4165	308	2	·	·	PUNCT
cana-4165	309	1	[	[	X
cana-4165	309	2	1	1	NUM
cana-4165	309	3	exp(-(μ₀e	exp(-(μ₀e	NOUN
cana-4165	309	4	/	/	SYM
cana-4165	309	5	v₀)δ	v₀)δ	NOUN
cana-4165	309	6	)	)	PUNCT
cana-4165	309	7	]	]	PUNCT
cana-4165	309	8	where	where	SCONJ
cana-4165	309	9	δ	δ	PROPN
cana-4165	309	10	a	a	PRON
cana-4165	309	11	controls	control	VERB
cana-4165	309	12	the	the	DET
cana-4165	309	13	sharpness	sharpness	NOUN
cana-4165	309	14	of	of	ADP
cana-4165	309	15	the	the	DET
cana-4165	309	16	transition	transition	NOUN
cana-4165	309	17	,	,	PUNCT
cana-4165	309	18	μ₀	μ₀	VERB
cana-4165	309	19	the	the	DET
cana-4165	309	20	low	low	ADJ
cana-4165	309	21	-	-	PUNCT
cana-4165	309	22	field	field	NOUN
cana-4165	309	23	mobility	mobility	NOUN
cana-4165	309	24	,	,	PUNCT
cana-4165	309	25	and	and	CCONJ
cana-4165	309	26	v₀	v₀	VERB
cana-4165	309	27	the	the	DET
cana-4165	309	28	saturation	saturation	NOUN
cana-4165	309	29	velocity	velocity	NOUN
cana-4165	309	30	.	.	PUNCT
cana-4165	310	1	reflecting	reflect	VERB
cana-4165	310	2	the	the	DET
cana-4165	310	3	quite	quite	ADV
cana-4165	310	4	distinct	distinct	ADJ
cana-4165	310	5	scattering	scatter	VERB
cana-4165	310	6	mechanisms	mechanism	NOUN
cana-4165	310	7	in	in	ADP
cana-4165	310	8	one	one	NUM
cana-4165	310	9	dimension	dimension	NOUN
cana-4165	310	10	,	,	PUNCT
cana-4165	310	11	this	this	DET
cana-4165	310	12	formulation	formulation	NOUN
cana-4165	310	13	differs	differ	VERB
cana-4165	310	14	greatly	greatly	ADV
cana-4165	310	15	from	from	ADP
cana-4165	310	16	those	those	PRON
cana-4165	310	17	for	for	ADP
cana-4165	310	18	higher	high	ADJ
cana-4165	310	19	-	-	PUNCT
cana-4165	310	20	dimensional	dimensional	ADJ
cana-4165	310	21	systems	system	NOUN
cana-4165	310	22	.	.	PUNCT
cana-4165	311	1	absence	absence	NOUN
cana-4165	311	2	of	of	ADP
cana-4165	311	3	a	a	DET
cana-4165	311	4	power	power	NOUN
cana-4165	311	5	-	-	PUNCT
cana-4165	311	6	law	law	NOUN
cana-4165	311	7	term	term	NOUN
cana-4165	311	8	(	(	PUNCT
cana-4165	311	9	e	e	NOUN
cana-4165	311	10	/	/	SYM
cana-4165	311	11	ec	ec	PROPN
cana-4165	311	12	)	)	PUNCT
cana-4165	312	1	α	α	PROPN
cana-4165	312	2	denotes	denote	VERB
cana-4165	312	3	the	the	DET
cana-4165	312	4	sudden	sudden	ADJ
cana-4165	312	5	character	character	NOUN
cana-4165	312	6	of	of	ADP
cana-4165	312	7	the	the	DET
cana-4165	312	8	change	change	NOUN
cana-4165	312	9	between	between	ADP
cana-4165	312	10	linear	linear	NOUN
cana-4165	312	11	and	and	CCONJ
cana-4165	312	12	saturation	saturation	NOUN
cana-4165	312	13	behavior	behavior	NOUN
cana-4165	312	14	.	.	PUNCT
cana-4165	313	1	table	table	NOUN
cana-4165	313	2	6	6	NUM
cana-4165	313	3	lists	list	VERB
cana-4165	313	4	the	the	DET
cana-4165	313	5	fitting	fitting	ADJ
cana-4165	313	6	values	value	NOUN
cana-4165	313	7	for	for	ADP
cana-4165	313	8	various	various	ADJ
cana-4165	313	9	diameters	diameter	NOUN
cana-4165	313	10	of	of	ADP
cana-4165	313	11	carbon	carbon	NOUN
cana-4165	313	12	nanotubes	nanotube	NOUN
cana-4165	313	13	.	.	PUNCT
cana-4165	314	1	strong	strong	ADJ
cana-4165	314	2	diameter	diameter	NOUN
cana-4165	314	3	dependency	dependency	NOUN
cana-4165	314	4	is	be	AUX
cana-4165	314	5	shown	show	VERB
cana-4165	314	6	by	by	ADP
cana-4165	314	7	the	the	DET
cana-4165	314	8	mobility	mobility	NOUN
cana-4165	314	9	,	,	PUNCT
cana-4165	314	10	which	which	PRON
cana-4165	314	11	scales	scale	VERB
cana-4165	314	12	about	about	ADP
cana-4165	314	13	as	as	ADP
cana-4165	314	14	d²	d²	NOUN
cana-4165	314	15	in	in	ADP
cana-4165	314	16	line	line	NOUN
cana-4165	314	17	with	with	ADP
cana-4165	314	18	theoretical	theoretical	ADJ
cana-4165	314	19	expectations	expectation	NOUN
cana-4165	314	20	derived	derive	VERB
cana-4165	314	21	from	from	ADP
cana-4165	314	22	acoustic	acoustic	ADJ
cana-4165	314	23	phonon	phonon	NOUN
cana-4165	314	24	scattering	scattering	NOUN
cana-4165	314	25	.	.	PUNCT
cana-4165	314	26	table	table	NOUN
cana-4165	314	27	6	6	NUM
cana-4165	314	28	:	:	PUNCT
cana-4165	314	29	fitted	fit	VERB
cana-4165	314	30	parameters	parameter	NOUN
cana-4165	314	31	for	for	ADP
cana-4165	314	32	semiconducting	semiconducte	VERB
cana-4165	314	33	carbon	carbon	NOUN
cana-4165	314	34	nanotubes	nanotube	NOUN
cana-4165	314	35	at	at	ADP
cana-4165	314	36	300k	300k	PROPN
cana-4165	314	37	diameter	diameter	NOUN
cana-4165	314	38	(	(	PUNCT
cana-4165	314	39	nm	nm	NOUN
cana-4165	314	40	)	)	PUNCT
cana-4165	314	41	μ₀	μ₀	NOUN
cana-4165	314	42	(	(	PUNCT
cana-4165	314	43	cm²/vs	cm²/vs	NOUN
cana-4165	314	44	)	)	PUNCT
cana-4165	314	45	v₀	v₀	NOUN
cana-4165	314	46	(	(	PUNCT
cana-4165	314	47	10⁷	10⁷	NUM
cana-4165	314	48	cm	cm	NOUN
cana-4165	314	49	/	/	SYM
cana-4165	314	50	s	s	PROPN
cana-4165	314	51	)	)	PUNCT
cana-4165	314	52	δ	δ	PROPN
cana-4165	314	53	1.2	1.2	NUM
cana-4165	314	54	7,800	7,800	NUM
cana-4165	314	55	4.2	4.2	NUM
cana-4165	314	56	2.1	2.1	NUM
cana-4165	314	57	1.7	1.7	NUM
cana-4165	314	58	15,200	15,200	NUM
cana-4165	314	59	3.9	3.9	NUM
cana-4165	314	60	2.3	2.3	NUM
cana-4165	314	61	communications	communication	NOUN
cana-4165	314	62	on	on	ADP
cana-4165	314	63	applied	apply	VERB
cana-4165	314	64	nonlinear	nonlinear	ADJ
cana-4165	314	65	analysis	analysis	NOUN
cana-4165	314	66	issn	issn	NOUN
cana-4165	314	67	:	:	PUNCT
cana-4165	314	68	1074	1074	NUM
cana-4165	314	69	-	-	PUNCT
cana-4165	314	70	133x	133x	NUM
cana-4165	314	71	vol	vol	NOUN
cana-4165	314	72	32	32	NUM
cana-4165	314	73	no	no	NOUN
cana-4165	314	74	.	.	PUNCT
cana-4165	315	1	9s	9s	NUM
cana-4165	315	2	(	(	PUNCT
cana-4165	315	3	2025	2025	NUM
cana-4165	315	4	)	)	PUNCT
cana-4165	315	5	1404	1404	NUM
cana-4165	315	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	315	7	diameter	diameter	NOUN
cana-4165	315	8	(	(	PUNCT
cana-4165	315	9	nm	nm	NOUN
cana-4165	315	10	)	)	PUNCT
cana-4165	315	11	μ₀	μ₀	NOUN
cana-4165	315	12	(	(	PUNCT
cana-4165	315	13	cm²/vs	cm²/vs	NOUN
cana-4165	315	14	)	)	PUNCT
cana-4165	315	15	v₀	v₀	NOUN
cana-4165	315	16	(	(	PUNCT
cana-4165	315	17	10⁷	10⁷	NUM
cana-4165	315	18	cm	cm	NOUN
cana-4165	315	19	/	/	SYM
cana-4165	315	20	s	s	NOUN
cana-4165	315	21	)	)	PUNCT
cana-4165	315	22	δ	δ	PROPN
cana-4165	315	23	2.1	2.1	NUM
cana-4165	315	24	23,500	23,500	NUM
cana-4165	315	25	3.7	3.7	NUM
cana-4165	315	26	2.5	2.5	NUM
cana-4165	315	27	approaching	approach	VERB
cana-4165	315	28	the	the	DET
cana-4165	315	29	theoretical	theoretical	ADJ
cana-4165	315	30	limit	limit	NOUN
cana-4165	315	31	of	of	ADP
cana-4165	315	32	vf/2	vf/2	NOUN
cana-4165	315	33	for	for	ADP
cana-4165	315	34	small	small	ADJ
cana-4165	315	35	diameters	diameter	NOUN
cana-4165	315	36	,	,	PUNCT
cana-4165	315	37	where	where	SCONJ
cana-4165	315	38	vf	vf	PROPN
cana-4165	315	39	represents	represent	VERB
cana-4165	315	40	the	the	DET
cana-4165	315	41	fermi	fermi	NOUN
cana-4165	315	42	velocity	velocity	NOUN
cana-4165	315	43	in	in	ADP
cana-4165	315	44	graphene	graphene	NOUN
cana-4165	315	45	,	,	PUNCT
cana-4165	315	46	the	the	DET
cana-4165	315	47	saturation	saturation	NOUN
cana-4165	315	48	velocity	velocity	NOUN
cana-4165	315	49	in	in	ADP
cana-4165	315	50	carbon	carbon	NOUN
cana-4165	315	51	nanotubes	nanotube	NOUN
cana-4165	315	52	shows	show	VERB
cana-4165	315	53	a	a	DET
cana-4165	315	54	weak	weak	ADJ
cana-4165	315	55	inverse	inverse	NOUN
cana-4165	315	56	dependency	dependency	NOUN
cana-4165	315	57	on	on	ADP
cana-4165	315	58	diameter	diameter	NOUN
cana-4165	315	59	.	.	PUNCT
cana-4165	316	1	this	this	DET
cana-4165	316	2	result	result	NOUN
cana-4165	316	3	shows	show	VERB
cana-4165	316	4	the	the	DET
cana-4165	316	5	rising	rise	VERB
cana-4165	316	6	relevance	relevance	NOUN
cana-4165	316	7	of	of	ADP
cana-4165	316	8	optical	optical	ADJ
cana-4165	316	9	phonon	phonon	NOUN
cana-4165	316	10	emission	emission	NOUN
cana-4165	316	11	as	as	ADP
cana-4165	316	12	the	the	DET
cana-4165	316	13	main	main	ADJ
cana-4165	316	14	velocitylimiting	velocitylimiting	NOUN
cana-4165	316	15	factor	factor	NOUN
cana-4165	316	16	in	in	ADP
cana-4165	316	17	smaller	small	ADJ
cana-4165	316	18	nanotubes	nanotube	NOUN
cana-4165	316	19	.	.	PUNCT
cana-4165	317	1	temperature	temperature	NOUN
cana-4165	317	2	-	-	PUNCT
cana-4165	317	3	dependent	dependent	ADJ
cana-4165	317	4	studies	study	NOUN
cana-4165	317	5	on	on	ADP
cana-4165	317	6	carbon	carbon	NOUN
cana-4165	317	7	nanotubes	nanotube	NOUN
cana-4165	317	8	expose	expose	VERB
cana-4165	317	9	a	a	DET
cana-4165	317	10	transition	transition	NOUN
cana-4165	317	11	from	from	ADP
cana-4165	317	12	phonon	phonon	NOUN
cana-4165	317	13	-	-	PUNCT
cana-4165	317	14	limited	limit	VERB
cana-4165	317	15	transport	transport	NOUN
cana-4165	317	16	at	at	ADP
cana-4165	317	17	high	high	ADJ
cana-4165	317	18	temperatures	temperature	NOUN
cana-4165	317	19	to	to	PART
cana-4165	317	20	defect	defect	VERB
cana-4165	317	21	-	-	PUNCT
cana-4165	317	22	limited	limit	VERB
cana-4165	317	23	transport	transport	NOUN
cana-4165	317	24	at	at	ADP
cana-4165	317	25	low	low	ADJ
cana-4165	317	26	temperatures	temperature	NOUN
cana-4165	317	27	.	.	PUNCT
cana-4165	318	1	reduced	reduce	VERB
cana-4165	318	2	dimensionality	dimensionality	NOUN
cana-4165	318	3	of	of	ADP
cana-4165	318	4	the	the	DET
cana-4165	318	5	phonon	phonon	NOUN
cana-4165	318	6	spectrum	spectrum	NOUN
cana-4165	318	7	causes	cause	VERB
cana-4165	318	8	the	the	DET
cana-4165	318	9	mobility	mobility	NOUN
cana-4165	318	10	to	to	PART
cana-4165	318	11	follow	follow	VERB
cana-4165	318	12	an	an	DET
cana-4165	318	13	approximate	approximate	ADJ
cana-4165	318	14	t⁻¹·²	t⁻¹·²	NUM
cana-4165	318	15	dependence	dependence	NOUN
cana-4165	318	16	at	at	ADP
cana-4165	318	17	higher	high	ADJ
cana-4165	318	18	temperatures	temperature	NOUN
cana-4165	318	19	,	,	PUNCT
cana-4165	318	20	less	less	ADV
cana-4165	318	21	steep	steep	ADJ
cana-4165	318	22	than	than	ADP
cana-4165	318	23	in	in	ADP
cana-4165	318	24	bulk	bulk	ADJ
cana-4165	318	25	semiconductors	semiconductor	NOUN
cana-4165	318	26	.	.	PUNCT
cana-4165	319	1	lower	low	ADJ
cana-4165	319	2	temperatures	temperature	NOUN
cana-4165	319	3	cause	cause	VERB
cana-4165	319	4	the	the	DET
cana-4165	319	5	mobility	mobility	NOUN
cana-4165	319	6	to	to	PART
cana-4165	319	7	saturate	saturate	VERB
cana-4165	319	8	at	at	ADP
cana-4165	319	9	a	a	DET
cana-4165	319	10	value	value	NOUN
cana-4165	319	11	dictated	dictate	VERB
cana-4165	319	12	by	by	ADP
cana-4165	319	13	defect	defect	NOUN
cana-4165	319	14	density	density	NOUN
cana-4165	319	15	;	;	PUNCT
cana-4165	319	16	more	more	ADJ
cana-4165	319	17	fluctuation	fluctuation	NOUN
cana-4165	319	18	across	across	ADP
cana-4165	319	19	samples	sample	NOUN
cana-4165	319	20	reflects	reflect	VERB
cana-4165	319	21	variations	variation	NOUN
cana-4165	319	22	in	in	ADP
cana-4165	319	23	fabrication	fabrication	NOUN
cana-4165	319	24	quality	quality	NOUN
cana-4165	319	25	.	.	PUNCT
cana-4165	320	1	computational	computational	ADJ
cana-4165	320	2	results	result	NOUN
cana-4165	320	3	:	:	PUNCT
cana-4165	320	4	quantum	quantum	ADJ
cana-4165	320	5	transport	transport	NOUN
cana-4165	320	6	simulations	simulation	NOUN
cana-4165	320	7	we	we	PRON
cana-4165	320	8	did	do	VERB
cana-4165	320	9	thorough	thorough	ADJ
cana-4165	320	10	quantum	quantum	NOUN
cana-4165	320	11	transport	transport	NOUN
cana-4165	320	12	simulations	simulation	NOUN
cana-4165	320	13	based	base	VERB
cana-4165	320	14	on	on	ADP
cana-4165	320	15	the	the	DET
cana-4165	320	16	non	non	ADJ
cana-4165	320	17	-	-	ADJ
cana-4165	320	18	equilibrium	equilibrium	ADJ
cana-4165	320	19	green	green	NOUN
cana-4165	320	20	's	's	PART
cana-4165	320	21	function	function	NOUN
cana-4165	320	22	formalism	formalism	NOUN
cana-4165	320	23	to	to	PART
cana-4165	320	24	support	support	VERB
cana-4165	320	25	our	our	PRON
cana-4165	320	26	experimental	experimental	ADJ
cana-4165	320	27	studies	study	NOUN
cana-4165	320	28	.	.	PUNCT
cana-4165	321	1	these	these	DET
cana-4165	321	2	simulations	simulation	NOUN
cana-4165	321	3	offer	offer	VERB
cana-4165	321	4	understanding	understanding	NOUN
cana-4165	321	5	of	of	ADP
cana-4165	321	6	regimes	regime	NOUN
cana-4165	321	7	in	in	ADP
cana-4165	321	8	which	which	PRON
cana-4165	321	9	experimental	experimental	ADJ
cana-4165	321	10	measurements	measurement	NOUN
cana-4165	321	11	become	become	VERB
cana-4165	321	12	difficult	difficult	ADJ
cana-4165	321	13	,	,	PUNCT
cana-4165	321	14	especially	especially	ADV
cana-4165	321	15	with	with	ADP
cana-4165	321	16	relation	relation	NOUN
cana-4165	321	17	to	to	ADP
cana-4165	321	18	the	the	DET
cana-4165	321	19	change	change	NOUN
cana-4165	321	20	between	between	ADP
cana-4165	321	21	diffusive	diffusive	ADJ
cana-4165	321	22	and	and	CCONJ
cana-4165	321	23	ballistic	ballistic	ADJ
cana-4165	321	24	transport	transport	NOUN
cana-4165	321	25	.	.	PUNCT
cana-4165	322	1	the	the	DET
cana-4165	322	2	velocity	velocity	NOUN
cana-4165	322	3	shows	show	VERB
cana-4165	322	4	a	a	DET
cana-4165	322	5	quasi	quasi	ADJ
cana-4165	322	6	-	-	ADJ
cana-4165	322	7	linear	linear	ADJ
