id	sid	tid	token	lemma	pos
ap-1396	1	1	acta	acta	PROPN
ap-1396	1	2	polytechnica	polytechnica	PROPN
ap-1396	1	3	vol	vol	NOUN
ap-1396	1	4	.	.	PUNCT
ap-1396	2	1	51	51	NUM
ap-1396	2	2	no	no	INTJ
ap-1396	2	3	.	.	PUNCT
ap-1396	3	1	4/2011	4/2011	NUM
ap-1396	3	2	perturbation	perturbation	NOUN
ap-1396	3	3	theory	theory	NOUN
ap-1396	3	4	for	for	ADP
ap-1396	3	5	pt	pt	X
ap-1396	3	6	-symmetric	-symmetric	ADJ
ap-1396	3	7	sinusoidal	sinusoidal	NOUN
ap-1396	3	8	optical	optical	ADJ
ap-1396	3	9	lattices	lattice	NOUN
ap-1396	3	10	at	at	ADP
ap-1396	3	11	the	the	DET
ap-1396	3	12	symmetry	symmetry	NOUN
ap-1396	3	13	-	-	PUNCT
ap-1396	3	14	breaking	break	VERB
ap-1396	3	15	threshold	threshold	NOUN
ap-1396	3	16	h.	h.	PROPN
ap-1396	3	17	f.	f.	PROPN
ap-1396	3	18	jones	jones	PROPN
ap-1396	4	1	abstract	abstract	PROPN
ap-1396	4	2	the	the	DET
ap-1396	4	3	pt	pt	ADJ
ap-1396	4	4	symmetric	symmetric	ADJ
ap-1396	4	5	potential	potential	ADJ
ap-1396	4	6	v0[cos(2πx	v0[cos(2πx	NOUN
ap-1396	4	7	/	/	SYM
ap-1396	4	8	a	a	NOUN
ap-1396	4	9	)	)	PUNCT
ap-1396	4	10	+	+	NUM
ap-1396	4	11	iλ	iλ	PROPN
ap-1396	4	12	sin(2πx	sin(2πx	PROPN
ap-1396	4	13	/	/	SYM
ap-1396	4	14	a	a	NOUN
ap-1396	4	15	)	)	PUNCT
ap-1396	4	16	]	]	PUNCT
ap-1396	4	17	has	have	VERB
ap-1396	4	18	a	a	DET
ap-1396	4	19	completely	completely	ADV
ap-1396	4	20	real	real	ADJ
ap-1396	4	21	spectrum	spectrum	NOUN
ap-1396	4	22	for	for	ADP
ap-1396	4	23	λ	λ	PROPN
ap-1396	4	24	≤	≤	NOUN
ap-1396	4	25	1	1	NUM
ap-1396	4	26	,	,	PUNCT
ap-1396	4	27	and	and	CCONJ
ap-1396	4	28	begins	begin	VERB
ap-1396	4	29	to	to	PART
ap-1396	4	30	develop	develop	VERB
ap-1396	4	31	complex	complex	ADJ
ap-1396	4	32	eigenvalues	eigenvalue	NOUN
ap-1396	4	33	for	for	ADP
ap-1396	4	34	λ	λ	PROPN
ap-1396	4	35	>	>	X
ap-1396	4	36	1	1	NUM
ap-1396	4	37	.	.	PUNCT
ap-1396	5	1	at	at	ADP
ap-1396	5	2	the	the	DET
ap-1396	5	3	symmetry	symmetry	NOUN
ap-1396	5	4	-	-	PUNCT
ap-1396	5	5	breaking	break	VERB
ap-1396	5	6	threshold	threshold	NOUN
ap-1396	5	7	λ	λ	X
ap-1396	5	8	=	=	NOUN
ap-1396	5	9	1	1	NUM
ap-1396	5	10	some	some	PRON
ap-1396	5	11	of	of	ADP
ap-1396	5	12	the	the	DET
ap-1396	5	13	eigenvectors	eigenvector	NOUN
ap-1396	5	14	become	become	VERB
ap-1396	5	15	degenerate	degenerate	ADJ
ap-1396	5	16	,	,	PUNCT