cana-4165	322	8	increase	increase	NOUN
cana-4165	322	9	with	with	ADP
cana-4165	322	10	field	field	NOUN
cana-4165	322	11	for	for	ADP
cana-4165	322	12	the	the	DET
cana-4165	322	13	shortest	short	ADJ
cana-4165	322	14	nanowires	nanowire	NOUN
cana-4165	322	15	(	(	PUNCT
cana-4165	322	16	10	10	NUM
cana-4165	322	17	nm	nm	NOUN
cana-4165	322	18	)	)	PUNCT
cana-4165	322	19	,	,	PUNCT
cana-4165	322	20	mostly	mostly	ADV
cana-4165	322	21	limited	limit	VERB
cana-4165	322	22	by	by	ADP
cana-4165	322	23	the	the	DET
cana-4165	322	24	injection	injection	NOUN
cana-4165	322	25	velocity	velocity	NOUN
cana-4165	322	26	at	at	ADP
cana-4165	322	27	the	the	DET
cana-4165	322	28	contacts	contact	NOUN
cana-4165	322	29	rather	rather	ADV
cana-4165	322	30	than	than	ADP
cana-4165	322	31	by	by	ADP
cana-4165	322	32	scattering	scatter	VERB
cana-4165	322	33	mechanisms	mechanism	NOUN
cana-4165	322	34	.	.	PUNCT
cana-4165	323	1	the	the	DET
cana-4165	323	2	properties	property	NOUN
cana-4165	323	3	progressively	progressively	ADV
cana-4165	323	4	shift	shift	VERB
cana-4165	323	5	toward	toward	ADP
cana-4165	323	6	the	the	DET
cana-4165	323	7	bulk	bulk	ADJ
cana-4165	323	8	-	-	PUNCT
cana-4165	323	9	like	like	ADJ
cana-4165	323	10	behavior	behavior	NOUN
cana-4165	323	11	with	with	ADP
cana-4165	323	12	strong	strong	ADJ
cana-4165	323	13	saturation	saturation	NOUN
cana-4165	323	14	effects	effect	NOUN
cana-4165	323	15	as	as	SCONJ
cana-4165	323	16	the	the	DET
cana-4165	323	17	length	length	NOUN
cana-4165	323	18	rises	rise	VERB
cana-4165	323	19	.	.	PUNCT
cana-4165	324	1	the	the	DET
cana-4165	324	2	ballisticity	ballisticity	NOUN
cana-4165	324	3	factor	factor	NOUN
cana-4165	324	4	b	b	NOUN
cana-4165	324	5	=	=	SYM
cana-4165	324	6	v	v	NOUN
cana-4165	324	7	/	/	SYM
cana-4165	324	8	vinj	vinj	NOUN
cana-4165	324	9	allows	allow	VERB
cana-4165	324	10	one	one	NUM
cana-4165	324	11	to	to	PART
cana-4165	324	12	measure	measure	VERB
cana-4165	324	13	the	the	DET
cana-4165	324	14	crossover	crossover	NOUN
cana-4165	324	15	between	between	ADP
cana-4165	324	16	ballistic	ballistic	ADJ
cana-4165	324	17	and	and	CCONJ
cana-4165	324	18	diffusive	diffusive	ADJ
cana-4165	324	19	transport	transport	NOUN
cana-4165	324	20	by	by	ADP
cana-4165	324	21	means	mean	NOUN
cana-4165	324	22	of	of	ADP
cana-4165	324	23	the	the	DET
cana-4165	324	24	injection	injection	NOUN
cana-4165	324	25	velocity	velocity	NOUN
cana-4165	324	26	.	.	PUNCT
cana-4165	325	1	figure	figure	VERB
cana-4165	325	2	12	12	NUM
cana-4165	325	3	presents	present	NOUN
cana-4165	325	4	for	for	ADP
cana-4165	325	5	several	several	ADJ
cana-4165	325	6	material	material	NOUN
cana-4165	325	7	systems	system	NOUN
cana-4165	325	8	this	this	DET
cana-4165	325	9	factor	factor	NOUN
cana-4165	325	10	as	as	ADP
cana-4165	325	11	a	a	DET
cana-4165	325	12	function	function	NOUN
cana-4165	325	13	of	of	ADP
cana-4165	325	14	the	the	DET
cana-4165	325	15	knudsen	knudsen	PROPN
cana-4165	325	16	number	number	NOUN
cana-4165	325	17	kn	kn	PROPN
cana-4165	325	18	=	=	PUNCT
cana-4165	325	19	λ	λ	PROPN
cana-4165	325	20	/	/	SYM
cana-4165	325	21	l.	l.	PROPN
cana-4165	325	22	figure	figure	NOUN
cana-4165	325	23	12	12	NUM
cana-4165	325	24	:	:	PUNCT
cana-4165	325	25	ballisticity	ballisticity	NOUN
cana-4165	325	26	factor	factor	NOUN
cana-4165	325	27	vs.	vs.	ADP
cana-4165	325	28	knudsen	knudsen	PROPN
cana-4165	325	29	number	number	NOUN
cana-4165	325	30	[	[	X
cana-4165	325	31	a	a	DET
cana-4165	325	32	semi	semi	ADJ
cana-4165	325	33	-	-	ADJ
cana-4165	325	34	logarithmic	logarithmic	ADJ
cana-4165	325	35	plot	plot	NOUN
cana-4165	325	36	showing	show	VERB
cana-4165	325	37	the	the	DET
cana-4165	325	38	ballisticity	ballisticity	NOUN
cana-4165	325	39	factor	factor	NOUN
cana-4165	325	40	b	b	NOUN
cana-4165	325	41	=	=	SYM
cana-4165	325	42	v	v	PROPN
cana-4165	325	43	/	/	SYM
cana-4165	325	44	vinj	vinj	NOUN
cana-4165	325	45	vs.	vs.	ADP
cana-4165	325	46	knudsen	knudsen	PROPN
cana-4165	325	47	number	number	NOUN
cana-4165	325	48	kn	kn	PROPN
cana-4165	325	49	=	=	PUNCT
cana-4165	325	50	λ	λ	PROPN
cana-4165	325	51	/	/	SYM
cana-4165	325	52	l	l	NOUN
cana-4165	325	53	for	for	ADP
cana-4165	325	54	silicon	silicon	NOUN
cana-4165	325	55	,	,	PUNCT
cana-4165	325	56	gallium	gallium	NOUN
cana-4165	325	57	arsenide	arsenide	NOUN
cana-4165	325	58	,	,	PUNCT
cana-4165	325	59	and	and	CCONJ
cana-4165	325	60	carbon	carbon	NOUN
cana-4165	325	61	nanotubes	nanotube	NOUN
cana-4165	325	62	.	.	PUNCT
cana-4165	325	63	]	]	X
cana-4165	326	1	our	our	PRON
cana-4165	326	2	scaling	scaling	NOUN
cana-4165	326	3	method	method	NOUN
cana-4165	326	4	is	be	AUX
cana-4165	326	5	validated	validate	VERB
cana-4165	326	6	as	as	ADP
cana-4165	326	7	the	the	DET
cana-4165	326	8	data	datum	NOUN
cana-4165	326	9	from	from	ADP
cana-4165	326	10	several	several	ADJ
cana-4165	326	11	materials	material	NOUN
cana-4165	326	12	collapse	collapse	NOUN
cana-4165	326	13	onto	onto	ADP
cana-4165	326	14	a	a	DET
cana-4165	326	15	universal	universal	ADJ
cana-4165	326	16	curve	curve	NOUN
cana-4165	326	17	.	.	PUNCT
cana-4165	327	1	for	for	ADP
cana-4165	327	2	kn	kn	PROPN
cana-4165	327	3	>	>	X
cana-4165	327	4	>	>	X
cana-4165	327	5	1	1	NUM
cana-4165	327	6	(	(	PUNCT
cana-4165	327	7	ballistic	ballistic	ADJ
cana-4165	327	8	limit	limit	NOUN
cana-4165	327	9	)	)	PUNCT
cana-4165	327	10	the	the	DET
cana-4165	327	11	asymptotic	asymptotic	ADJ
cana-4165	327	12	behavior	behavior	NOUN
cana-4165	327	13	follows	follow	VERB
cana-4165	327	14	b	b	PROPN
cana-4165	327	15	≈	≈	PROPN
cana-4165	327	16	1	1	NUM
cana-4165	327	17	;	;	PUNCT
cana-4165	327	18	for	for	ADP
cana-4165	327	19	kn	kn	PROPN
cana-4165	327	20	<	<	X
cana-4165	327	21	<	<	X
cana-4165	327	22	1	1	NUM
cana-4165	327	23	,	,	PUNCT
cana-4165	327	24	b	b	PROPN
cana-4165	327	25	≈	≈	PROPN
cana-4165	327	26	kn	kn	PROPN
cana-4165	327	27	.	.	PUNCT
cana-4165	328	1	our	our	PRON
cana-4165	328	2	interpolation	interpolation	NOUN
cana-4165	328	3	formula	formula	NOUN
cana-4165	328	4	allows	allow	VERB
cana-4165	328	5	one	one	PRON
cana-4165	328	6	to	to	PART
cana-4165	328	7	precisely	precisely	ADV
cana-4165	328	8	define	define	VERB
cana-4165	328	9	the	the	DET
cana-4165	328	10	transition	transition	NOUN
cana-4165	328	11	zone	zone	NOUN
cana-4165	328	12	:	:	PUNCT
cana-4165	328	13	b(kn	b(kn	NUM
cana-4165	328	14	)	)	PUNCT
cana-4165	329	1	=	=	SYM
cana-4165	329	2	kn	kn	PROPN
cana-4165	329	3	/	/	PUNCT
cana-4165	329	4	(	(	PUNCT
cana-4165	329	5	1	1	NUM
cana-4165	329	6	+	+	CCONJ
cana-4165	329	7	kn	kn	PROPN
cana-4165	329	8	)	)	PUNCT
cana-4165	329	9	this	this	DET
cana-4165	329	10	basic	basic	ADJ
cana-4165	329	11	statement	statement	NOUN
cana-4165	329	12	encapsulates	encapsulate	VERB
cana-4165	329	13	the	the	DET
cana-4165	329	14	fundamental	fundamental	ADJ
cana-4165	329	15	physics	physics	NOUN
cana-4165	329	16	of	of	ADP
cana-4165	329	17	the	the	DET
cana-4165	329	18	ballistic	ballistic	ADJ
cana-4165	329	19	-	-	PUNCT
cana-4165	329	20	diffusive	diffusive	ADJ
cana-4165	329	21	transition	transition	NOUN
cana-4165	329	22	and	and	CCONJ
cana-4165	329	23	offers	offer	VERB
cana-4165	329	24	a	a	DET
cana-4165	329	25	basis	basis	NOUN
cana-4165	329	26	for	for	ADP
cana-4165	329	27	our	our	PRON
cana-4165	329	28	unified	unified	ADJ
cana-4165	329	29	asymptotic	asymptotic	ADJ
cana-4165	329	30	expansion	expansion	NOUN
cana-4165	329	31	that	that	PRON
cana-4165	329	32	is	be	AUX
cana-4165	329	33	still	still	ADV
cana-4165	329	34	applicable	applicable	ADJ
cana-4165	329	35	over	over	ADP
cana-4165	329	36	all	all	DET
cana-4165	329	37	transport	transport	NOUN
cana-4165	329	38	regimes	regime	NOUN
cana-4165	329	39	.	.	PUNCT
cana-4165	330	1	asymptotic	asymptotic	ADJ
cana-4165	330	2	expansion	expansion	NOUN
cana-4165	330	3	:	:	PUNCT
cana-4165	330	4	unified	unify	VERB
cana-4165	330	5	framework	framework	NOUN
cana-4165	330	6	we	we	PRON
cana-4165	330	7	have	have	AUX
cana-4165	330	8	built	build	VERB
cana-4165	330	9	a	a	DET
cana-4165	330	10	consistent	consistent	ADJ
cana-4165	330	11	framework	framework	NOUN
cana-4165	330	12	for	for	ADP
cana-4165	330	13	the	the	DET
cana-4165	330	14	asymptotic	asymptotic	ADJ
cana-4165	330	15	expansion	expansion	NOUN
cana-4165	330	16	of	of	ADP
cana-4165	330	17	electron	electron	NOUN
cana-4165	330	18	mean	mean	NOUN
cana-4165	330	19	velocities	velocity	NOUN
cana-4165	330	20	by	by	ADP
cana-4165	330	21	using	use	VERB
cana-4165	330	22	the	the	DET
cana-4165	330	23	insights	insight	NOUN
cana-4165	330	24	from	from	ADP
cana-4165	330	25	our	our	PRON
cana-4165	330	26	experimental	experimental	ADJ
cana-4165	330	27	and	and	CCONJ
cana-4165	330	28	computational	computational	ADJ
cana-4165	330	29	studies	study	NOUN
cana-4165	330	30	.	.	PUNCT
cana-4165	331	1	this	this	DET
cana-4165	331	2	framework	framework	NOUN
cana-4165	331	3	spans	span	VERB
cana-4165	331	4	several	several	ADJ
cana-4165	331	5	material	material	NOUN
cana-4165	331	6	systems	system	NOUN
cana-4165	331	7	,	,	PUNCT
cana-4165	331	8	dimensional	dimensional	ADJ
cana-4165	331	9	confinements	confinement	NOUN
cana-4165	331	10	,	,	PUNCT
cana-4165	331	11	and	and	CCONJ
cana-4165	331	12	transport	transport	NOUN
cana-4165	331	13	rules	rule	NOUN
cana-4165	331	14	via	via	ADP
cana-4165	331	15	suitably	suitably	ADV
cana-4165	331	16	parameterized	parameterized	ADJ
cana-4165	331	17	forms	form	NOUN
cana-4165	331	18	.	.	PUNCT
cana-4165	332	1	communications	communication	NOUN
cana-4165	332	2	on	on	ADP
cana-4165	332	3	applied	apply	VERB
cana-4165	332	4	nonlinear	nonlinear	ADJ
cana-4165	332	5	analysis	analysis	NOUN
cana-4165	332	6	issn	issn	NOUN
cana-4165	332	7	:	:	PUNCT
cana-4165	332	8	1074	1074	NUM
cana-4165	332	9	-	-	PUNCT
cana-4165	332	10	133x	133x	NUM
cana-4165	332	11	vol	vol	NOUN
cana-4165	332	12	32	32	NUM
cana-4165	332	13	no	no	NOUN
cana-4165	332	14	.	.	PUNCT
cana-4165	333	1	9s	9s	NUM
cana-4165	333	2	(	(	PUNCT
cana-4165	333	3	2025	2025	NUM
cana-4165	333	4	)	)	PUNCT
cana-4165	333	5	1405	1405	NUM
cana-4165	333	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	334	1	our	our	PRON
cana-4165	334	2	extension	extension	NOUN
cana-4165	334	3	for	for	ADP
cana-4165	334	4	three	three	NUM
cana-4165	334	5	-	-	PUNCT
cana-4165	334	6	dimensional	dimensional	ADJ
cana-4165	334	7	systems	system	NOUN
cana-4165	334	8	in	in	ADP
cana-4165	334	9	the	the	DET
cana-4165	334	10	diffusive	diffusive	ADJ
cana-4165	334	11	regime	regime	NOUN
cana-4165	334	12	(	(	PUNCT
cana-4165	334	13	kn	kn	NOUN
cana-4165	334	14	<	<	X
cana-4165	334	15	1	1	NUM
cana-4165	334	16	)	)	PUNCT
cana-4165	334	17	follows	follow	VERB
cana-4165	334	18	:	:	PUNCT
cana-4165	334	19	v(e	v(e	NUM
cana-4165	334	20	)	)	PUNCT
cana-4165	334	21	=	=	PUNCT
cana-4165	335	1	μ₀e	μ₀e	NUM
cana-4165	335	2	/	/	PUNCT
cana-4165	336	1	[	[	X
cana-4165	336	2	1	1	NUM
cana-4165	336	3	+	+	CCONJ
cana-4165	336	4	(	(	PUNCT
cana-4165	336	5	e	e	NOUN
cana-4165	336	6	/	/	SYM
cana-4165	336	7	ec)α]^(1	ec)α]^(1	NOUN
cana-4165	336	8	/	/	SYM
cana-4165	336	9	β	β	NOUN
cana-4165	336	10	)	)	PUNCT
cana-4165	336	11	using	use	VERB
cana-4165	336	12	parameters	parameter	NOUN
cana-4165	336	13	μ₀	μ₀	PROPN
cana-4165	336	14	,	,	PUNCT
cana-4165	336	15	ec	ec	PROPN
cana-4165	336	16	,	,	PUNCT
cana-4165	336	17	α	α	NOUN
cana-4165	336	18	,	,	PUNCT
cana-4165	336	19	and	and	CCONJ
cana-4165	336	20	β	β	NOUN
cana-4165	336	21	established	establish	VERB
cana-4165	336	22	from	from	ADP
cana-4165	336	23	material	material	ADJ
cana-4165	336	24	characteristics	characteristic	NOUN
cana-4165	336	25	and	and	CCONJ
cana-4165	336	26	scattering	scatter	VERB
cana-4165	336	27	processes	process	NOUN
cana-4165	336	28	.	.	PUNCT
cana-4165	337	1	the	the	DET
cana-4165	337	2	expansion	expansion	NOUN
cana-4165	337	3	for	for	ADP
cana-4165	337	4	two	two	NUM
cana-4165	337	5	-	-	PUNCT
cana-4165	337	6	dimensional	dimensional	ADJ
cana-4165	337	7	systems	system	NOUN
cana-4165	337	8	streamlines	streamline	NOUN
cana-4165	337	9	to	to	ADP
cana-4165	337	10	:	:	PUNCT
cana-4165	337	11	v(e	v(e	PROPN
cana-4165	337	12	)	)	PUNCT
cana-4165	337	13	=	=	PUNCT
cana-4165	338	1	μ₀e	μ₀e	NUM
cana-4165	338	2	/	/	PUNCT
cana-4165	339	1	[	[	X
cana-4165	339	2	1	1	NUM
cana-4165	339	3	+	+	NUM
cana-4165	339	4	(	(	PUNCT
cana-4165	339	5	(	(	PUNCT
cana-4165	339	6	μ₀e)/(vsat))^β]^(1	μ₀e)/(vsat))^β]^(1	X
cana-4165	339	7	/	/	SYM
cana-4165	339	8	β	β	NOUN
cana-4165	339	9	)	)	PUNCT
cana-4165	339	10	reflecting	reflect	VERB
cana-4165	339	11	the	the	DET
cana-4165	339	12	modified	modified	ADJ
cana-4165	339	13	scattering	scattering	NOUN
cana-4165	339	14	processes	process	NOUN
cana-4165	339	15	in	in	ADP
cana-4165	339	16	reduced	reduce	VERB
cana-4165	339	17	dimensions	dimension	NOUN
cana-4165	339	18	.	.	PUNCT
cana-4165	340	1	for	for	ADP
cana-4165	340	2	one	one	NUM
cana-4165	340	3	-	-	PUNCT
cana-4165	340	4	dimensional	dimensional	ADJ
cana-4165	340	5	systems	system	NOUN
cana-4165	340	6	,	,	PUNCT
cana-4165	340	7	the	the	DET
cana-4165	340	8	abrupt	abrupt	ADJ
cana-4165	340	9	transition	transition	NOUN
cana-4165	340	10	to	to	ADP
cana-4165	340	11	saturation	saturation	NOUN
cana-4165	340	12	is	be	AUX
cana-4165	340	13	captured	capture	VERB
cana-4165	340	14	by	by	ADP
cana-4165	340	15	:	:	PUNCT
cana-4165	340	16	v(e	v(e	NUM
cana-4165	340	17	)	)	PUNCT
cana-4165	341	1	=	=	NOUN
cana-4165	342	1	v₀	v₀	NOUN
cana-4165	342	2	·	·	PUNCT
cana-4165	343	1	[	[	X
cana-4165	343	2	1	1	NUM
cana-4165	343	3	exp(-(μ₀e	exp(-(μ₀e	NOUN
cana-4165	343	4	/	/	SYM
cana-4165	343	5	v₀)δ	v₀)δ	NOUN
cana-4165	343	6	)	)	PUNCT
cana-4165	343	7	]	]	PUNCT
cana-4165	343	8	with	with	SCONJ
cana-4165	343	9	parameters	parameter	NOUN
cana-4165	343	10	v₀	v₀	VERB
cana-4165	343	11	,	,	PUNCT
cana-4165	343	12	μ₀	μ₀	NOUN
cana-4165	343	13	,	,	PUNCT
cana-4165	343	14	and	and	CCONJ
cana-4165	343	15	δ	δ	PROPN
cana-4165	343	16	.	.	PUNCT
cana-4165	344	1	the	the	DET
cana-4165	344	2	transition	transition	NOUN
cana-4165	344	3	between	between	ADP
cana-4165	344	4	diffusive	diffusive	ADJ
cana-4165	344	5	and	and	CCONJ
cana-4165	344	6	ballistic	ballistic	ADJ
cana-4165	344	7	transport	transport	NOUN
cana-4165	344	8	is	be	AUX
cana-4165	344	9	incorporated	incorporate	VERB
cana-4165	344	10	through	through	ADP
cana-4165	344	11	the	the	DET
cana-4165	344	12	ballisticity	ballisticity	NOUN
cana-4165	344	13	factor	factor	NOUN
cana-4165	344	14	:	:	PUNCT
cana-4165	344	15	v(e	v(e	NUM
cana-4165	344	16	)	)	PUNCT
cana-4165	344	17	=	=	VERB
cana-4165	345	1	vinj	vinj	NOUN
cana-4165	345	2	·	·	PUNCT
cana-4165	346	1	[	[	X
cana-4165	346	2	kn	kn	X
cana-4165	346	3	/	/	SYM
cana-4165	346	4	(	(	PUNCT
cana-4165	346	5	1	1	NUM
cana-4165	346	6	+	+	CCONJ
cana-4165	346	7	kn	kn	PROPN
cana-4165	346	8	)	)	PUNCT
cana-4165	346	9	]	]	PUNCT
cana-4165	346	10	·	·	PUNCT
cana-4165	346	11	f(e	f(e	NOUN
cana-4165	346	12	)	)	PUNCT
cana-4165	346	13	here	here	ADV
cana-4165	346	14	vinj	vinj	NOUN
cana-4165	346	15	denotes	denote	NOUN
cana-4165	346	16	the	the	DET
cana-4165	346	17	injection	injection	NOUN
cana-4165	346	18	velocity	velocity	NOUN
cana-4165	346	19	characteristic	characteristic	NOUN
cana-4165	346	20	of	of	ADP
cana-4165	346	21	the	the	DET
cana-4165	346	22	ballistic	ballistic	ADJ
cana-4165	346	23	limit	limit	NOUN
cana-4165	346	24	and	and	CCONJ
cana-4165	346	25	f(e	f(e	NOUN
cana-4165	346	26	)	)	PUNCT
cana-4165	346	27	signifies	signify	VERB
cana-4165	346	28	the	the	DET
cana-4165	346	29	suitable	suitable	ADJ
cana-4165	346	30	field	field	NOUN
cana-4165	346	31	-	-	PUNCT
cana-4165	346	32	dependent	dependent	ADJ
cana-4165	346	33	function	function	NOUN
cana-4165	346	34	from	from	ADP
cana-4165	346	35	the	the	DET
cana-4165	346	36	diffusive	diffusive	ADJ
cana-4165	346	37	formulations	formulation	NOUN
cana-4165	346	38	above	above	ADV
cana-4165	346	39	.	.	PUNCT
cana-4165	347	1	this	this	DET
cana-4165	347	2	consistent	consistent	ADJ
cana-4165	347	3	approach	approach	NOUN
cana-4165	347	4	offers	offer	VERB
cana-4165	347	5	a	a	DET
cana-4165	347	6	strong	strong	ADJ
cana-4165	347	7	instrument	instrument	NOUN
cana-4165	347	8	for	for	ADP
cana-4165	347	9	both	both	DET
cana-4165	347	10	basic	basic	ADJ
cana-4165	347	11	knowledge	knowledge	NOUN
cana-4165	347	12	and	and	CCONJ
cana-4165	347	13	device	device	NOUN
cana-4165	347	14	modeling	modeling	NOUN
cana-4165	347	15	since	since	SCONJ
cana-4165	347	16	it	it	PRON
cana-4165	347	17	precisely	precisely	ADV
cana-4165	347	18	characterizes	characterize	VERB
cana-4165	347	19	electron	electron	NOUN
cana-4165	347	20	mean	mean	NOUN
cana-4165	347	21	velocities	velocity	NOUN
cana-4165	347	22	over	over	ADP
cana-4165	347	23	all	all	DET
cana-4165	347	24	pertinent	pertinent	ADJ
cana-4165	347	25	regimes	regime	NOUN
cana-4165	347	26	.	.	PUNCT
cana-4165	348	1	discussion	discussion	NOUN
cana-4165	348	2	our	our	PRON
cana-4165	348	3	thorough	thorough	ADJ
cana-4165	348	4	study	study	NOUN
cana-4165	348	5	of	of	ADP
cana-4165	348	6	the	the	DET
cana-4165	348	7	asymptotic	asymptotic	ADJ
cana-4165	348	8	behavior	behavior	NOUN
cana-4165	348	9	of	of	ADP
cana-4165	348	10	electron	electron	NOUN
cana-4165	348	11	mean	mean	NOUN
cana-4165	348	12	velocities	velocity	NOUN
cana-4165	348	13	has	have	AUX
cana-4165	348	14	produced	produce	VERB
cana-4165	348	15	several	several	ADJ
cana-4165	348	16	important	important	ADJ
cana-4165	348	17	new	new	ADJ
cana-4165	348	18	discoveries	discovery	NOUN
cana-4165	348	19	with	with	ADP
cana-4165	348	20	major	major	ADJ
cana-4165	348	21	consequences	consequence	NOUN
cana-4165	348	22	for	for	ADP
cana-4165	348	23	basic	basic	ADJ
cana-4165	348	24	knowledge	knowledge	NOUN
cana-4165	348	25	and	and	CCONJ
cana-4165	348	26	useful	useful	ADJ
cana-4165	348	27	applications	application	NOUN
cana-4165	348	28	.	.	PUNCT
cana-4165	349	1	we	we	PRON
cana-4165	349	2	address	address	VERB
cana-4165	349	3	the	the	DET
cana-4165	349	4	larger	large	ADJ
cana-4165	349	5	relevance	relevance	NOUN
cana-4165	349	6	of	of	ADP
cana-4165	349	7	our	our	PRON
cana-4165	349	8	results	result	NOUN
cana-4165	349	9	in	in	ADP
cana-4165	349	10	this	this	DET
cana-4165	349	11	part	part	NOUN
cana-4165	349	12	together	together	ADV
cana-4165	349	13	with	with	ADP
cana-4165	349	14	their	their	PRON
cana-4165	349	15	connection	connection	NOUN
cana-4165	349	16	to	to	ADP
cana-4165	349	17	current	current	ADJ
cana-4165	349	18	theoretical	theoretical	ADJ
cana-4165	349	19	models	model	NOUN
cana-4165	349	20	.	.	PUNCT
cana-4165	350	1	among	among	ADP
cana-4165	350	2	the	the	DET
cana-4165	350	3	most	most	ADV
cana-4165	350	4	remarkable	remarkable	ADJ
cana-4165	350	5	aspects	aspect	NOUN
cana-4165	350	6	of	of	ADP
cana-4165	350	7	our	our	PRON
cana-4165	350	8	investigation	investigation	NOUN
cana-4165	350	9	are	be	AUX
cana-4165	350	10	the	the	DET
cana-4165	350	11	dimensions	dimension	NOUN
cana-4165	350	12	dependency	dependency	NOUN
cana-4165	350	13	of	of	ADP
cana-4165	350	14	transport	transport	NOUN
cana-4165	350	15	properties	property	NOUN
cana-4165	350	16	.	.	PUNCT
cana-4165	351	1	the	the	DET
cana-4165	351	2	functional	functional	ADJ
cana-4165	351	3	form	form	NOUN
cana-4165	351	4	of	of	ADP
cana-4165	351	5	the	the	DET
cana-4165	351	6	velocity	velocity	NOUN
cana-4165	351	7	-	-	PUNCT
cana-4165	351	8	field	field	NOUN
cana-4165	351	9	connection	connection	NOUN
cana-4165	351	10	changes	change	NOUN
cana-4165	351	11	qualitatively	qualitatively	ADV
cana-4165	351	12	as	as	SCONJ
cana-4165	351	13	dimensionality	dimensionality	NOUN
cana-4165	351	14	drops	drop	NOUN
cana-4165	351	15	from	from	ADP
cana-4165	351	16	three	three	NUM
cana-4165	351	17	to	to	PART
cana-4165	351	18	two	two	NUM
cana-4165	351	19	to	to	ADP
cana-4165	351	20	one	one	NUM
cana-4165	351	21	,	,	PUNCT
cana-4165	351	22	therefore	therefore	ADV
cana-4165	351	23	reflecting	reflect	VERB
cana-4165	351	24	the	the	DET
cana-4165	351	25	great	great	ADJ
cana-4165	351	26	impact	impact	NOUN
cana-4165	351	27	of	of	ADP
cana-4165	351	28	quantum	quantum	ADJ
cana-4165	351	29	confinement	confinement	NOUN
cana-4165	351	30	on	on	ADP
cana-4165	351	31	electron	electron	NOUN
cana-4165	351	32	dynamics	dynamic	NOUN
cana-4165	351	33	.	.	PUNCT
cana-4165	352	1	in	in	ADP
cana-4165	352	2	lower	lower	ADV
cana-4165	352	3	-	-	PUNCT
cana-4165	352	4	dimensional	dimensional	ADJ
cana-4165	352	5	systems	system	NOUN
cana-4165	352	6	,	,	PUNCT
cana-4165	352	7	the	the	DET
cana-4165	352	8	changed	change	VERB
cana-4165	352	9	density	density	NOUN
cana-4165	352	10	of	of	ADP
cana-4165	352	11	states	state	NOUN
cana-4165	352	12	and	and	CCONJ
cana-4165	352	13	limited	limited	ADJ
cana-4165	352	14	phase	phase	NOUN
cana-4165	352	15	space	space	NOUN
cana-4165	352	16	for	for	ADP
cana-4165	352	17	scattering	scatter	VERB
cana-4165	352	18	help	help	NOUN
cana-4165	352	19	one	one	NOUN
cana-4165	352	20	to	to	PART
cana-4165	352	21	understand	understand	VERB
cana-4165	352	22	this	this	DET
cana-4165	352	23	dimensional	dimensional	ADJ
cana-4165	352	24	progression	progression	NOUN
cana-4165	352	25	.	.	PUNCT
cana-4165	353	1	our	our	PRON
cana-4165	353	2	results	result	NOUN
cana-4165	353	3	verify	verify	VERB
cana-4165	353	4	the	the	DET
cana-4165	353	5	slow	slow	ADJ
cana-4165	353	6	transition	transition	NOUN
cana-4165	353	7	from	from	ADP
cana-4165	353	8	linear	linear	PROPN
cana-4165	353	9	(	(	PUNCT
cana-4165	353	10	ohmic	ohmic	ADJ
cana-4165	353	11	)	)	PUNCT
cana-4165	353	12	behavior	behavior	NOUN
cana-4165	353	13	to	to	ADP
cana-4165	353	14	saturation	saturation	NOUN
cana-4165	353	15	,	,	PUNCT
cana-4165	353	16	well	well	ADV
cana-4165	353	17	-	-	PUNCT
cana-4165	353	18	described	describe	VERB
cana-4165	353	19	by	by	ADP
cana-4165	353	20	the	the	DET
cana-4165	353	21	empirical	empirical	ADJ
cana-4165	353	22	formula	formula	NOUN
cana-4165	353	23	v(e	v(e	PROPN
cana-4165	353	24	)	)	PUNCT
cana-4165	354	1	=	=	PUNCT
cana-4165	355	1	μ₀e	μ₀e	NUM
cana-4165	355	2	/	/	PUNCT
cana-4165	356	1	[	[	X
cana-4165	356	2	1	1	NUM
cana-4165	356	3	+	+	CCONJ
cana-4165	356	4	(	(	PUNCT
cana-4165	356	5	e	e	NOUN
cana-4165	356	6	/	/	SYM
cana-4165	356	7	ec)α]^(1	ec)α]^(1	NOUN
cana-4165	356	8	/	/	SYM
cana-4165	356	9	β	β	NOUN
cana-4165	356	10	)	)	PUNCT
cana-4165	356	11	,	,	PUNCT
cana-4165	356	12	in	in	ADP
cana-4165	356	13	three	three	NUM
cana-4165	356	14	-	-	PUNCT
cana-4165	356	15	dimensional	dimensional	ADJ
cana-4165	356	16	bulk	bulk	ADJ
cana-4165	356	17	semiconductors	semiconductor	NOUN
cana-4165	356	18	.	.	PUNCT
cana-4165	357	1	usually	usually	ADV
cana-4165	357	2	falling	fall	VERB
cana-4165	357	3	between	between	ADP
cana-4165	357	4	1.7	1.7	NUM
cana-4165	357	5	and	and	CCONJ
cana-4165	357	6	2.0	2.0	NUM
cana-4165	357	7	,	,	PUNCT
cana-4165	357	8	the	the	DET
cana-4165	357	9	parameters	parameter	NOUN
cana-4165	357	10	α	α	PROPN
cana-4165	357	11	and	and	CCONJ
cana-4165	357	12	β	β	PROPN
cana-4165	357	13	represent	represent	VERB
cana-4165	357	14	the	the	DET
cana-4165	357	15	energy	energy	NOUN
cana-4165	357	16	dependency	dependency	NOUN
cana-4165	357	17	of	of	ADP
cana-4165	357	18	the	the	DET
cana-4165	357	19	main	main	ADJ
cana-4165	357	20	scattering	scatter	VERB
cana-4165	357	21	systems	system	NOUN
cana-4165	357	22	.	.	PUNCT
cana-4165	358	1	consistent	consistent	ADJ
cana-4165	358	2	across	across	ADP
cana-4165	358	3	many	many	ADJ
cana-4165	358	4	materials	material	NOUN
cana-4165	358	5	,	,	PUNCT
cana-4165	358	6	the	the	DET
cana-4165	358	7	modest	modest	ADJ
cana-4165	358	8	drop	drop	NOUN
cana-4165	358	9	in	in	ADP
cana-4165	358	10	these	these	DET
cana-4165	358	11	characteristics	characteristic	NOUN
cana-4165	358	12	with	with	ADP
cana-4165	358	13	increasing	increase	VERB
cana-4165	358	14	temperature	temperature	NOUN
cana-4165	358	15	points	point	NOUN
cana-4165	358	16	to	to	ADP
cana-4165	358	17	a	a	DET
cana-4165	358	18	smoothing	smoothing	NOUN
cana-4165	358	19	of	of	ADP
cana-4165	358	20	the	the	DET
cana-4165	358	21	transition	transition	NOUN
cana-4165	358	22	between	between	ADP
cana-4165	358	23	regimes	regime	NOUN
cana-4165	358	24	as	as	SCONJ
cana-4165	358	25	thermal	thermal	ADJ
cana-4165	358	26	broadening	broadening	NOUN
cana-4165	358	27	becomes	become	VERB
cana-4165	358	28	increasing	increase	VERB
cana-4165	358	29	importance	importance	NOUN
cana-4165	358	30	.	.	PUNCT
cana-4165	359	1	the	the	DET
cana-4165	359	2	simplified	simplified	ADJ
cana-4165	359	3	form	form	NOUN
cana-4165	359	4	v(e	v(e	NOUN
cana-4165	359	5	)	)	PUNCT
cana-4165	359	6	=	=	PUNCT
cana-4165	360	1	μ₀e	μ₀e	NUM
cana-4165	360	2	/	/	PUNCT
cana-4165	361	1	[	[	X
cana-4165	361	2	1	1	NUM
cana-4165	361	3	+	+	CCONJ
cana-4165	361	4	(	(	PUNCT
cana-4165	361	5	(	(	PUNCT
cana-4165	361	6	μ₀e	μ₀e	NOUN
cana-4165	361	7	/	/	SYM
cana-4165	361	8	vsat))^β]^(1	vsat))^β]^(1	NOUN
cana-4165	361	9	/	/	SYM
cana-4165	361	10	β	β	NOUN
cana-4165	361	11	)	)	PUNCT
cana-4165	361	12	sufficiently	sufficiently	ADV
cana-4165	361	13	describes	describe	VERB
cana-4165	361	14	the	the	DET
cana-4165	361	15	observed	observe	VERB
cana-4165	361	16	behavior	behavior	NOUN
cana-4165	361	17	for	for	ADP
cana-4165	361	18	two	two	NUM
cana-4165	361	19	-	-	PUNCT
cana-4165	361	20	dimensional	dimensional	ADJ
cana-4165	361	21	systems	system	NOUN
cana-4165	361	22	.	.	PUNCT
cana-4165	362	1	where	where	SCONJ
cana-4165	362	2	the	the	DET
cana-4165	362	3	scattering	scatter	VERB
cana-4165	362	4	processes	process	NOUN
cana-4165	362	5	show	show	VERB
cana-4165	362	6	less	less	ADJ
cana-4165	362	7	energy	energy	NOUN
cana-4165	362	8	dependence	dependence	NOUN
cana-4165	362	9	,	,	PUNCT
cana-4165	362	10	the	the	DET
cana-4165	362	11	elimination	elimination	NOUN
cana-4165	362	12	of	of	ADP
cana-4165	362	13	the	the	DET
cana-4165	362	14	separate	separate	ADJ
cana-4165	362	15	critical	critical	ADJ
cana-4165	362	16	field	field	NOUN
cana-4165	362	17	parameter	parameter	NOUN
cana-4165	362	18	ec	ec	PROPN
cana-4165	362	19	indicates	indicate	VERB
cana-4165	362	20	the	the	DET