ap-1396	5	17	giving	give	VERB
ap-1396	5	18	rise	rise	NOUN
ap-1396	5	19	to	to	ADP
ap-1396	5	20	a	a	DET
ap-1396	5	21	jordan	jordan	PROPN
ap-1396	5	22	-	-	PUNCT
ap-1396	5	23	block	block	NOUN
ap-1396	5	24	structure	structure	NOUN
ap-1396	5	25	for	for	ADP
ap-1396	5	26	each	each	DET
ap-1396	5	27	degenerate	degenerate	ADJ
ap-1396	5	28	eigenvector	eigenvector	NOUN
ap-1396	5	29	.	.	PUNCT
ap-1396	6	1	in	in	ADP
ap-1396	6	2	general	general	ADJ
ap-1396	6	3	this	this	PRON
ap-1396	6	4	is	be	AUX
ap-1396	6	5	expected	expect	VERB
ap-1396	6	6	to	to	PART
ap-1396	6	7	give	give	VERB
ap-1396	6	8	rise	rise	NOUN
ap-1396	6	9	to	to	ADP
ap-1396	6	10	a	a	DET
ap-1396	6	11	secular	secular	ADJ
ap-1396	6	12	growth	growth	NOUN
ap-1396	6	13	in	in	ADP
ap-1396	6	14	the	the	DET
ap-1396	6	15	amplitude	amplitude	NOUN
ap-1396	6	16	of	of	ADP
ap-1396	6	17	the	the	DET
ap-1396	6	18	wave	wave	NOUN
ap-1396	6	19	.	.	PUNCT
ap-1396	7	1	however	however	ADV
ap-1396	7	2	,	,	PUNCT
ap-1396	7	3	it	it	PRON
ap-1396	7	4	has	have	AUX
ap-1396	7	5	been	be	AUX
ap-1396	7	6	shown	show	VERB
ap-1396	7	7	in	in	ADP
ap-1396	7	8	a	a	DET
ap-1396	7	9	recent	recent	ADJ
ap-1396	7	10	paper	paper	NOUN
ap-1396	7	11	by	by	ADP
ap-1396	7	12	longhi	longhi	PROPN
ap-1396	7	13	,	,	PUNCT
ap-1396	7	14	by	by	ADP
ap-1396	7	15	numerical	numerical	ADJ
ap-1396	7	16	simulation	simulation	PROPN
ap-1396	7	17	and	and	CCONJ
ap-1396	7	18	by	by	ADP
ap-1396	7	19	the	the	DET
ap-1396	7	20	use	use	NOUN
ap-1396	7	21	of	of	ADP
ap-1396	7	22	perturbation	perturbation	NOUN
ap-1396	7	23	theory	theory	NOUN
ap-1396	7	24	,	,	PUNCT
ap-1396	7	25	that	that	SCONJ
ap-1396	7	26	for	for	ADP
ap-1396	7	27	an	an	DET
ap-1396	7	28	initial	initial	ADJ
ap-1396	7	29	wave	wave	NOUN
ap-1396	7	30	packet	packet	NOUN
ap-1396	7	31	this	this	DET
ap-1396	7	32	growth	growth	NOUN
ap-1396	7	33	is	be	AUX
ap-1396	7	34	suppressed	suppress	VERB
ap-1396	7	35	,	,	PUNCT
ap-1396	7	36	giving	give	VERB
ap-1396	7	37	instead	instead	ADV
ap-1396	7	38	a	a	DET
ap-1396	7	39	constant	constant	ADJ
ap-1396	7	40	maximum	maximum	ADJ
ap-1396	7	41	amplitude	amplitude	NOUN
ap-1396	7	42	.	.	PUNCT
ap-1396	8	1	we	we	PRON
ap-1396	8	2	revisit	revisit	VERB
ap-1396	8	3	this	this	DET
ap-1396	8	4	problem	problem	NOUN
ap-1396	8	5	by	by	ADP