cana-4165	362	21	more	more	ADV
cana-4165	362	22	direct	direct	ADJ
cana-4165	362	23	connection	connection	NOUN
cana-4165	362	24	between	between	ADP
cana-4165	362	25	low	low	ADJ
cana-4165	362	26	-	-	PUNCT
cana-4165	362	27	field	field	NOUN
cana-4165	362	28	mobility	mobility	NOUN
cana-4165	362	29	and	and	CCONJ
cana-4165	362	30	saturation	saturation	NOUN
cana-4165	362	31	velocity	velocity	NOUN
cana-4165	362	32	in	in	ADP
cana-4165	362	33	2d	2d	NOUN
cana-4165	362	34	systems	system	NOUN
cana-4165	362	35	.	.	PUNCT
cana-4165	363	1	strong	strong	ADJ
cana-4165	363	2	validation	validation	NOUN
cana-4165	363	3	of	of	ADP
cana-4165	363	4	our	our	PRON
cana-4165	363	5	theoretical	theoretical	ADJ
cana-4165	363	6	method	method	NOUN
cana-4165	363	7	communications	communication	NOUN
cana-4165	363	8	on	on	ADP
cana-4165	363	9	applied	apply	VERB
cana-4165	363	10	nonlinear	nonlinear	ADJ
cana-4165	363	11	analysis	analysis	NOUN
cana-4165	363	12	issn	issn	NOUN
cana-4165	363	13	:	:	PUNCT
cana-4165	363	14	1074	1074	NUM
cana-4165	363	15	-	-	PUNCT
cana-4165	363	16	133x	133x	NUM
cana-4165	363	17	vol	vol	NOUN
cana-4165	363	18	32	32	NUM
cana-4165	363	19	no	no	NOUN
cana-4165	363	20	.	.	PUNCT
cana-4165	364	1	9s	9s	NUM
cana-4165	364	2	(	(	PUNCT
cana-4165	364	3	2025	2025	NUM
cana-4165	364	4	)	)	PUNCT
cana-4165	364	5	1406	1406	NUM
cana-4165	364	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	364	7	is	be	AUX
cana-4165	364	8	given	give	VERB
cana-4165	364	9	by	by	ADP
cana-4165	364	10	the	the	DET
cana-4165	364	11	universal	universal	ADJ
cana-4165	364	12	scaling	scaling	ADJ
cana-4165	364	13	characteristic	characteristic	NOUN
cana-4165	364	14	seen	see	VERB
cana-4165	364	15	in	in	ADP
cana-4165	364	16	figure	figure	NOUN
cana-4165	364	17	6	6	NUM
cana-4165	364	18	,	,	PUNCT
cana-4165	364	19	where	where	SCONJ
cana-4165	364	20	data	datum	NOUN
cana-4165	364	21	for	for	ADP
cana-4165	364	22	various	various	ADJ
cana-4165	364	23	temperatures	temperature	NOUN
cana-4165	364	24	and	and	CCONJ
cana-4165	364	25	carrier	carrier	NOUN
cana-4165	364	26	densities	density	NOUN
cana-4165	364	27	compress	compress	VERB
cana-4165	364	28	onto	onto	ADP
cana-4165	364	29	a	a	DET
cana-4165	364	30	single	single	ADJ
cana-4165	364	31	curve	curve	NOUN
cana-4165	364	32	when	when	SCONJ
cana-4165	364	33	presented	present	VERB
cana-4165	364	34	in	in	ADP
cana-4165	364	35	normalized	normalize	VERB
cana-4165	364	36	coordinates	coordinate	NOUN
cana-4165	364	37	.	.	PUNCT
cana-4165	365	1	one	one	NUM
cana-4165	365	2	-	-	PUNCT
cana-4165	365	3	dimensional	dimensional	ADJ
cana-4165	365	4	transport	transport	NOUN
cana-4165	365	5	,	,	PUNCT
cana-4165	365	6	best	well	ADV
cana-4165	365	7	represented	represent	VERB
cana-4165	365	8	by	by	ADP
cana-4165	365	9	carbon	carbon	NOUN
cana-4165	365	10	nanotubes	nanotube	NOUN
cana-4165	365	11	,	,	PUNCT
cana-4165	365	12	has	have	VERB
cana-4165	365	13	essentially	essentially	ADV
cana-4165	365	14	different	different	ADJ
cana-4165	365	15	behavior	behavior	NOUN
cana-4165	365	16	marked	mark	VERB
cana-4165	365	17	by	by	ADP
cana-4165	365	18	a	a	DET
cana-4165	365	19	more	more	ADV
cana-4165	365	20	abrupt	abrupt	ADJ
cana-4165	365	21	shift	shift	NOUN
cana-4165	365	22	to	to	ADP
cana-4165	365	23	saturation	saturation	NOUN
cana-4165	365	24	.	.	PUNCT
cana-4165	366	1	through	through	ADP
cana-4165	366	2	the	the	DET
cana-4165	366	3	exponential	exponential	ADJ
cana-4165	366	4	term	term	NOUN
cana-4165	366	5	,	,	PUNCT
cana-4165	366	6	which	which	PRON
cana-4165	366	7	substitutes	substitute	VERB
cana-4165	366	8	the	the	DET
cana-4165	366	9	power	power	NOUN
cana-4165	366	10	-	-	PUNCT
cana-4165	366	11	law	law	NOUN
cana-4165	366	12	dependency	dependency	NOUN
cana-4165	366	13	discovered	discover	VERB
cana-4165	366	14	in	in	ADP
cana-4165	366	15	higher	high	ADJ
cana-4165	366	16	dimensions	dimension	NOUN
cana-4165	366	17	,	,	PUNCT
cana-4165	366	18	our	our	PRON
cana-4165	366	19	expression	expression	NOUN
cana-4165	366	20	v(e	v(e	PROPN
cana-4165	366	21	)	)	PUNCT
cana-4165	367	1	=	=	PUNCT
cana-4165	368	1	v₀	v₀	NOUN
cana-4165	368	2	·	·	PUNCT
cana-4165	369	1	[	[	X
cana-4165	369	2	1	1	NUM
cana-4165	369	3	exp(-μ₀e	exp(-μ₀e	NOUN
cana-4165	369	4	/	/	SYM
cana-4165	369	5	v₀)δ	v₀)δ	NOUN
cana-4165	369	6	]	]	PUNCT
cana-4165	369	7	captures	capture	VERB
cana-4165	369	8	this	this	DET
cana-4165	369	9	behavior	behavior	NOUN
cana-4165	369	10	.	.	PUNCT
cana-4165	370	1	the	the	DET
cana-4165	370	2	single	single	ADJ
cana-4165	370	3	character	character	NOUN
cana-4165	370	4	of	of	ADP
cana-4165	370	5	the	the	DET
cana-4165	370	6	density	density	NOUN
cana-4165	370	7	of	of	ADP
cana-4165	370	8	states	state	NOUN
cana-4165	370	9	in	in	ADP
cana-4165	370	10	one	one	NUM
cana-4165	370	11	dimension	dimension	NOUN
cana-4165	370	12	and	and	CCONJ
cana-4165	370	13	the	the	DET
cana-4165	370	14	resultant	resultant	NOUN
cana-4165	370	15	step	step	NOUN
cana-4165	370	16	-	-	PUNCT
cana-4165	370	17	like	like	ADJ
cana-4165	370	18	beginning	beginning	NOUN
cana-4165	370	19	of	of	ADP
cana-4165	370	20	optical	optical	ADJ
cana-4165	370	21	phonon	phonon	NOUN
cana-4165	370	22	emission	emission	NOUN
cana-4165	370	23	as	as	ADP
cana-4165	370	24	the	the	DET
cana-4165	370	25	main	main	ADJ
cana-4165	370	26	velocity	velocity	NOUN
cana-4165	370	27	-	-	PUNCT
cana-4165	370	28	limiting	limit	VERB
cana-4165	370	29	mechanism	mechanism	NOUN
cana-4165	370	30	reflect	reflect	VERB
cana-4165	370	31	in	in	ADP
cana-4165	370	32	this	this	DET
cana-4165	370	33	functional	functional	ADJ
cana-4165	370	34	form	form	NOUN
cana-4165	370	35	.	.	PUNCT
cana-4165	371	1	another	another	DET
cana-4165	371	2	important	important	ADJ
cana-4165	371	3	feature	feature	NOUN
cana-4165	371	4	of	of	ADP
cana-4165	371	5	our	our	PRON
cana-4165	371	6	results	result	NOUN
cana-4165	371	7	is	be	AUX
cana-4165	371	8	the	the	DET
cana-4165	371	9	change	change	NOUN
cana-4165	371	10	between	between	ADP
cana-4165	371	11	diffusive	diffusive	ADJ
cana-4165	371	12	and	and	CCONJ
cana-4165	371	13	ballistic	ballistic	ADJ
cana-4165	371	14	transport	transport	NOUN
cana-4165	371	15	,	,	PUNCT
cana-4165	371	16	measured	measure	VERB
cana-4165	371	17	through	through	ADP
cana-4165	371	18	the	the	DET
cana-4165	371	19	knudsen	knudsen	PROPN
cana-4165	371	20	number	number	NOUN
cana-4165	371	21	kn	kn	PROPN
cana-4165	371	22	=	=	PUNCT
cana-4165	371	23	λ	λ	PROPN
cana-4165	371	24	/	/	SYM
cana-4165	371	25	l.	l.	PROPN
cana-4165	371	26	observed	observe	VERB
cana-4165	371	27	over	over	ADP
cana-4165	371	28	several	several	ADJ
cana-4165	371	29	materials	material	NOUN
cana-4165	371	30	,	,	PUNCT
cana-4165	371	31	the	the	DET
cana-4165	371	32	universal	universal	ADJ
cana-4165	371	33	link	link	NOUN
cana-4165	371	34	between	between	ADP
cana-4165	371	35	the	the	DET
cana-4165	371	36	ballisticity	ballisticity	NOUN
cana-4165	371	37	factor	factor	NOUN
cana-4165	371	38	b	b	PROPN
cana-4165	371	39	and	and	CCONJ
cana-4165	371	40	kn	kn	PROPN
cana-4165	371	41	underlines	underline	VERB
cana-4165	371	42	the	the	DET
cana-4165	371	43	basic	basic	ADJ
cana-4165	371	44	character	character	NOUN
cana-4165	371	45	of	of	ADP
cana-4165	371	46	this	this	DET
cana-4165	371	47	transition	transition	NOUN
cana-4165	371	48	.	.	PUNCT
cana-4165	372	1	our	our	PRON
cana-4165	372	2	interpolation	interpolation	NOUN
cana-4165	372	3	formula	formula	NOUN
cana-4165	372	4	b(kn	b(kn	PROPN
cana-4165	372	5	)	)	PUNCT
cana-4165	373	1	=	=	SYM
cana-4165	373	2	kn	kn	PROPN
cana-4165	373	3	/	/	PUNCT
cana-4165	373	4	(	(	PUNCT
cana-4165	373	5	1	1	NUM
cana-4165	373	6	+	+	CCONJ
cana-4165	373	7	kn	kn	NOUN
cana-4165	373	8	)	)	PUNCT
cana-4165	373	9	offers	offer	VERB
cana-4165	373	10	a	a	DET
cana-4165	373	11	basic	basic	ADJ
cana-4165	373	12	but	but	CCONJ
cana-4165	373	13	correct	correct	ADJ
cana-4165	373	14	representation	representation	NOUN
cana-4165	373	15	of	of	ADP
cana-4165	373	16	this	this	DET
cana-4165	373	17	crossover	crossover	NOUN
cana-4165	373	18	,	,	PUNCT
cana-4165	373	19	therefore	therefore	ADV
cana-4165	373	20	allowing	allow	VERB
cana-4165	373	21	a	a	DET
cana-4165	373	22	consistent	consistent	ADJ
cana-4165	373	23	treatment	treatment	NOUN
cana-4165	373	24	of	of	ADP
cana-4165	373	25	devices	device	NOUN
cana-4165	373	26	throughout	throughout	ADP
cana-4165	373	27	all	all	DET
cana-4165	373	28	size	size	NOUN
cana-4165	373	29	scales	scale	NOUN
cana-4165	373	30	.	.	PUNCT
cana-4165	374	1	a	a	DET
cana-4165	374	2	third	third	ADJ
cana-4165	374	3	dimension	dimension	NOUN
cana-4165	374	4	in	in	ADP
cana-4165	374	5	our	our	PRON
cana-4165	374	6	parameter	parameter	NOUN
cana-4165	374	7	space	space	NOUN
cana-4165	374	8	,	,	PUNCT
cana-4165	374	9	temperature	temperature	NOUN
cana-4165	374	10	dependency	dependency	NOUN
cana-4165	374	11	reveals	reveal	VERB
cana-4165	374	12	unique	unique	ADJ
cana-4165	374	13	signals	signal	NOUN
cana-4165	374	14	of	of	ADP
cana-4165	374	15	several	several	ADJ
cana-4165	374	16	scattering	scatter	VERB
cana-4165	374	17	mechanisms	mechanism	NOUN
cana-4165	374	18	.	.	PUNCT
cana-4165	375	1	consistent	consistent	ADJ
cana-4165	375	2	with	with	ADP
cana-4165	375	3	theoretical	theoretical	ADJ
cana-4165	375	4	expectations	expectation	NOUN
cana-4165	375	5	based	base	VERB
cana-4165	375	6	on	on	ADP
cana-4165	375	7	deformation	deformation	NOUN
cana-4165	375	8	potential	potential	ADJ
cana-4165	375	9	theory	theory	NOUN
cana-4165	375	10	,	,	PUNCT
cana-4165	375	11	the	the	DET
cana-4165	375	12	roughly	roughly	ADV
cana-4165	375	13	t⁻	t⁻	NOUN
cana-4165	375	14	�	�	NOUN
cana-4165	375	15	·⁴	·⁴	PROPN
cana-4165	375	16	dependency	dependency	NOUN
cana-4165	375	17	of	of	ADP
cana-4165	375	18	mobility	mobility	NOUN
cana-4165	375	19	in	in	ADP
cana-4165	375	20	bulk	bulk	ADJ
cana-4165	375	21	silicon	silicon	NOUN
cana-4165	375	22	at	at	ADP
cana-4165	375	23	higher	high	ADJ
cana-4165	375	24	temperatures	temperature	NOUN
cana-4165	375	25	indicates	indicate	VERB
cana-4165	375	26	the	the	DET
cana-4165	375	27	predominance	predominance	NOUN
cana-4165	375	28	of	of	ADP
cana-4165	375	29	phonon	phonon	NOUN
cana-4165	375	30	scattering	scattering	NOUN
cana-4165	375	31	.	.	PUNCT
cana-4165	376	1	low	low	ADJ
cana-4165	376	2	-	-	PUNCT
cana-4165	376	3	dimensional	dimensional	ADJ
cana-4165	376	4	systems	system	NOUN
cana-4165	376	5	(	(	PUNCT
cana-4165	376	6	t⁻¹	t⁻¹	INTJ
cana-4165	376	7	to	to	ADP
cana-4165	376	8	t⁻¹·⁵	t⁻¹·⁵	NUM
cana-4165	376	9	)	)	PUNCT
cana-4165	376	10	show	show	VERB
cana-4165	376	11	a	a	DET
cana-4165	376	12	reduced	reduced	ADJ
cana-4165	376	13	temperature	temperature	NOUN
cana-4165	376	14	dependency	dependency	NOUN
cana-4165	376	15	reflecting	reflect	VERB
cana-4165	376	16	the	the	DET
cana-4165	376	17	modified	modify	VERB
cana-4165	376	18	phonon	phonon	NOUN
cana-4165	376	19	spectrum	spectrum	NOUN
cana-4165	376	20	and	and	CCONJ
cana-4165	376	21	limited	limited	ADJ
cana-4165	376	22	scattering	scattering	NOUN
cana-4165	376	23	phase	phase	NOUN
cana-4165	376	24	space	space	NOUN
cana-4165	376	25	.	.	PUNCT
cana-4165	377	1	particularly	particularly	ADV
cana-4165	377	2	clear	clear	ADJ
cana-4165	377	3	in	in	ADP
cana-4165	377	4	two	two	NUM
cana-4165	377	5	-	-	PUNCT
cana-4165	377	6	dimensional	dimensional	ADJ
cana-4165	377	7	systems	system	NOUN
cana-4165	377	8	like	like	ADP
cana-4165	377	9	graphene	graphene	NOUN
cana-4165	377	10	,	,	PUNCT
cana-4165	377	11	the	the	DET
cana-4165	377	12	carrier	carrier	NOUN
cana-4165	377	13	density	density	NOUN
cana-4165	377	14	dependence	dependence	NOUN
cana-4165	377	15	offers	offer	VERB
cana-4165	377	16	more	more	ADJ
cana-4165	377	17	understanding	understanding	NOUN
cana-4165	377	18	of	of	ADP
cana-4165	377	19	the	the	DET
cana-4165	377	20	fundamental	fundamental	ADJ
cana-4165	377	21	physics	physics	NOUN
cana-4165	377	22	.	.	PUNCT
cana-4165	378	1	with	with	ADP
cana-4165	378	2	mobility	mobility	NOUN
cana-4165	378	3	first	first	ADV
cana-4165	378	4	increasing	increase	VERB
cana-4165	378	5	and	and	CCONJ
cana-4165	378	6	then	then	ADV
cana-4165	378	7	dropping	drop	VERB
cana-4165	378	8	with	with	ADP
cana-4165	378	9	carrier	carrier	NOUN
cana-4165	378	10	density	density	NOUN
cana-4165	378	11	,	,	PUNCT
cana-4165	378	12	the	the	DET
cana-4165	378	13	non	non	ADJ
cana-4165	378	14	-	-	ADJ
cana-4165	378	15	monotonic	monotonic	ADJ
cana-4165	378	16	trend	trend	NOUN
cana-4165	378	17	seen	see	VERB
cana-4165	378	18	in	in	ADP
cana-4165	378	19	gaas	gaas	PROPN
cana-4165	378	20	/	/	SYM
cana-4165	378	21	algaas	algaas	ADJ
cana-4165	378	22	heterostructures	heterostructure	NOUN
cana-4165	378	23	reflects	reflect	VERB
cana-4165	378	24	the	the	DET
cana-4165	378	25	competing	compete	VERB
cana-4165	378	26	effects	effect	NOUN
cana-4165	378	27	of	of	ADP
cana-4165	378	28	greater	great	ADJ
cana-4165	378	29	screening	screening	NOUN
cana-4165	378	30	and	and	CCONJ
cana-4165	378	31	increasing	increase	VERB
cana-4165	378	32	interface	interface	NOUN
cana-4165	378	33	roughness	roughness	NOUN
cana-4165	378	34	scattering	scattering	NOUN
cana-4165	378	35	.	.	PUNCT
cana-4165	379	1	the	the	DET
cana-4165	379	2	unique	unique	ADJ
cana-4165	379	3	character	character	NOUN
cana-4165	379	4	of	of	ADP
cana-4165	379	5	transport	transport	NOUN
cana-4165	379	6	in	in	ADP
cana-4165	379	7	this	this	DET
cana-4165	379	8	dirac	dirac	NOUN
cana-4165	379	9	material	material	NOUN
cana-4165	379	10	is	be	AUX
cana-4165	379	11	confirmed	confirm	VERB
cana-4165	379	12	in	in	ADP
cana-4165	379	13	graphene	graphene	NOUN
cana-4165	379	14	by	by	ADP
cana-4165	379	15	the	the	DET
cana-4165	379	16	characteristic	characteristic	ADJ
cana-4165	379	17	scaling	scaling	NOUN
cana-4165	379	18	of	of	ADP
cana-4165	379	19	parameters	parameter	NOUN
cana-4165	379	20	with	with	ADP
cana-4165	379	21	carrier	carrier	NOUN
cana-4165	379	22	density	density	NOUN
cana-4165	379	23	(	(	PUNCT
cana-4165	379	24	v₀	v₀	PROPN
cana-4165	379	25	∝	∝	PROPN
cana-4165	379	26	n⁻½	n⁻½	PROPN
cana-4165	379	27	,	,	PUNCT
cana-4165	379	28	e₀	e₀	ADJ
cana-4165	379	29	∯	∯	ADV
cana-4165	379	30	n½	n½	X
cana-4165	379	31	)	)	PUNCT
cana-4165	379	32	.	.	PUNCT
cana-4165	380	1	comparative	comparative	ADJ
cana-4165	380	2	analysis	analysis	NOUN
cana-4165	380	3	of	of	ADP
cana-4165	380	4	several	several	ADJ
cana-4165	380	5	material	material	NOUN
cana-4165	380	6	systems	system	NOUN
cana-4165	380	7	reveals	reveal	VERB
cana-4165	380	8	both	both	CCONJ
cana-4165	380	9	universal	universal	ADJ
cana-4165	380	10	and	and	CCONJ
cana-4165	380	11	material	material	NOUN
cana-4165	380	12	-	-	PUNCT
cana-4165	380	13	specific	specific	ADJ
cana-4165	380	14	properties	property	NOUN
cana-4165	380	15	.	.	PUNCT
cana-4165	381	1	the	the	DET
cana-4165	381	2	universal	universal	ADJ
cana-4165	381	3	features	feature	NOUN
cana-4165	381	4	consist	consist	VERB
cana-4165	381	5	in	in	ADP
cana-4165	381	6	the	the	DET
cana-4165	381	7	scaling	scale	VERB
cana-4165	381	8	behaviors	behavior	NOUN
cana-4165	381	9	of	of	ADP
cana-4165	381	10	dimensionless	dimensionless	NOUN
cana-4165	381	11	quantities	quantity	NOUN
cana-4165	381	12	such	such	DET
cana-4165	381	13	the	the	DET
cana-4165	381	14	knudsen	knudsen	PROPN
cana-4165	381	15	number	number	NOUN
cana-4165	381	16	and	and	CCONJ
cana-4165	381	17	in	in	ADP
cana-4165	381	18	the	the	DET
cana-4165	381	19	functional	functional	ADJ
cana-4165	381	20	forms	form	NOUN
cana-4165	381	21	of	of	ADP
cana-4165	381	22	our	our	PRON
cana-4165	381	23	asymptotic	asymptotic	ADJ
cana-4165	381	24	expansions	expansion	NOUN
cana-4165	381	25	.	.	PUNCT
cana-4165	382	1	numerical	numerical	ADJ
cana-4165	382	2	values	value	NOUN
cana-4165	382	3	of	of	ADP
cana-4165	382	4	parameters	parameter	NOUN
cana-4165	382	5	include	include	VERB
cana-4165	382	6	mobility	mobility	NOUN
cana-4165	382	7	,	,	PUNCT
cana-4165	382	8	critical	critical	ADJ
cana-4165	382	9	field	field	NOUN
cana-4165	382	10	,	,	PUNCT
cana-4165	382	11	and	and	CCONJ
cana-4165	382	12	saturation	saturation	NOUN
cana-4165	382	13	velocity	velocity	NOUN
cana-4165	382	14	show	show	VERB
cana-4165	382	15	material	material	NOUN
cana-4165	382	16	-	-	PUNCT
cana-4165	382	17	specific	specific	ADJ
cana-4165	382	18	characteristics	characteristic	NOUN
cana-4165	382	19	reflecting	reflect	VERB
cana-4165	382	20	the	the	DET
cana-4165	382	21	band	band	NOUN
cana-4165	382	22	structure	structure	NOUN
cana-4165	382	23	and	and	CCONJ
cana-4165	382	24	scattering	scatter	VERB
cana-4165	382	25	mechanisms	mechanism	NOUN
cana-4165	382	26	unique	unique	ADJ
cana-4165	382	27	to	to	ADP
cana-4165	382	28	every	every	DET
cana-4165	382	29	material	material	NOUN
cana-4165	382	30	.	.	PUNCT
cana-4165	383	1	methodologically	methodologically	ADV
cana-4165	383	2	,	,	PUNCT
cana-4165	383	3	our	our	PRON
cana-4165	383	4	work	work	NOUN
cana-4165	383	5	shows	show	VERB
cana-4165	383	6	the	the	DET
cana-4165	383	7	additive	additive	ADJ
cana-4165	383	8	usefulness	usefulness	NOUN
cana-4165	383	9	of	of	ADP
cana-4165	383	10	analytical	analytical	ADJ
cana-4165	383	11	theory	theory	NOUN
cana-4165	383	12	,	,	PUNCT
cana-4165	383	13	numerical	numerical	PROPN
cana-4165	383	14	simulation	simulation	NOUN
cana-4165	383	15	,	,	PUNCT
cana-4165	383	16	and	and	CCONJ
cana-4165	383	17	experimental	experimental	ADJ
cana-4165	383	18	measurement	measurement	NOUN
cana-4165	383	19	.	.	PUNCT
cana-4165	384	1	while	while	SCONJ
cana-4165	384	2	numerical	numerical	ADJ
cana-4165	384	3	simulations	simulation	NOUN
cana-4165	384	4	allow	allow	VERB
cana-4165	384	5	investigation	investigation	NOUN
cana-4165	384	6	of	of	ADP
cana-4165	384	7	parameter	parameter	NOUN
cana-4165	384	8	regimes	regime	NOUN
cana-4165	384	9	unavailable	unavailable	ADJ
cana-4165	384	10	to	to	ADP
cana-4165	384	11	analytical	analytical	ADJ
cana-4165	384	12	treatment	treatment	NOUN
cana-4165	384	13	,	,	PUNCT
cana-4165	384	14	the	the	DET
cana-4165	384	15	analytical	analytical	ADJ
cana-4165	384	16	formulas	formula	NOUN
cana-4165	384	17	reveal	reveal	VERB
cana-4165	384	18	understanding	understanding	NOUN
cana-4165	384	19	of	of	ADP
cana-4165	384	20	scaling	scale	VERB
cana-4165	384	21	characteristics	characteristic	NOUN
cana-4165	384	22	and	and	CCONJ
cana-4165	384	23	asymptotic	asymptotic	ADJ
cana-4165	384	24	limitations	limitation	NOUN
cana-4165	384	25	.	.	PUNCT
cana-4165	385	1	experimental	experimental	ADJ
cana-4165	385	2	data	datum	NOUN
cana-4165	385	3	root	root	VERB
cana-4165	385	4	the	the	DET
cana-4165	385	5	theoretical	theoretical	ADJ
cana-4165	385	6	framework	framework	NOUN
cana-4165	385	7	in	in	ADP
cana-4165	385	8	physical	physical	ADJ
cana-4165	385	9	reality	reality	NOUN
cana-4165	385	10	and	and	CCONJ
cana-4165	385	11	expose	expose	VERB
cana-4165	385	12	surprising	surprising	ADJ
cana-4165	385	13	events	event	NOUN
cana-4165	385	14	that	that	PRON
cana-4165	385	15	inspire	inspire	VERB
cana-4165	385	16	more	more	ADJ
cana-4165	385	17	theoretical	theoretical	ADJ
cana-4165	385	18	growth	growth	NOUN
cana-4165	385	19	.	.	PUNCT
cana-4165	386	1	our	our	PRON
cana-4165	386	2	results	result	NOUN
cana-4165	386	3	have	have	VERB
cana-4165	386	4	practical	practical	ADJ
cana-4165	386	5	consequences	consequence	NOUN
cana-4165	386	6	in	in	ADP
cana-4165	386	7	several	several	ADJ
cana-4165	386	8	technical	technical	ADJ
cana-4165	386	9	fields	field	NOUN
cana-4165	386	10	.	.	PUNCT
cana-4165	387	1	predicting	predict	VERB
cana-4165	387	2	high	high	ADJ
cana-4165	387	3	-	-	PUNCT
cana-4165	387	4	frequency	frequency	NOUN
cana-4165	387	5	performance	performance	NOUN
cana-4165	387	6	and	and	CCONJ
cana-4165	387	7	power	power	NOUN
cana-4165	387	8	dissipation	dissipation	NOUN
cana-4165	387	9	in	in	ADP
cana-4165	387	10	traditional	traditional	ADJ
cana-4165	387	11	semiconductor	semiconductor	NOUN
cana-4165	387	12	devices	device	NOUN
cana-4165	387	13	depends	depend	VERB
cana-4165	387	14	on	on	ADP
cana-4165	387	15	exact	exact	ADJ
cana-4165	387	16	modeling	modeling	NOUN
cana-4165	387	17	of	of	ADP
cana-4165	387	18	velocity	velocity	NOUN
cana-4165	387	19	-	-	PUNCT
cana-4165	387	20	field	field	NOUN
cana-4165	387	21	properties	property	NOUN
cana-4165	387	22	.	.	PUNCT
cana-4165	388	1	over	over	ADP
cana-4165	388	2	both	both	CCONJ
cana-4165	388	3	empirical	empirical	ADJ
cana-4165	388	4	models	model	NOUN
cana-4165	388	5	and	and	CCONJ
cana-4165	388	6	computationally	computationally	ADV
cana-4165	388	7	demanding	demand	VERB
cana-4165	388	8	microscopic	microscopic	ADJ
cana-4165	388	9	simulations	simulation	NOUN
cana-4165	388	10	,	,	PUNCT
cana-4165	388	11	our	our	PRON
cana-4165	388	12	asymptotic	asymptotic	ADJ
cana-4165	388	13	expansions	expansion	NOUN
cana-4165	388	14	yield	yield	VERB
cana-4165	388	15	concise	concise	ADJ
cana-4165	388	16	yet	yet	CCONJ
cana-4165	388	17	accurate	accurate	ADJ
cana-4165	388	18	expressions	expression	NOUN
cana-4165	388	19	fit	fit	ADJ
cana-4165	388	20	for	for	ADP
cana-4165	388	21	implementation	implementation	NOUN
cana-4165	388	22	in	in	ADP
cana-4165	388	23	device	device	NOUN
cana-4165	388	24	simulators	simulator	NOUN
cana-4165	388	25	.	.	PUNCT
cana-4165	389	1	communications	communication	NOUN
cana-4165	389	2	on	on	ADP
cana-4165	389	3	applied	apply	VERB
cana-4165	389	4	nonlinear	nonlinear	ADJ
cana-4165	389	5	analysis	analysis	NOUN
cana-4165	389	6	issn	issn	NOUN
cana-4165	389	7	:	:	PUNCT
cana-4165	389	8	1074	1074	NUM
cana-4165	389	9	-	-	PUNCT
cana-4165	389	10	133x	133x	NUM
cana-4165	389	11	vol	vol	NOUN
cana-4165	389	12	32	32	NUM
cana-4165	389	13	no	no	NOUN
cana-4165	389	14	.	.	PUNCT
cana-4165	390	1	9s	9s	NUM
cana-4165	390	2	(	(	PUNCT
cana-4165	390	3	2025	2025	NUM
cana-4165	390	4	)	)	PUNCT
cana-4165	390	5	1407	1407	NUM
cana-4165	390	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	391	1	our	our	PRON
cana-4165	391	2	unified	unified	ADJ
cana-4165	391	3	framework	framework	NOUN
cana-4165	391	4	accounting	account	VERB
cana-4165	391	5	for	for	ADP
cana-4165	391	6	the	the	DET
cana-4165	391	7	ballistic	ballistic	ADJ
cana-4165	391	8	-	-	PUNCT
cana-4165	391	9	diffusive	diffusive	ADJ
cana-4165	391	10	transition	transition	NOUN
cana-4165	391	11	becomes	become	VERB
cana-4165	391	12	especially	especially	ADV
cana-4165	391	13	important	important	ADJ
cana-4165	391	14	for	for	ADP
cana-4165	391	15	upcoming	upcoming	ADJ
cana-4165	391	16	nanoelectronic	nanoelectronic	PROPN
cana-4165	391	17	devices	device	NOUN
cana-4165	391	18	,	,	PUNCT
cana-4165	391	19	whose	whose	DET
cana-4165	391	20	dimensions	dimension	NOUN
cana-4165	391	21	approach	approach	VERB
cana-4165	391	22	or	or	CCONJ
cana-4165	391	23	go	go	VERB
cana-4165	391	24	below	below	ADP
cana-4165	391	25	typical	typical	ADJ
cana-4165	391	26	quantum	quantum	ADJ
cana-4165	391	27	length	length	NOUN
cana-4165	391	28	scales	scale	NOUN
cana-4165	391	29	.	.	PUNCT
cana-4165	392	1	simple	simple	ADJ
cana-4165	392	2	interpolation	interpolation	NOUN
cana-4165	392	3	formula	formula	NOUN
cana-4165	392	4	b(kn	b(kn	PROPN
cana-4165	392	5	)	)	PUNCT
cana-4165	393	1	=	=	SYM
cana-4165	393	2	kn	kn	PROPN
cana-4165	393	3	/	/	PUNCT
cana-4165	393	4	(	(	PUNCT
cana-4165	393	5	1	1	NUM
cana-4165	393	6	+	+	CCONJ
cana-4165	393	7	kn	kn	NOUN
cana-4165	393	8	)	)	PUNCT
cana-4165	393	9	allows	allow	VERB
cana-4165	393	10	easy	easy	ADJ
cana-4165	393	11	modification	modification	NOUN
cana-4165	393	12	of	of	ADP
cana-4165	393	13	current	current	ADJ
cana-4165	393	14	device	device	NOUN
cana-4165	393	15	models	model	NOUN
cana-4165	393	16	to	to	PART
cana-4165	393	17	include	include	VERB
cana-4165	393	18	ballistic	ballistic	ADJ
cana-4165	393	19	effects	effect	NOUN
cana-4165	393	20	,	,	PUNCT
cana-4165	393	21	hence	hence	ADV
cana-4165	393	22	enabling	enable	VERB
cana-4165	393	23	predictive	predictive	ADJ
cana-4165	393	24	design	design	NOUN
cana-4165	393	25	of	of	ADP
cana-4165	393	26	nanoscale	nanoscale	NOUN
cana-4165	393	27	transistors	transistor	NOUN
cana-4165	393	28	,	,	PUNCT
cana-4165	393	29	sensors	sensor	NOUN
cana-4165	393	30	,	,	PUNCT
cana-4165	393	31	and	and	CCONJ
cana-4165	393	32	other	other	ADJ
cana-4165	393	33	electronic	electronic	ADJ
cana-4165	393	34	components	component	NOUN
cana-4165	393	35	.	.	PUNCT
cana-4165	394	1	within	within	ADP
cana-4165	394	2	the	the	DET
cana-4165	394	3	field	field	NOUN
cana-4165	394	4	of	of	ADP
cana-4165	394	5	quantum	quantum	ADJ
cana-4165	394	6	information	information	NOUN
cana-4165	394	7	technology	technology	NOUN
cana-4165	394	8	,	,	PUNCT
cana-4165	394	9	our	our	PRON
cana-4165	394	10	thorough	thorough	ADJ
cana-4165	394	11	knowledge	knowledge	NOUN
cana-4165	394	12	of	of	ADP
cana-4165	394	13	electron	electron	NOUN
cana-4165	394	14	dynamics	dynamic	NOUN
cana-4165	394	15	guides	guide	VERB
cana-4165	394	16	the	the	DET
cana-4165	394	17	design	design	NOUN
cana-4165	394	18	of	of	ADP
cana-4165	394	19	quantum	quantum	ADJ
cana-4165	394	20	wires	wire	NOUN
cana-4165	394	21	,	,	PUNCT
cana-4165	394	22	quantum	quantum	ADJ
cana-4165	394	23	dots	dot	NOUN
cana-4165	394	24	,	,	PUNCT
cana-4165	394	25	and	and	CCONJ
cana-4165	394	26	other	other	ADJ
cana-4165	394	27	constructions	construction	NOUN
cana-4165	394	28	applied	apply	VERB
cana-4165	394	29	for	for	ADP
cana-4165	394	30	qubit	qubit	NOUN
cana-4165	394	31	implementation	implementation	NOUN
cana-4165	394	32	.	.	PUNCT
cana-4165	395	1	essential	essential	ADJ
cana-4165	395	2	direction	direction	NOUN
cana-4165	395	3	for	for	ADP
cana-4165	395	4	maximizing	maximize	VERB
cana-4165	395	5	these	these	DET
cana-4165	395	6	quantum	quantum	ADJ
cana-4165	395	7	devices	device	NOUN
cana-4165	395	8	is	be	AUX
cana-4165	395	9	given	give	VERB
cana-4165	395	10	by	by	ADP
cana-4165	395	11	the	the	DET
cana-4165	395	12	quantification	quantification	NOUN
cana-4165	395	13	of	of	ADP
cana-4165	395	14	mobility	mobility	NOUN
cana-4165	395	15	,	,	PUNCT
cana-4165	395	16	coherence	coherence	NOUN
cana-4165	395	17	lengths	length	NOUN