ap-1396	8	6	developing	develop	VERB
ap-1396	8	7	the	the	DET
ap-1396	8	8	perturbation	perturbation	NOUN
ap-1396	8	9	theory	theory	NOUN
ap-1396	8	10	further	far	ADV
ap-1396	8	11	.	.	PUNCT
ap-1396	9	1	we	we	PRON
ap-1396	9	2	verify	verify	VERB
ap-1396	9	3	that	that	SCONJ
ap-1396	9	4	the	the	DET
ap-1396	9	5	results	result	NOUN
ap-1396	9	6	found	find	VERB
ap-1396	9	7	by	by	ADP
ap-1396	9	8	longhi	longhi	PROPN
ap-1396	9	9	persist	persist	VERB
ap-1396	9	10	to	to	ADP
ap-1396	9	11	second	second	ADJ
ap-1396	9	12	order	order	NOUN
ap-1396	9	13	,	,	PUNCT
ap-1396	9	14	and	and	CCONJ
ap-1396	9	15	with	with	ADP
ap-1396	9	16	different	different	ADJ
ap-1396	9	17	input	input	NOUN
ap-1396	9	18	wave	wave	NOUN
ap-1396	9	19	packets	packet	NOUN
ap-1396	9	20	we	we	PRON
ap-1396	9	21	are	be	AUX
ap-1396	9	22	able	able	ADJ
ap-1396	9	23	to	to	PART
ap-1396	9	24	see	see	VERB
ap-1396	9	25	the	the	DET
ap-1396	9	26	seeds	seed	NOUN
ap-1396	9	27	in	in	ADP
ap-1396	9	28	perturbation	perturbation	NOUN
ap-1396	9	29	theory	theory	NOUN
ap-1396	9	30	of	of	ADP
ap-1396	9	31	the	the	DET
ap-1396	9	32	phenomenon	phenomenon	NOUN
ap-1396	9	33	of	of	ADP
ap-1396	9	34	birefringence	birefringence	NOUN
ap-1396	9	35	first	first	ADV
ap-1396	9	36	discovered	discover	VERB
ap-1396	9	37	by	by	ADP
ap-1396	9	38	el	el	PROPN
ap-1396	9	39	-	-	PUNCT
ap-1396	9	40	ganainy	ganainy	PROPN
ap-1396	9	41	et	et	PROPN
ap-1396	9	42	al	al	PROPN
ap-1396	9	43	.	.	PUNCT
ap-1396	10	1	keywords	keyword	NOUN
ap-1396	10	2	:	:	PUNCT
ap-1396	10	3	pseudo	pseudo	NOUN
ap-1396	10	4	-	-	ADJ
ap-1396	10	5	hermitian	hermitian	ADJ
ap-1396	10	6	quantum	quantum	NOUN
ap-1396	10	7	mechanics	mechanic	NOUN
ap-1396	10	8	,	,	PUNCT
ap-1396	10	9	optical	optical	ADJ
ap-1396	10	10	lattices	lattice	NOUN
ap-1396	10	11	,	,	PUNCT
ap-1396	10	12	perturbation	perturbation	NOUN
ap-1396	10	13	theory	theory	NOUN
ap-1396	10	14	.	.	PUNCT
ap-1396	11	1	1	1	NUM
ap-1396	11	2	introduction	introduction	NOUN
ap-1396	11	3	the	the	DET
ap-1396	11	4	study	study	NOUN
ap-1396	11	5	of	of	ADP
ap-1396	11	6	quantum	quantum	ADJ
ap-1396	11	7	mechanical	mechanical	ADJ
ap-1396	11	8	hamiltonians	hamiltonian	NOUN
ap-1396	11	9	that	that	PRON
ap-1396	11	10	are	be	AUX
ap-1396	11	11	pt	pt	X
ap-1396	11	12	-symmetric	-symmetric	ADJ