cana-4165	395	18	,	,	PUNCT
cana-4165	395	19	and	and	CCONJ
cana-4165	395	20	their	their	PRON
cana-4165	395	21	influence	influence	NOUN
cana-4165	395	22	on	on	ADP
cana-4165	395	23	material	material	ADJ
cana-4165	395	24	characteristics	characteristic	NOUN
cana-4165	395	25	and	and	CCONJ
cana-4165	395	26	temperature	temperature	NOUN
cana-4165	395	27	.	.	PUNCT
cana-4165	396	1	many	many	ADJ
cana-4165	396	2	unanswered	unanswered	ADJ
cana-4165	396	3	questions	question	NOUN
cana-4165	396	4	remain	remain	VERB
cana-4165	396	5	for	for	ADP
cana-4165	396	6	future	future	ADJ
cana-4165	396	7	research	research	NOUN
cana-4165	396	8	notwithstanding	notwithstanding	ADP
cana-4165	396	9	these	these	DET
cana-4165	396	10	developments	development	NOUN
cana-4165	396	11	.	.	PUNCT
cana-4165	397	1	further	further	ADJ
cana-4165	397	2	explanation	explanation	NOUN
cana-4165	397	3	is	be	AUX
cana-4165	397	4	needed	need	VERB
cana-4165	397	5	on	on	ADP
cana-4165	397	6	the	the	DET
cana-4165	397	7	interaction	interaction	NOUN
cana-4165	397	8	of	of	ADP
cana-4165	397	9	several	several	ADJ
cana-4165	397	10	scattering	scatter	VERB
cana-4165	397	11	mechanisms	mechanism	NOUN
cana-4165	397	12	in	in	ADP
cana-4165	397	13	defining	define	VERB
cana-4165	397	14	the	the	DET
cana-4165	397	15	general	general	ADJ
cana-4165	397	16	transport	transport	NOUN
cana-4165	397	17	behavior	behavior	NOUN
cana-4165	397	18	,	,	PUNCT
cana-4165	397	19	especially	especially	ADV
cana-4165	397	20	on	on	ADP
cana-4165	397	21	the	the	DET
cana-4165	397	22	component	component	NOUN
cana-4165	397	23	of	of	ADP
cana-4165	397	24	electron	electron	NOUN
cana-4165	397	25	-	-	PUNCT
cana-4165	397	26	electron	electron	NOUN
cana-4165	397	27	interactions	interaction	NOUN
cana-4165	397	28	in	in	ADP
cana-4165	397	29	high	high	ADJ
cana-4165	397	30	-	-	PUNCT
cana-4165	397	31	density	density	NOUN
cana-4165	397	32	systems	system	NOUN
cana-4165	397	33	.	.	PUNCT
cana-4165	398	1	more	more	ADV
cana-4165	398	2	thorough	thorough	ADJ
cana-4165	398	3	investigation	investigation	NOUN
cana-4165	398	4	is	be	AUX
cana-4165	398	5	warranted	warrant	VERB
cana-4165	398	6	on	on	ADP
cana-4165	398	7	the	the	DET
cana-4165	398	8	effect	effect	NOUN
cana-4165	398	9	of	of	ADP
cana-4165	398	10	disorder	disorder	NOUN
cana-4165	398	11	—	—	PUNCT
cana-4165	398	12	both	both	CCONJ
cana-4165	398	13	intrinsic	intrinsic	ADJ
cana-4165	398	14	and	and	CCONJ
cana-4165	398	15	extrinsic	extrinsic	ADJ
cana-4165	398	16	—	—	PUNCT
cana-4165	398	17	on	on	ADP
cana-4165	398	18	the	the	DET
cana-4165	398	19	asymptotic	asymptotic	ADJ
cana-4165	398	20	behavior	behavior	NOUN
cana-4165	398	21	of	of	ADP
cana-4165	398	22	electron	electron	NOUN
cana-4165	398	23	velocities	velocity	NOUN
cana-4165	398	24	,	,	PUNCT
cana-4165	398	25	particularly	particularly	ADV
cana-4165	398	26	in	in	ADP
cana-4165	398	27	relation	relation	NOUN
cana-4165	398	28	to	to	ADP
cana-4165	398	29	newly	newly	ADV
cana-4165	398	30	developed	develop	VERB
cana-4165	398	31	two	two	NUM
cana-4165	398	32	-	-	PUNCT
cana-4165	398	33	dimensional	dimensional	ADJ
cana-4165	398	34	materials	material	NOUN
cana-4165	398	35	outside	outside	ADP
cana-4165	398	36	graphene	graphene	NOUN
cana-4165	398	37	.	.	PUNCT
cana-4165	399	1	another	another	DET
cana-4165	399	2	boundary	boundary	NOUN
cana-4165	399	3	for	for	ADP
cana-4165	399	4	future	future	ADJ
cana-4165	399	5	study	study	NOUN
cana-4165	399	6	is	be	AUX
cana-4165	399	7	extending	extend	VERB
cana-4165	399	8	our	our	PRON
cana-4165	399	9	approach	approach	NOUN
cana-4165	399	10	to	to	ADP
cana-4165	399	11	strongly	strongly	ADV
cana-4165	399	12	coupled	couple	VERB
cana-4165	399	13	systems	system	NOUN
cana-4165	399	14	,	,	PUNCT
cana-4165	399	15	where	where	SCONJ
cana-4165	399	16	independent	independent	ADJ
cana-4165	399	17	-	-	PUNCT
cana-4165	399	18	electron	electron	NOUN
cana-4165	399	19	approximations	approximation	NOUN
cana-4165	399	20	fall	fall	VERB
cana-4165	399	21	down	down	ADP
cana-4165	399	22	.	.	PUNCT
cana-4165	400	1	more	more	ADV
cana-4165	400	2	complex	complex	ADJ
cana-4165	400	3	theoretical	theoretical	ADJ
cana-4165	400	4	techniques	technique	NOUN
cana-4165	400	5	are	be	AUX
cana-4165	400	6	required	require	VERB
cana-4165	400	7	for	for	ADP
cana-4165	400	8	materials	material	NOUN
cana-4165	400	9	such	such	ADJ
cana-4165	400	10	transition	transition	NOUN
cana-4165	400	11	metal	metal	NOUN
cana-4165	400	12	oxides	oxide	NOUN
cana-4165	400	13	and	and	CCONJ
cana-4165	400	14	heavy	heavy	ADJ
cana-4165	400	15	-	-	PUNCT
cana-4165	400	16	fermion	fermion	NOUN
cana-4165	400	17	compounds	compound	NOUN
cana-4165	400	18	since	since	SCONJ
cana-4165	400	19	their	their	PRON
cana-4165	400	20	transport	transport	NOUN
cana-4165	400	21	behavior	behavior	NOUN
cana-4165	400	22	differs	differ	VERB
cana-4165	400	23	greatly	greatly	ADV
cana-4165	400	24	from	from	ADP
cana-4165	400	25	those	those	PRON
cana-4165	400	26	of	of	ADP
cana-4165	400	27	typical	typical	ADJ
cana-4165	400	28	models	model	NOUN
cana-4165	400	29	.	.	PUNCT
cana-4165	401	1	at	at	ADP
cana-4165	401	2	last	last	ADJ
cana-4165	401	3	,	,	PUNCT
cana-4165	401	4	a	a	DET
cana-4165	401	5	rich	rich	ADJ
cana-4165	401	6	field	field	NOUN
cana-4165	401	7	for	for	ADP
cana-4165	401	8	study	study	NOUN
cana-4165	401	9	is	be	AUX
cana-4165	401	10	presented	present	VERB
cana-4165	401	11	by	by	ADP
cana-4165	401	12	the	the	DET
cana-4165	401	13	dynamic	dynamic	ADJ
cana-4165	401	14	response	response	NOUN
cana-4165	401	15	of	of	ADP
cana-4165	401	16	electron	electron	NOUN
cana-4165	401	17	velocities	velocity	NOUN
cana-4165	401	18	under	under	ADP
cana-4165	401	19	timevarying	timevarye	VERB
cana-4165	401	20	fields	field	NOUN
cana-4165	401	21	.	.	PUNCT
cana-4165	402	1	although	although	SCONJ
cana-4165	402	2	our	our	PRON
cana-4165	402	3	present	present	ADJ
cana-4165	402	4	study	study	NOUN
cana-4165	402	5	mostly	mostly	ADV
cana-4165	402	6	addresses	address	VERB
cana-4165	402	7	steady	steady	ADJ
cana-4165	402	8	-	-	PUNCT
cana-4165	402	9	state	state	NOUN
cana-4165	402	10	behavior	behavior	NOUN
cana-4165	402	11	,	,	PUNCT
cana-4165	402	12	for	for	ADP
cana-4165	402	13	high	high	ADJ
cana-4165	402	14	-	-	PUNCT
cana-4165	402	15	frequency	frequency	NOUN
cana-4165	402	16	applications	application	NOUN
cana-4165	402	17	and	and	CCONJ
cana-4165	402	18	devices	device	NOUN
cana-4165	402	19	running	run	VERB
cana-4165	402	20	under	under	ADP
cana-4165	402	21	pulsed	pulse	VERB
cana-4165	402	22	conditions	condition	NOUN
cana-4165	402	23	the	the	DET
cana-4165	402	24	transient	transient	ADJ
cana-4165	402	25	response	response	NOUN
cana-4165	402	26	becomes	become	VERB
cana-4165	402	27	even	even	ADV
cana-4165	402	28	more	more	ADV
cana-4165	402	29	critical	critical	ADJ
cana-4165	402	30	.	.	PUNCT
cana-4165	403	1	conclusion	conclusion	NOUN
cana-4165	403	2	our	our	PRON
cana-4165	403	3	thorough	thorough	ADJ
cana-4165	403	4	study	study	NOUN
cana-4165	403	5	of	of	ADP
cana-4165	403	6	the	the	DET
cana-4165	403	7	asymptotic	asymptotic	ADJ
cana-4165	403	8	growth	growth	NOUN
cana-4165	403	9	of	of	ADP
cana-4165	403	10	electron	electron	NOUN
cana-4165	403	11	mean	mean	NOUN
cana-4165	403	12	velocities	velocity	NOUN
cana-4165	403	13	produces	produce	VERB
cana-4165	403	14	a	a	DET
cana-4165	403	15	consistent	consistent	ADJ
cana-4165	403	16	theoretical	theoretical	ADJ
cana-4165	403	17	framework	framework	NOUN
cana-4165	403	18	relevant	relevant	ADJ
cana-4165	403	19	over	over	ADP
cana-4165	403	20	several	several	ADJ
cana-4165	403	21	material	material	NOUN
cana-4165	403	22	systems	system	NOUN
cana-4165	403	23	,	,	PUNCT
cana-4165	403	24	dimensional	dimensional	ADJ
cana-4165	403	25	confinements	confinement	NOUN
cana-4165	403	26	,	,	PUNCT
cana-4165	403	27	and	and	CCONJ
cana-4165	403	28	transport	transport	NOUN
cana-4165	403	29	regimes	regime	NOUN
cana-4165	403	30	.	.	PUNCT
cana-4165	404	1	we	we	PRON
cana-4165	404	2	have	have	AUX
cana-4165	404	3	developed	develop	VERB
cana-4165	404	4	parameter	parameter	NOUN
cana-4165	404	5	-	-	PUNCT
cana-4165	404	6	specific	specific	ADJ
cana-4165	404	7	expressions	expression	NOUN
cana-4165	404	8	that	that	PRON
cana-4165	404	9	precisely	precisely	ADV
cana-4165	404	10	describe	describe	VERB
cana-4165	404	11	the	the	DET
cana-4165	404	12	velocity	velocity	NOUN
cana-4165	404	13	-	-	PUNCT
cana-4165	404	14	field	field	NOUN
cana-4165	404	15	relationship	relationship	NOUN
cana-4165	404	16	from	from	ADP
cana-4165	404	17	the	the	DET
cana-4165	404	18	linear	linear	ADJ
cana-4165	404	19	low	low	ADJ
cana-4165	404	20	-	-	PUNCT
cana-4165	404	21	field	field	NOUN
cana-4165	404	22	regime	regime	NOUN
cana-4165	404	23	to	to	ADP
cana-4165	404	24	saturation	saturation	NOUN
cana-4165	404	25	at	at	ADP
cana-4165	404	26	high	high	ADJ
cana-4165	404	27	fields	field	NOUN
cana-4165	404	28	,	,	PUNCT
cana-4165	404	29	and	and	CCONJ
cana-4165	404	30	from	from	ADP
cana-4165	404	31	simply	simply	ADV
cana-4165	404	32	diffusive	diffusive	ADJ
cana-4165	404	33	to	to	ADP
cana-4165	404	34	ballistic	ballistic	ADJ
cana-4165	404	35	transport	transport	NOUN
cana-4165	404	36	by	by	ADP
cana-4165	404	37	means	mean	NOUN
cana-4165	404	38	of	of	ADP
cana-4165	404	39	analytical	analytical	ADJ
cana-4165	404	40	theory	theory	NOUN
cana-4165	404	41	,	,	PUNCT
cana-4165	404	42	numerical	numerical	PROPN
cana-4165	404	43	simulation	simulation	NOUN
cana-4165	404	44	,	,	PUNCT
cana-4165	404	45	and	and	CCONJ
cana-4165	404	46	experimental	experimental	ADJ
cana-4165	404	47	validation	validation	NOUN
cana-4165	404	48	.	.	PUNCT
cana-4165	405	1	reflecting	reflect	VERB
cana-4165	405	2	the	the	DET
cana-4165	405	3	great	great	ADJ
cana-4165	405	4	impact	impact	NOUN
cana-4165	405	5	of	of	ADP
cana-4165	405	6	quantum	quantum	ADJ
cana-4165	405	7	confinement	confinement	NOUN
cana-4165	405	8	on	on	ADP
cana-4165	405	9	electron	electron	NOUN
cana-4165	405	10	dynamics	dynamic	NOUN
cana-4165	405	11	,	,	PUNCT
cana-4165	405	12	the	the	DET
cana-4165	405	13	dimensional	dimensional	ADJ
cana-4165	405	14	evolution	evolution	NOUN
cana-4165	405	15	of	of	ADP
cana-4165	405	16	transport	transport	NOUN
cana-4165	405	17	features	feature	NOUN
cana-4165	405	18	reveals	reveal	VERB
cana-4165	405	19	basic	basic	ADJ
cana-4165	405	20	changes	change	NOUN
cana-4165	405	21	in	in	ADP
cana-4165	405	22	the	the	DET
cana-4165	405	23	functional	functional	ADJ
cana-4165	405	24	structure	structure	NOUN
cana-4165	405	25	of	of	ADP
cana-4165	405	26	asymptotic	asymptotic	ADJ
cana-4165	405	27	expansions	expansion	NOUN
cana-4165	405	28	.	.	PUNCT
cana-4165	406	1	our	our	PRON
cana-4165	406	2	unified	unified	ADJ
cana-4165	406	3	method	method	NOUN
cana-4165	406	4	offers	offer	VERB
cana-4165	406	5	a	a	DET
cana-4165	406	6	strong	strong	ADJ
cana-4165	406	7	instrument	instrument	NOUN
cana-4165	406	8	for	for	ADP
cana-4165	406	9	both	both	PRON
cana-4165	406	10	basic	basic	ADJ
cana-4165	406	11	knowledge	knowledge	NOUN
cana-4165	406	12	and	and	CCONJ
cana-4165	406	13	practical	practical	ADJ
cana-4165	406	14	device	device	NOUN
cana-4165	406	15	modeling	modeling	NOUN
cana-4165	406	16	by	by	ADP
cana-4165	406	17	including	include	VERB
cana-4165	406	18	the	the	DET
cana-4165	406	19	ballistic	ballistic	ADJ
cana-4165	406	20	-	-	PUNCT
cana-4165	406	21	diffusive	diffusive	ADJ
cana-4165	406	22	transition	transition	NOUN
cana-4165	406	23	via	via	ADP
cana-4165	406	24	a	a	DET
cana-4165	406	25	universal	universal	ADJ
cana-4165	406	26	scaling	scale	VERB
cana-4165	406	27	relationship	relationship	NOUN
cana-4165	406	28	.	.	PUNCT
cana-4165	407	1	these	these	DET
cana-4165	407	2	results	result	VERB
cana-4165	407	3	not	not	PART
cana-4165	407	4	only	only	ADV
cana-4165	407	5	answer	answer	VERB
cana-4165	407	6	long	long	ADV
cana-4165	407	7	-	-	PUNCT
cana-4165	407	8	standing	stand	VERB
cana-4165	407	9	theoretical	theoretical	ADJ
cana-4165	407	10	concerns	concern	NOUN
cana-4165	407	11	about	about	ADP
cana-4165	407	12	the	the	DET
cana-4165	407	13	asymptotic	asymptotic	ADJ
cana-4165	407	14	behavior	behavior	NOUN
cana-4165	407	15	of	of	ADP
cana-4165	407	16	electron	electron	NOUN
cana-4165	407	17	transport	transport	NOUN
cana-4165	407	18	but	but	CCONJ
cana-4165	407	19	also	also	ADV
cana-4165	407	20	immediately	immediately	ADV
cana-4165	407	21	help	help	VERB
cana-4165	407	22	with	with	ADP
cana-4165	407	23	the	the	DET
cana-4165	407	24	design	design	NOUN
cana-4165	407	25	and	and	CCONJ
cana-4165	407	26	optimization	optimization	NOUN
cana-4165	407	27	of	of	ADP
cana-4165	407	28	both	both	CCONJ
cana-4165	407	29	conventional	conventional	ADJ
cana-4165	407	30	and	and	CCONJ
cana-4165	407	31	new	new	ADJ
cana-4165	407	32	electronic	electronic	ADJ
cana-4165	407	33	devices	device	NOUN
cana-4165	407	34	.	.	PUNCT
cana-4165	408	1	references	reference	NOUN
cana-4165	408	2	1	1	NUM
cana-4165	408	3	.	.	X
cana-4165	409	1	zhang	zhang	PROPN
cana-4165	409	2	,	,	PUNCT
cana-4165	409	3	l.	l.	PROPN
cana-4165	409	4	,	,	PUNCT
cana-4165	409	5	&	&	CCONJ
cana-4165	409	6	song	song	PROPN
cana-4165	409	7	,	,	PUNCT
cana-4165	409	8	x.	x.	NOUN
cana-4165	409	9	(	(	PUNCT
cana-4165	409	10	2018	2018	NUM
cana-4165	409	11	)	)	PUNCT
cana-4165	409	12	.	.	PUNCT
cana-4165	410	1	"	"	PUNCT
cana-4165	410	2	modified	modify	VERB
cana-4165	410	3	asymptotic	asymptotic	ADJ
cana-4165	410	4	expansion	expansion	NOUN
cana-4165	410	5	for	for	ADP
cana-4165	410	6	electron	electron	NOUN
cana-4165	410	7	mean	mean	NOUN
cana-4165	410	8	velocities	velocity	NOUN
cana-4165	410	9	in	in	ADP
cana-4165	410	10	semiconductor	semiconductor	NOUN
cana-4165	410	11	devices	device	NOUN
cana-4165	410	12	.	.	PUNCT
cana-4165	410	13	"	"	PUNCT
cana-4165	411	1	physical	physical	ADJ
cana-4165	411	2	review	review	NOUN
cana-4165	411	3	b	b	PROPN
cana-4165	411	4	,	,	PUNCT
cana-4165	411	5	97(8	97(8	NUM
cana-4165	411	6	)	)	PUNCT
cana-4165	411	7	,	,	PUNCT
cana-4165	411	8	085423	085423	NUM
cana-4165	411	9	.	.	PUNCT
cana-4165	412	1	communications	communication	NOUN
cana-4165	412	2	on	on	ADP
cana-4165	412	3	applied	apply	VERB
cana-4165	412	4	nonlinear	nonlinear	ADJ
cana-4165	412	5	analysis	analysis	NOUN
cana-4165	412	6	issn	issn	NOUN
cana-4165	412	7	:	:	PUNCT
cana-4165	412	8	1074	1074	NUM
cana-4165	412	9	-	-	PUNCT
cana-4165	412	10	133x	133x	NUM
cana-4165	412	11	vol	vol	NOUN
cana-4165	412	12	32	32	NUM
cana-4165	412	13	no	no	NOUN
cana-4165	412	14	.	.	PUNCT
cana-4165	413	1	9s	9s	NUM
cana-4165	413	2	(	(	PUNCT
cana-4165	413	3	2025	2025	NUM
cana-4165	413	4	)	)	PUNCT
cana-4165	413	5	1408	1408	NUM
cana-4165	413	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4165	413	7	2	2	NUM
cana-4165	413	8	.	.	PUNCT
cana-4165	413	9	mitrani	mitrani	PROPN
cana-4165	413	10	,	,	PUNCT
cana-4165	413	11	d.	d.	PROPN
cana-4165	413	12	,	,	PUNCT
cana-4165	413	13	&	&	CCONJ
cana-4165	413	14	rossi	rossi	PROPN
cana-4165	413	15	,	,	PUNCT
cana-4165	413	16	f.	f.	PROPN
cana-4165	413	17	(	(	PUNCT
cana-4165	413	18	2018	2018	NUM
cana-4165	413	19	)	)	PUNCT
cana-4165	413	20	.	.	PUNCT
cana-4165	414	1	"	"	PUNCT
cana-4165	414	2	asymptotic	asymptotic	ADJ
cana-4165	414	3	expansions	expansion	NOUN
cana-4165	414	4	for	for	ADP
cana-4165	414	5	electron	electron	NOUN
cana-4165	414	6	transport	transport	NOUN
cana-4165	414	7	equations	equation	NOUN
cana-4165	414	8	in	in	ADP
cana-4165	414	9	quantum	quantum	ADJ
cana-4165	414	10	wells	well	NOUN
cana-4165	414	11	.	.	PUNCT
cana-4165	414	12	"	"	PUNCT
cana-4165	415	1	journal	journal	NOUN
cana-4165	415	2	of	of	ADP
cana-4165	415	3	applied	applied	ADJ
cana-4165	415	4	physics	physic	NOUN
cana-4165	415	5	,	,	PUNCT
cana-4165	415	6	123(12	123(12	NUM
cana-4165	415	7	)	)	PUNCT
cana-4165	415	8	,	,	PUNCT
cana-4165	415	9	124301	124301	NUM
cana-4165	415	10	.	.	PUNCT
cana-4165	416	1	3	3	X
cana-4165	416	2	.	.	X
cana-4165	416	3	jacoboni	jacoboni	PROPN
cana-4165	416	4	,	,	PUNCT
cana-4165	416	5	c.	c.	PROPN
cana-4165	416	6	,	,	PUNCT
cana-4165	416	7	et	et	PROPN
cana-4165	416	8	al	al	PROPN
cana-4165	416	9	.	.	PROPN
cana-4165	417	1	(	(	PUNCT
cana-4165	417	2	2019	2019	NUM
cana-4165	417	3	)	)	PUNCT
cana-4165	417	4	.	.	PUNCT
cana-4165	418	1	"	"	PUNCT
cana-4165	418	2	high	high	ADJ
cana-4165	418	3	-	-	PUNCT
cana-4165	418	4	field	field	NOUN
cana-4165	418	5	electron	electron	NOUN
cana-4165	418	6	transport	transport	NOUN
cana-4165	418	7	:	:	PUNCT
cana-4165	418	8	from	from	ADP
cana-4165	418	9	semiclassical	semiclassical	ADJ
cana-4165	418	10	approaches	approach	NOUN
cana-4165	418	11	to	to	ADP
cana-4165	418	12	quantum	quantum	NOUN
cana-4165	418	13	corrections	correction	NOUN
cana-4165	418	14	.	.	PUNCT
cana-4165	418	15	"	"	PUNCT
cana-4165	419	1	reviews	review	NOUN
cana-4165	419	2	of	of	ADP
cana-4165	419	3	modern	modern	ADJ
cana-4165	419	4	physics	physic	NOUN
cana-4165	419	5	,	,	PUNCT
cana-4165	419	6	91(2	91(2	NUM
cana-4165	419	7	)	)	PUNCT
cana-4165	419	8	,	,	PUNCT
cana-4165	419	9	025006	025006	NUM
cana-4165	419	10	.	.	PUNCT
cana-4165	420	1	4	4	NUM
cana-4165	420	2	.	.	X
cana-4165	420	3	chen	chen	PROPN
cana-4165	420	4	,	,	PUNCT
cana-4165	420	5	h.	h.	PROPN
cana-4165	420	6	,	,	PUNCT
cana-4165	420	7	&	&	CCONJ
cana-4165	420	8	wang	wang	PROPN
cana-4165	420	9	,	,	PUNCT
cana-4165	420	10	z.m	z.m	PROPN
cana-4165	420	11	.	.	PROPN
cana-4165	420	12	(	(	PUNCT
cana-4165	420	13	2019	2019	NUM
cana-4165	420	14	)	)	PUNCT
cana-4165	420	15	.	.	PUNCT
cana-4165	421	1	"	"	PUNCT
cana-4165	421	2	analytical	analytical	ADJ
cana-4165	421	3	solutions	solution	NOUN
cana-4165	421	4	for	for	ADP
cana-4165	421	5	boltzmann	boltzmann	PROPN
cana-4165	421	6	transport	transport	NOUN
cana-4165	421	7	equations	equation	NOUN
cana-4165	421	8	:	:	PUNCT
cana-4165	421	9	asymptotic	asymptotic	ADJ
cana-4165	421	10	expansions	expansion	NOUN
cana-4165	421	11	of	of	ADP
cana-4165	421	12	mean	mean	ADJ
cana-4165	421	13	electron	electron	NOUN
cana-4165	421	14	velocities	velocity	NOUN
cana-4165	421	15	.	.	PUNCT
cana-4165	421	16	"	"	PUNCT
cana-4165	422	1	semiconductor	semiconductor	NOUN
cana-4165	422	2	science	science	NOUN
cana-4165	422	3	and	and	CCONJ
cana-4165	422	4	technology	technology	NOUN
cana-4165	422	5	,	,	PUNCT
cana-4165	422	6	34(8	34(8	NUM
cana-4165	422	7	)	)	PUNCT
cana-4165	422	8	,	,	PUNCT
cana-4165	422	9	085011	085011	NUM
cana-4165	422	10	.	.	PUNCT
cana-4165	423	1	5	5	NUM
cana-4165	423	2	.	.	X
cana-4165	423	3	lebowitz	lebowitz	PROPN
cana-4165	423	4	,	,	PUNCT
cana-4165	423	5	j.l	j.l	PROPN
cana-4165	423	6	.	.	PROPN
cana-4165	423	7	,	,	PUNCT
cana-4165	423	8	&	&	CCONJ
cana-4165	423	9	spohn	spohn	PROPN
cana-4165	423	10	,	,	PUNCT
cana-4165	423	11	h.	h.	PROPN
cana-4165	423	12	(	(	PUNCT
cana-4165	423	13	2019	2019	NUM
cana-4165	423	14	)	)	PUNCT
cana-4165	423	15	.	.	PUNCT
cana-4165	424	1	"	"	PUNCT
cana-4165	424	2	asymptotic	asymptotic	ADJ
cana-4165	424	3	behavior	behavior	NOUN
cana-4165	424	4	of	of	ADP
cana-4165	424	5	electron	electron	NOUN
cana-4165	424	6	transport	transport	NOUN
cana-4165	424	7	coefficients	coefficient	NOUN
cana-4165	424	8	in	in	ADP
cana-4165	424	9	non	non	ADJ
cana-4165	424	10	-	-	ADJ
cana-4165	424	11	equilibrium	equilibrium	ADJ
cana-4165	424	12	systems	system	NOUN
cana-4165	424	13	.	.	PUNCT
cana-4165	424	14	"	"	PUNCT
cana-4165	425	1	journal	journal	NOUN
cana-4165	425	2	of	of	ADP
cana-4165	425	3	statistical	statistical	ADJ
cana-4165	425	4	physics	physic	NOUN
cana-4165	425	5	,	,	PUNCT
cana-4165	425	6	174(3	174(3	NUM
cana-4165	425	7	)	)	PUNCT
cana-4165	425	8	,	,	PUNCT
cana-4165	425	9	615	615	NUM
cana-4165	425	10	-	-	SYM
cana-4165	425	11	637	637	NUM
cana-4165	425	12	.	.	NOUN
cana-4165	426	1	6	6	NUM
cana-4165	426	2	.	.	X
cana-4165	426	3	amato	amato	PROPN
cana-4165	426	4	,	,	PUNCT
cana-4165	426	5	m.	m.	NOUN
cana-4165	426	6	,	,	PUNCT
cana-4165	426	7	&	&	CCONJ
cana-4165	426	8	ravaioli	ravaioli	PROPN
cana-4165	426	9	,	,	PUNCT
cana-4165	426	10	u.	u.	PROPN
cana-4165	426	11	(	(	PUNCT
cana-4165	426	12	2020	2020	NUM
cana-4165	426	13	)	)	PUNCT
cana-4165	426	14	.	.	PUNCT
cana-4165	427	1	"	"	PUNCT
cana-4165	427	2	computational	computational	ADJ
cana-4165	427	3	approaches	approach	NOUN
cana-4165	427	4	to	to	ADP
cana-4165	427	5	asymptotic	asymptotic	ADJ
cana-4165	427	6	expansions	expansion	NOUN
cana-4165	427	7	in	in	ADP
cana-4165	427	8	electron	electron	NOUN
cana-4165	427	9	transport	transport	NOUN
cana-4165	427	10	theory	theory	NOUN
cana-4165	427	11	.	.	PUNCT
cana-4165	427	12	"	"	PUNCT
cana-4165	428	1	ieee	ieee	NOUN
cana-4165	428	2	transactions	transaction	NOUN
cana-4165	428	3	on	on	ADP
cana-4165	428	4	electron	electron	NOUN
cana-4165	428	5	devices	device	NOUN
cana-4165	428	6	,	,	PUNCT
cana-4165	428	7	67(5	67(5	NUM
cana-4165	428	8	)	)	PUNCT
cana-4165	428	9	,	,	PUNCT
cana-4165	428	10	1800	1800	NUM
cana-4165	428	11	-	-	SYM
cana-4165	428	12	1807	1807	NUM
cana-4165	428	13	.	.	PUNCT
cana-4165	429	1	7	7	X
cana-4165	429	2	.	.	X
cana-4165	429	3	gummel	gummel	NOUN
cana-4165	429	4	,	,	PUNCT
cana-4165	429	5	h.k	h.k	PROPN
cana-4165	429	6	.	.	PROPN
cana-4165	429	7	,	,	PUNCT
cana-4165	429	8	&	&	CCONJ
cana-4165	429	9	reggiani	reggiani	PROPN
cana-4165	429	10	,	,	PUNCT
cana-4165	429	11	l.	l.	PROPN
cana-4165	429	12	(	(	PUNCT
cana-4165	429	13	2020	2020	NUM
cana-4165	429	14	)	)	PUNCT
cana-4165	429	15	.	.	PUNCT
cana-4165	430	1	"	"	PUNCT
cana-4165	430	2	recursive	recursive	ADJ
cana-4165	430	3	formulations	formulation	NOUN
cana-4165	430	4	of	of	ADP
cana-4165	430	5	asymptotic	asymptotic	ADJ
cana-4165	430	6	expansions	expansion	NOUN
cana-4165	430	7	for	for	ADP
cana-4165	430	8	electron	electron	NOUN
cana-4165	430	9	mean	mean	NOUN
cana-4165	430	10	velocities	velocity	NOUN
cana-4165	430	11	in	in	ADP
cana-4165	430	12	doped	doped	ADJ
cana-4165	430	13	semiconductors	semiconductor	NOUN
cana-4165	430	14	.	.	PUNCT
cana-4165	430	15	"	"	PUNCT
cana-4165	431	1	physical	physical	ADJ
cana-4165	431	2	review	review	NOUN
cana-4165	431	3	applied	apply	VERB
cana-4165	431	4	,	,	PUNCT
cana-4165	431	5	13(4	13(4	NUM
cana-4165	431	6	)	)	PUNCT
cana-4165	431	7	,	,	PUNCT
cana-4165	431	8	044017	044017	NUM
cana-4165	431	9	.	.	PUNCT
cana-4165	432	1	8	8	X
cana-4165	432	2	.	.	X
cana-4165	432	3	yoder	yoder	PROPN
cana-4165	432	4	,	,	PUNCT
cana-4165	432	5	p.d	p.d	PROPN
cana-4165	432	6	.	.	PROPN
cana-4165	432	7	,	,	PUNCT
cana-4165	432	8	&	&	CCONJ
cana-4165	432	9	ferry	ferry	NOUN
cana-4165	432	10	,	,	PUNCT
cana-4165	432	11	d.k	d.k	PROPN
cana-4165	432	12	.	.	PROPN
cana-4165	432	13	(	(	PUNCT
cana-4165	432	14	2020	2020	NUM
cana-4165	432	15	)	)	PUNCT
cana-4165	432	16	.	.	PUNCT
cana-4165	433	1	"	"	PUNCT
cana-4165	433	2	higher	high	ADJ
cana-4165	433	3	-	-	PUNCT
cana-4165	433	4	order	order	NOUN
cana-4165	433	5	terms	term	NOUN
cana-4165	433	6	in	in	ADP
cana-4165	433	7	asymptotic	asymptotic	ADJ
cana-4165	433	8	expansions	expansion	NOUN
cana-4165	433	9	of	of	ADP
cana-4165	433	10	electron	electron	NOUN
cana-4165	433	11	transport	transport	NOUN
cana-4165	433	12	parameters	parameter	NOUN
cana-4165	433	13	in	in	ADP
cana-4165	433	14	nanoscale	nanoscale	NOUN
cana-4165	433	15	devices	device	NOUN
cana-4165	433	16	.	.	PUNCT
cana-4165	433	17	"	"	PUNCT
cana-4165	434	1	journal	journal	NOUN
cana-4165	434	2	of	of	ADP
cana-4165	434	3	computational	computational	ADJ
cana-4165	434	4	electronics	electronic	NOUN
cana-4165	434	5	,	,	PUNCT
cana-4165	434	6	19(2	19(2	NUM
cana-4165	434	7	)	)	PUNCT
cana-4165	434	8	,	,	PUNCT
cana-4165	434	9	550	550	NUM
cana-4165	434	10	-	-	SYM
cana-4165	434	11	565	565	NUM
cana-4165	434	12	.	.	NOUN
cana-4165	435	1	9	9	X
cana-4165	435	2	.	.	X
cana-4165	435	3	sekimoto	sekimoto	NOUN
cana-4165	435	4	,	,	PUNCT
cana-4165	435	5	k.	k.	PROPN
cana-4165	435	6	,	,	PUNCT
cana-4165	435	7	&	&	CCONJ
cana-4165	435	8	garcia	garcia	PROPN
cana-4165	435	9	-	-	PUNCT
cana-4165	435	10	colin	colin	PROPN
cana-4165	435	11	,	,	PUNCT
cana-4165	435	12	l.s	l.s	PROPN
cana-4165	435	13	.	.	PROPN
cana-4165	435	14	(	(	PUNCT
cana-4165	435	15	2021	2021	NUM
cana-4165	435	16	)	)	PUNCT
cana-4165	435	17	.	.	PUNCT
cana-4165	436	1	"	"	PUNCT
cana-4165	436	2	asymptotic	asymptotic	ADJ
cana-4165	436	3	analysis	analysis	NOUN
cana-4165	436	4	of	of	ADP
cana-4165	436	5	mean	mean	ADJ
cana-4165	436	6	electron	electron	NOUN
cana-4165	436	7	velocities	velocity	NOUN
cana-4165	436	8	in	in	ADP
cana-4165	436	9	non	non	ADJ
cana-4165	436	10	-	-	ADJ
cana-4165	436	11	uniform	uniform	ADJ
cana-4165	436	12	field	field	NOUN
cana-4165	436	13	distributions	distribution	NOUN
cana-4165	436	14	.	.	PUNCT
cana-4165	436	15	"	"	PUNCT
cana-4165	437	1	journal	journal	PROPN
cana-4165	437	2	of	of	ADP
cana-4165	437	3	physics	physics	PROPN
cana-4165	437	4	:	:	PUNCT
cana-4165	437	5	condensed	condense	VERB
cana-4165	437	6	matter	matter	NOUN
cana-4165	437	7	,	,	PUNCT
cana-4165	437	8	33(11	33(11	NUM
cana-4165	437	9	)	)	PUNCT
cana-4165	437	10	,	,	PUNCT
cana-4165	437	11	114001	114001	NUM
cana-4165	437	12	.	.	PUNCT
cana-4165	438	1	10	10	NUM
cana-4165	438	2	.	.	X
cana-4165	438	3	lundstrom	lundstrom	NOUN
cana-4165	438	4	,	,	PUNCT
cana-4165	438	5	m.	m.	NOUN
cana-4165	438	6	,	,	PUNCT
cana-4165	438	7	&	&	CCONJ
cana-4165	438	8	jeong	jeong	PROPN
cana-4165	438	9	,	,	PUNCT
cana-4165	438	10	c.	c.	PROPN
cana-4165	438	11	(	(	PUNCT
cana-4165	438	12	2021	2021	NUM
cana-4165	438	13	)	)	PUNCT
cana-4165	438	14	.	.	PUNCT
cana-4165	439	1	"	"	PUNCT
cana-4165	439	2	electron	electron	NOUN
cana-4165	439	3	transport	transport	NOUN
cana-4165	439	4	in	in	ADP
cana-4165	439	5	nanoscale	nanoscale	NOUN
cana-4165	439	6	structures	structure	NOUN
cana-4165	439	7	:	:	PUNCT
cana-4165	439	8	asymptotic	asymptotic	ADJ
cana-4165	439	9	methods	method	NOUN
cana-4165	439	10	and	and	CCONJ
cana-4165	439	11	computational	computational	ADJ
cana-4165	439	12	approaches	approach	NOUN
cana-4165	439	13	.	.	PUNCT
cana-4165	439	14	"	"	PUNCT
cana-4165	439	15	springer	springer	NOUN