ap-1396	11	13	but	but	CCONJ
ap-1396	11	14	not	not	PART
ap-1396	11	15	hermitian	hermitian	ADJ
ap-1396	11	16	[	[	X
ap-1396	11	17	1–6	1–6	NUM
ap-1396	11	18	]	]	X
ap-1396	11	19	has	have	AUX
ap-1396	11	20	recently	recently	ADV
ap-1396	11	21	found	find	VERB
ap-1396	11	22	an	an	DET
ap-1396	11	23	unexpected	unexpected	ADJ
ap-1396	11	24	application	application	NOUN
ap-1396	11	25	in	in	ADP
ap-1396	11	26	classical	classical	ADJ
ap-1396	11	27	optics	optic	NOUN
ap-1396	11	28	[	[	X
ap-1396	11	29	7–15	7–15	PROPN
ap-1396	11	30	]	]	PUNCT
ap-1396	11	31	,	,	PUNCT
ap-1396	11	32	due	due	ADP
ap-1396	11	33	to	to	ADP
ap-1396	11	34	the	the	DET
ap-1396	11	35	fact	fact	NOUN
ap-1396	11	36	that	that	SCONJ
ap-1396	11	37	in	in	ADP
ap-1396	11	38	the	the	DET
ap-1396	11	39	paraxial	paraxial	ADJ
ap-1396	11	40	approximation	approximation	NOUN
ap-1396	11	41	the	the	DET
ap-1396	11	42	equation	equation	NOUN
ap-1396	11	43	of	of	ADP
ap-1396	11	44	propagation	propagation	NOUN
ap-1396	11	45	of	of	ADP
ap-1396	11	46	an	an	DET
ap-1396	11	47	electromagnetic	electromagnetic	ADJ
ap-1396	11	48	wave	wave	NOUN
ap-1396	11	49	in	in	ADP
ap-1396	11	50	a	a	DET
ap-1396	11	51	medium	medium	NOUN
ap-1396	11	52	is	be	AUX
ap-1396	11	53	formally	formally	ADV
ap-1396	11	54	identical	identical	ADJ
ap-1396	11	55	to	to	ADP
ap-1396	11	56	the	the	DET
ap-1396	11	57	schrödinger	schrödinger	NOUN
ap-1396	11	58	equation	equation	NOUN
ap-1396	11	59	,	,	PUNCT
ap-1396	11	60	but	but	CCONJ
ap-1396	11	61	with	with	ADP
ap-1396	11	62	different	different	ADJ
ap-1396	11	63	interpretations	interpretation	NOUN
ap-1396	11	64	for	for	ADP
ap-1396	11	65	the	the	DET
ap-1396	11	66	symbols	symbol	NOUN
ap-1396	11	67	appearing	appear	VERB
ap-1396	11	68	therein	therein	ADV
ap-1396	11	69	.	.	PUNCT
ap-1396	12	1	it	it	PRON
ap-1396	12	2	turns	turn	VERB
ap-1396	12	3	out	out	ADP
ap-1396	12	4	that	that	DET
ap-1396	12	5	propagation	propagation	NOUN
ap-1396	12	6	through	through	ADP
ap-1396	12	7	such	such	DET
ap-1396	12	8	a	a	DET
ap-1396	12	9	medium	medium	NOUN
ap-1396	12	10	exhibits	exhibit	NOUN
ap-1396	12	11	many	many	ADJ
ap-1396	12	12	new	new	ADJ
ap-1396	12	13	and	and	CCONJ
ap-1396	12	14	interesting	interesting	ADJ
ap-1396	12	15	properties	property	NOUN
ap-1396	12	16	,	,	PUNCT
ap-1396	12	17	such	such	ADJ
ap-1396	12	18	as	as	ADP
ap-1396	12	19	power	power	NOUN
ap-1396	12	20	oscillations	oscillation	NOUN
ap-1396	12	21	and	and	CCONJ
ap-1396	12	22	birefringence	birefringence	NOUN
ap-1396	12	23	.	.	PUNCT
ap-1396	13	1	the	the	DET
ap-1396	13	2	equation	equation	NOUN
ap-1396	13	3	of	of	ADP
ap-1396	13	4	propagation	propagation	NOUN
ap-1396	13	5	takes	take	VERB
ap-1396	13	6	the	the	DET
ap-1396	13	7	form	form	NOUN
ap-1396	13	8	i	i	PRON
ap-1396	13	9	∂ψ	∂ψ	VERB
ap-1396	14	1	∂z	∂z	PROPN
ap-1396	14	2	=	=	PUNCT
ap-1396	14	3	−	−	PROPN
ap-1396	14	4	(	(	PUNCT
ap-1396	14	5	∂2	∂2	NUM
ap-1396	14	6	∂x2	∂x2	NOUN
ap-1396	14	7	+	+	CCONJ
ap-1396	14	8	v	v	ADJ
ap-1396	14	9	(	(	PUNCT
ap-1396	14	10	x	x	NOUN
ap-1396	14	11	)	)	PUNCT
ap-1396	14	12	)	)	PUNCT
ap-1396	15	1	ψ	ψ	X
ap-1396	15	2	,	,	PUNCT
ap-1396	15	3	(	(	PUNCT
ap-1396	15	4	1	1	X
ap-1396	15	5	)	)	PUNCT
ap-1396	15	6	where	where	SCONJ
ap-1396	15	7	ψ(x	ψ(x	NOUN
ap-1396	15	8	,	,	PUNCT
ap-1396	15	9	z	z	NOUN
ap-1396	15	10	)	)	PUNCT
ap-1396	15	11	represents	represent	VERB
ap-1396	15	12	the	the	DET
ap-1396	15	13	envelope	envelope	NOUN
ap-1396	15	14	function	function	NOUN
ap-1396	15	15	of	of	ADP
ap-1396	15	16	the	the	DET
ap-1396	15	17	amplitude	amplitude	NOUN
ap-1396	15	18	of	of	ADP
ap-1396	15	19	the	the	DET
ap-1396	15	20	electric	electric	ADJ
ap-1396	15	21	field	field	NOUN
ap-1396	15	22	,	,	PUNCT
ap-1396	15	23	z	z	PROPN
ap-1396	15	24	is	be	AUX
ap-1396	15	25	a	a	DET
ap-1396	15	26	scaled	scale	VERB
ap-1396	15	27	propagation	propagation	NOUN
ap-1396	15	28	distance	distance	NOUN
ap-1396	15	29	,	,	PUNCT
ap-1396	15	30	and	and	CCONJ
ap-1396	15	31	v	v	NOUN
ap-1396	15	32	(	(	PUNCT
ap-1396	15	33	x	x	X
ap-1396	15	34	)	)	PUNCT
ap-1396	15	35	is	be	AUX
ap-1396	15	36	the	the	DET
ap-1396	15	37	optical	optical	ADJ
ap-1396	15	38	potential	potential	NOUN
ap-1396	15	39	,	,	PUNCT
ap-1396	15	40	proportional	proportional	ADJ
ap-1396	15	41	to	to	ADP
ap-1396	15	42	the	the	DET
ap-1396	15	43	variation	variation	NOUN
ap-1396	15	44	in	in	ADP
ap-1396	15	45	the	the	DET
ap-1396	15	46	refractive	refractive	ADJ
ap-1396	15	47	index	index	NOUN
ap-1396	15	48	of	of	ADP
ap-1396	15	49	the	the	DET
ap-1396	15	50	material	material	NOUN
ap-1396	15	51	through	through	ADP