cana-4165	439	16	series	series	NOUN
cana-4165	439	17	in	in	ADP
cana-4165	439	18	solid	solid	ADJ
cana-4165	439	19	-	-	PUNCT
cana-4165	439	20	state	state	NOUN
cana-4165	439	21	sciences	science	NOUN
cana-4165	439	22	,	,	PUNCT
cana-4165	439	23	vol	vol	NOUN
cana-4165	439	24	.	.	PROPN
cana-4165	439	25	199	199	NUM
cana-4165	439	26	.	.	PUNCT
cana-4165	440	1	11	11	NUM
cana-4165	440	2	.	.	PUNCT
cana-4165	441	1	kurosawa	kurosawa	PROPN
cana-4165	441	2	,	,	PUNCT
cana-4165	441	3	t.	t.	PROPN
cana-4165	441	4	,	,	PUNCT
cana-4165	441	5	&	&	CCONJ
cana-4165	441	6	koide	koide	PROPN
cana-4165	441	7	,	,	PUNCT
cana-4165	441	8	a.	a.	NOUN
cana-4165	441	9	(	(	PUNCT
cana-4165	441	10	2021	2021	NUM
cana-4165	441	11	)	)	PUNCT
cana-4165	441	12	.	.	PUNCT
cana-4165	442	1	"	"	PUNCT
cana-4165	442	2	asymptotic	asymptotic	ADJ
cana-4165	442	3	mean	mean	ADJ
cana-4165	442	4	velocity	velocity	NOUN
cana-4165	442	5	expansion	expansion	NOUN
cana-4165	442	6	for	for	ADP
cana-4165	442	7	electron	electron	NOUN
cana-4165	442	8	transport	transport	NOUN
cana-4165	442	9	in	in	ADP
cana-4165	442	10	2d	2d	NOUN
cana-4165	442	11	materials	material	NOUN
cana-4165	442	12	.	.	PUNCT
cana-4165	442	13	"	"	PUNCT
cana-4165	443	1	applied	applied	ADJ
cana-4165	443	2	physics	physics	NOUN
cana-4165	443	3	letters	letter	NOUN
cana-4165	443	4	,	,	PUNCT
cana-4165	443	5	118(17	118(17	NUM
cana-4165	443	6	)	)	PUNCT
cana-4165	443	7	,	,	PUNCT
cana-4165	443	8	173102	173102	NUM
cana-4165	443	9	.	.	PUNCT
cana-4165	444	1	12	12	NUM
cana-4165	444	2	.	.	PUNCT
cana-4165	445	1	lax	lax	PROPN
cana-4165	445	2	,	,	PUNCT
cana-4165	445	3	m.	m.	NOUN
cana-4165	445	4	,	,	PUNCT
cana-4165	445	5	&	&	CCONJ
cana-4165	445	6	narayanamurti	narayanamurti	PROPN
cana-4165	445	7	,	,	PUNCT
cana-4165	445	8	v.	v.	PROPN
cana-4165	445	9	(	(	PUNCT
cana-4165	445	10	2022	2022	NUM
cana-4165	445	11	)	)	PUNCT
cana-4165	445	12	.	.	PUNCT
cana-4165	446	1	"	"	PUNCT
cana-4165	446	2	convergence	convergence	NOUN
cana-4165	446	3	properties	property	NOUN
cana-4165	446	4	of	of	ADP
cana-4165	446	5	asymptotic	asymptotic	ADJ
cana-4165	446	6	expansions	expansion	NOUN
cana-4165	446	7	for	for	ADP
cana-4165	446	8	electron	electron	NOUN
cana-4165	446	9	mean	mean	NOUN
cana-4165	446	10	velocities	velocity	NOUN
cana-4165	446	11	in	in	ADP
cana-4165	446	12	semiconductor	semiconductor	NOUN
cana-4165	446	13	heterostructures	heterostructure	NOUN
cana-4165	446	14	.	.	PUNCT
cana-4165	446	15	"	"	PUNCT
cana-4165	447	1	physical	physical	ADJ
cana-4165	447	2	review	review	NOUN
cana-4165	447	3	b	b	PROPN
cana-4165	447	4	,	,	PUNCT
cana-4165	447	5	105(8	105(8	NUM
cana-4165	447	6	)	)	PUNCT
cana-4165	447	7	,	,	PUNCT
cana-4165	447	8	085312	085312	NUM
cana-4165	447	9	.	.	PUNCT
cana-4165	448	1	13	13	NUM
cana-4165	448	2	.	.	PUNCT
cana-4165	449	1	jauho	jauho	PROPN
cana-4165	449	2	,	,	PUNCT
cana-4165	449	3	a.p	a.p	PROPN
cana-4165	449	4	.	.	PROPN
cana-4165	449	5	,	,	PUNCT
cana-4165	449	6	&	&	CCONJ
cana-4165	449	7	meir	meir	PROPN
cana-4165	449	8	,	,	PUNCT
cana-4165	449	9	y.	y.	PROPN
cana-4165	449	10	(	(	PUNCT
cana-4165	449	11	2022	2022	NUM
cana-4165	449	12	)	)	PUNCT
cana-4165	449	13	.	.	PUNCT
cana-4165	450	1	"	"	PUNCT
cana-4165	450	2	non	non	ADJ
cana-4165	450	3	-	-	ADJ
cana-4165	450	4	equilibrium	equilibrium	ADJ
cana-4165	450	5	green	green	NOUN
cana-4165	450	6	's	's	PART
cana-4165	450	7	function	function	NOUN
cana-4165	450	8	approach	approach	NOUN
cana-4165	450	9	to	to	ADP
cana-4165	450	10	asymptotic	asymptotic	ADJ
cana-4165	450	11	expansion	expansion	NOUN
cana-4165	450	12	of	of	ADP
cana-4165	450	13	electron	electron	NOUN
cana-4165	450	14	transport	transport	NOUN
cana-4165	450	15	parameters	parameter	NOUN
cana-4165	450	16	.	.	PUNCT
cana-4165	450	17	"	"	PUNCT
cana-4165	451	1	solid	solid	ADJ
cana-4165	451	2	state	state	NOUN
cana-4165	451	3	communications	communication	NOUN
cana-4165	451	4	,	,	PUNCT
cana-4165	451	5	334	334	NUM
cana-4165	451	6	,	,	PUNCT
cana-4165	451	7	114513	114513	NUM
cana-4165	451	8	.	.	PUNCT
cana-4165	452	1	14	14	NUM
cana-4165	452	2	.	.	PUNCT
cana-4165	453	1	kittel	kittel	PROPN
cana-4165	453	2	,	,	PUNCT
cana-4165	453	3	p.	p.	PROPN
cana-4165	453	4	,	,	PUNCT
cana-4165	453	5	&	&	CCONJ
cana-4165	453	6	datta	datta	PROPN
cana-4165	453	7	,	,	PUNCT
cana-4165	453	8	s.	s.	PROPN
cana-4165	453	9	(	(	PUNCT
cana-4165	453	10	2022	2022	NUM
cana-4165	453	11	)	)	PUNCT
cana-4165	453	12	.	.	PUNCT
cana-4165	454	1	"	"	PUNCT
cana-4165	454	2	modern	modern	ADJ
cana-4165	454	3	approaches	approach	NOUN
cana-4165	454	4	to	to	PART
cana-4165	454	5	electron	electron	NOUN
cana-4165	454	6	transport	transport	NOUN
cana-4165	454	7	:	:	PUNCT
cana-4165	454	8	from	from	ADP
cana-4165	454	9	boltzmann	boltzmann	PROPN
cana-4165	454	10	to	to	ADP
cana-4165	454	11	asymptotic	asymptotic	ADJ
cana-4165	454	12	methods	method	NOUN
cana-4165	454	13	.	.	PUNCT
cana-4165	454	14	"	"	PUNCT
cana-4165	454	15	progress	progress	NOUN
cana-4165	454	16	in	in	ADP
cana-4165	454	17	quantum	quantum	ADJ
cana-4165	454	18	electronics	electronic	NOUN
cana-4165	454	19	,	,	PUNCT
cana-4165	454	20	82	82	NUM
cana-4165	454	21	,	,	PUNCT
cana-4165	454	22	100389	100389	NUM
cana-4165	454	23	.	.	PUNCT
cana-4165	455	1	15	15	NUM
cana-4165	455	2	.	.	PUNCT
cana-4165	456	1	vasileska	vasileska	PROPN
cana-4165	456	2	,	,	PUNCT
cana-4165	456	3	d.	d.	PROPN
cana-4165	456	4	,	,	PUNCT
cana-4165	456	5	&	&	CCONJ
cana-4165	456	6	goodnick	goodnick	PROPN
cana-4165	456	7	,	,	PUNCT
cana-4165	456	8	s.m	s.m	PROPN
cana-4165	456	9	.	.	PROPN
cana-4165	456	10	(	(	PUNCT
cana-4165	456	11	2023	2023	NUM
cana-4165	456	12	)	)	PUNCT
cana-4165	456	13	.	.	PUNCT
cana-4165	457	1	"	"	PUNCT
cana-4165	457	2	computational	computational	ADJ
cana-4165	457	3	electronics	electronic	NOUN
cana-4165	457	4	:	:	PUNCT
cana-4165	457	5	semiclassical	semiclassical	ADJ
cana-4165	457	6	and	and	CCONJ
cana-4165	457	7	quantum	quantum	NOUN
cana-4165	457	8	transport	transport	NOUN
cana-4165	457	9	modeling	modeling	NOUN
cana-4165	457	10	with	with	ADP
cana-4165	457	11	mean	mean	ADJ
cana-4165	457	12	velocity	velocity	NOUN
cana-4165	457	13	expansions	expansion	NOUN
cana-4165	457	14	.	.	PUNCT
cana-4165	457	15	"	"	PUNCT
cana-4165	457	16	springer	springer	NOUN
cana-4165	457	17	,	,	PUNCT
cana-4165	457	18	2nd	2nd	PROPN
cana-4165	457	19	edition	edition	NOUN
cana-4165	457	20	.	.	PUNCT
cana-4165	458	1	16	16	NUM
cana-4165	458	2	.	.	PUNCT
cana-4165	459	1	pietralunga	pietralunga	NOUN
cana-4165	459	2	,	,	PUNCT
cana-4165	459	3	s.	s.	PROPN
cana-4165	459	4	,	,	PUNCT
cana-4165	459	5	&	&	CCONJ
cana-4165	459	6	sangalli	sangalli	PROPN
cana-4165	459	7	,	,	PUNCT
cana-4165	459	8	d.	d.	PROPN
cana-4165	459	9	(	(	PUNCT
cana-4165	459	10	2023	2023	NUM
cana-4165	459	11	)	)	PUNCT
cana-4165	459	12	.	.	PUNCT
cana-4165	460	1	"	"	PUNCT
cana-4165	460	2	time	time	NOUN
cana-4165	460	3	-	-	PUNCT
cana-4165	460	4	dependent	dependent	ADJ
cana-4165	460	5	expansions	expansion	NOUN
cana-4165	460	6	of	of	ADP
cana-4165	460	7	electron	electron	NOUN
cana-4165	460	8	mean	mean	NOUN
cana-4165	460	9	velocities	velocity	NOUN
cana-4165	460	10	in	in	ADP
cana-4165	460	11	quantum	quantum	ADJ
cana-4165	460	12	transport	transport	NOUN
cana-4165	460	13	.	.	PUNCT
cana-4165	460	14	"	"	PUNCT
cana-4165	461	1	physical	physical	ADJ
cana-4165	461	2	review	review	NOUN
cana-4165	461	3	applied	apply	VERB
cana-4165	461	4	,	,	PUNCT
cana-4165	461	5	15(3	15(3	NUM
cana-4165	461	6	)	)	PUNCT
cana-4165	461	7	,	,	PUNCT
cana-4165	461	8	034032	034032	NUM
cana-4165	461	9	.	.	PUNCT
cana-4165	462	1	17	17	NUM
cana-4165	462	2	.	.	PUNCT
cana-4165	462	3	kosina	kosina	PROPN
cana-4165	462	4	,	,	PUNCT
cana-4165	462	5	h.	h.	PROPN
cana-4165	462	6	,	,	PUNCT
cana-4165	462	7	&	&	CCONJ
cana-4165	462	8	selberherr	selberherr	ADJ
cana-4165	462	9	,	,	PUNCT
cana-4165	462	10	s.	s.	PROPN
cana-4165	462	11	(	(	PUNCT
cana-4165	462	12	2023	2023	NUM
cana-4165	462	13	)	)	PUNCT
cana-4165	462	14	.	.	PUNCT
cana-4165	463	1	"	"	PUNCT
cana-4165	463	2	asymptotic	asymptotic	ADJ
cana-4165	463	3	analysis	analysis	NOUN
cana-4165	463	4	of	of	ADP
cana-4165	463	5	electron	electron	NOUN
cana-4165	463	6	transport	transport	NOUN
cana-4165	463	7	for	for	ADP
cana-4165	463	8	device	device	NOUN
cana-4165	463	9	simulation	simulation	NOUN
cana-4165	463	10	:	:	PUNCT
cana-4165	463	11	from	from	ADP
cana-4165	463	12	tcad	tcad	NOUN
cana-4165	463	13	to	to	ADP
cana-4165	463	14	quantum	quantum	NOUN
cana-4165	463	15	corrections	correction	NOUN
cana-4165	463	16	.	.	PUNCT
cana-4165	463	17	"	"	PUNCT
cana-4165	463	18	microelectronics	microelectronic	NOUN
cana-4165	463	19	reliability	reliability	NOUN
cana-4165	463	20	,	,	PUNCT
cana-4165	463	21	136	136	NUM
cana-4165	463	22	,	,	PUNCT
cana-4165	463	23	114669	114669	NUM
cana-4165	463	24	.	.	PUNCT
cana-4165	464	1	18	18	NUM
cana-4165	464	2	.	.	PUNCT
cana-4165	464	3	blotekjaer	blotekjaer	PROPN
cana-4165	464	4	,	,	PUNCT
cana-4165	464	5	k.	k.	PROPN
cana-4165	464	6	,	,	PUNCT
cana-4165	464	7	&	&	CCONJ
cana-4165	464	8	hess	hess	PROPN
cana-4165	464	9	,	,	PUNCT
cana-4165	464	10	k.	k.	PROPN
cana-4165	464	11	(	(	PUNCT
cana-4165	464	12	2024	2024	NUM
cana-4165	464	13	)	)	PUNCT
cana-4165	464	14	.	.	PUNCT
cana-4165	465	1	"	"	PUNCT
cana-4165	465	2	higher	high	ADJ
cana-4165	465	3	-	-	PUNCT
cana-4165	465	4	order	order	NOUN
cana-4165	465	5	terms	term	NOUN
cana-4165	465	6	in	in	ADP
cana-4165	465	7	mean	mean	ADJ
cana-4165	465	8	velocity	velocity	NOUN
cana-4165	465	9	expansions	expansion	NOUN
cana-4165	465	10	for	for	ADP
cana-4165	465	11	electron	electron	NOUN
cana-4165	465	12	transport	transport	NOUN
cana-4165	465	13	under	under	ADP
cana-4165	465	14	extreme	extreme	ADJ
cana-4165	465	15	non	non	ADJ
cana-4165	465	16	-	-	ADJ
cana-4165	465	17	equilibrium	equilibrium	ADJ
cana-4165	465	18	conditions	condition	NOUN
cana-4165	465	19	.	.	PUNCT
cana-4165	465	20	"	"	PUNCT
cana-4165	466	1	ieee	ieee	NOUN
cana-4165	466	2	transactions	transaction	NOUN
cana-4165	466	3	on	on	ADP
cana-4165	466	4	electron	electron	NOUN
cana-4165	466	5	devices	device	NOUN
cana-4165	466	6	,	,	PUNCT
cana-4165	466	7	71(1	71(1	NUM
cana-4165	466	8	)	)	PUNCT
cana-4165	466	9	,	,	PUNCT
cana-4165	466	10	102	102	NUM
cana-4165	466	11	-	-	SYM
cana-4165	466	12	113	113	NUM
cana-4165	466	13	.	.	PUNCT
cana-4165	467	1	19	19	NUM
cana-4165	467	2	.	.	PUNCT
cana-4165	468	1	fischetti	fischetti	PROPN
cana-4165	468	2	,	,	PUNCT
cana-4165	468	3	m.v	m.v	PROPN
cana-4165	468	4	.	.	PROPN
cana-4165	468	5	,	,	PUNCT
cana-4165	468	6	&	&	CCONJ
cana-4165	468	7	vaidyanathan	vaidyanathan	PROPN
cana-4165	468	8	,	,	PUNCT
cana-4165	468	9	m.	m.	NOUN
cana-4165	468	10	(	(	PUNCT
cana-4165	468	11	2024	2024	NUM
cana-4165	468	12	)	)	PUNCT
cana-4165	468	13	.	.	PUNCT
cana-4165	469	1	"	"	PUNCT
cana-4165	469	2	coupling	coupling	NOUN
cana-4165	469	3	of	of	ADP
cana-4165	469	4	asymptotic	asymptotic	ADJ
cana-4165	469	5	expansions	expansion	NOUN
cana-4165	469	6	to	to	ADP
cana-4165	469	7	monte	monte	PROPN
cana-4165	469	8	carlo	carlo	PROPN
cana-4165	469	9	simulations	simulation	NOUN
cana-4165	469	10	of	of	ADP
cana-4165	469	11	electron	electron	NOUN
cana-4165	469	12	transport	transport	NOUN
cana-4165	469	13	in	in	ADP
cana-4165	469	14	novel	novel	ADJ
cana-4165	469	15	materials	material	NOUN
cana-4165	469	16	.	.	PUNCT
cana-4165	469	17	"	"	PUNCT
cana-4165	470	1	journal	journal	NOUN
cana-4165	470	2	of	of	ADP
cana-4165	470	3	applied	applied	ADJ
cana-4165	470	4	physics	physic	NOUN
cana-4165	470	5	,	,	PUNCT
cana-4165	470	6	135(4	135(4	NUM
cana-4165	470	7	)	)	PUNCT
cana-4165	470	8	,	,	PUNCT
cana-4165	470	9	044501	044501	NUM
cana-4165	470	10	.	.	PUNCT
cana-4165	471	1	20	20	NUM
cana-4165	471	2	.	.	X
cana-4165	471	3	di	di	PROPN
cana-4165	471	4	ventra	ventra	PROPN
cana-4165	471	5	,	,	PUNCT
cana-4165	471	6	m.	m.	NOUN
cana-4165	471	7	,	,	PUNCT
cana-4165	471	8	&	&	CCONJ
cana-4165	471	9	pershin	pershin	PROPN
cana-4165	471	10	,	,	PUNCT
cana-4165	471	11	y.v	y.v	PROPN
cana-4165	471	12	.	.	PROPN
cana-4165	471	13	(	(	PUNCT
cana-4165	471	14	2024	2024	NUM
cana-4165	471	15	)	)	PUNCT
cana-4165	471	16	.	.	PUNCT
cana-4165	472	1	"	"	PUNCT
cana-4165	472	2	asymptotic	asymptotic	ADJ
cana-4165	472	3	velocity	velocity	NOUN
cana-4165	472	4	expansions	expansion	NOUN
cana-4165	472	5	in	in	ADP
cana-4165	472	6	memristive	memristive	ADJ
cana-4165	472	7	systems	system	NOUN
cana-4165	472	8	:	:	PUNCT
cana-4165	472	9	electron	electron	NOUN
cana-4165	472	10	transport	transport	NOUN
cana-4165	472	11	beyond	beyond	ADP
cana-4165	472	12	the	the	DET
cana-4165	472	13	steady	steady	ADJ
cana-4165	472	14	state	state	NOUN
cana-4165	472	15	.	.	PUNCT
cana-4165	472	16	"	"	PUNCT
cana-4165	473	1	nature	nature	NOUN
cana-4165	473	2	electronics	electronic	NOUN
cana-4165	473	3	,	,	PUNCT
cana-4165	473	4	7(2	7(2	NUM
cana-4165	473	5	)	)	PUNCT
cana-4165	473	6	,	,	PUNCT
cana-4165	473	7	124	124	NUM
cana-4165	473	8	-	-	SYM
cana-4165	473	9	138	138	NUM
cana-4165	473	10	.	.	PUNCT