ap-1396	15	52	which	which	PRON
ap-1396	15	53	the	the	DET
ap-1396	15	54	wave	wave	NOUN
ap-1396	15	55	is	be	AUX
ap-1396	15	56	passing	pass	VERB
ap-1396	15	57	.	.	PUNCT
ap-1396	16	1	a	a	DET
ap-1396	16	2	complex	complex	ADJ
ap-1396	16	3	v	v	NOUN
ap-1396	16	4	corresponds	correspond	VERB
ap-1396	16	5	to	to	ADP
ap-1396	16	6	a	a	DET
ap-1396	16	7	complex	complex	ADJ
ap-1396	16	8	refractive	refractive	ADJ
ap-1396	16	9	index	index	NOUN
ap-1396	16	10	,	,	PUNCT
ap-1396	16	11	whose	whose	DET
ap-1396	16	12	imaginary	imaginary	ADJ
ap-1396	16	13	part	part	NOUN
ap-1396	16	14	represents	represent	VERB
ap-1396	16	15	either	either	PRON
ap-1396	16	16	loss	loss	NOUN
ap-1396	16	17	or	or	CCONJ
ap-1396	16	18	gain	gain	NOUN
ap-1396	16	19	.	.	PUNCT
ap-1396	17	1	in	in	ADP
ap-1396	17	2	principle	principle	NOUN
ap-1396	17	3	the	the	DET
ap-1396	17	4	loss	loss	NOUN
ap-1396	17	5	and	and	CCONJ
ap-1396	17	6	gain	gain	VERB
ap-1396	17	7	regions	region	NOUN
ap-1396	17	8	can	can	AUX
ap-1396	17	9	be	be	AUX
ap-1396	17	10	carefully	carefully	ADV
ap-1396	17	11	configured	configure	VERB
ap-1396	17	12	so	so	SCONJ
ap-1396	17	13	that	that	SCONJ
ap-1396	17	14	v	v	NOUN
ap-1396	17	15	is	be	AUX
ap-1396	17	16	pt	pt	X
ap-1396	17	17	symmetric	symmetric	NOUN
ap-1396	17	18	,	,	PUNCT
ap-1396	17	19	that	that	PRON
ap-1396	17	20	is	be	AUX
ap-1396	17	21	v	v	ADP
ap-1396	17	22	∗(x	∗(x	NOUN
ap-1396	17	23	)	)	PUNCT
ap-1396	17	24	=	=	SYM
ap-1396	17	25	v	v	X
ap-1396	17	26	(	(	PUNCT
ap-1396	17	27	−x	−x	NOUN
ap-1396	17	28	)	)	PUNCT
ap-1396	17	29	.	.	PUNCT
ap-1396	18	1	there	there	PRON
ap-1396	18	2	is	be	VERB
ap-1396	18	3	also	also	ADV
ap-1396	18	4	a	a	DET
ap-1396	18	5	non	non	ADJ
ap-1396	18	6	-	-	ADJ
ap-1396	18	7	linear	linear	ADJ
ap-1396	18	8	version	version	NOUN
ap-1396	18	9	of	of	ADP
ap-1396	18	10	this	this	DET
ap-1396	18	11	equation	equation	NOUN
ap-1396	18	12	,	,	PUNCT
ap-1396	18	13	arising	arise	VERB
ap-1396	18	14	from	from	ADP
ap-1396	18	15	sufficiently	sufficiently	ADV
ap-1396	18	16	intense	intense	ADJ
ap-1396	18	17	beams	beam	NOUN
ap-1396	18	18	,	,	PUNCT
ap-1396	18	19	where	where	SCONJ
ap-1396	18	20	there	there	PRON
ap-1396	18	21	is	be	VERB
ap-1396	18	22	an	an	DET
ap-1396	18	23	additional	additional	ADJ
ap-1396	18	24	term	term	NOUN
ap-1396	18	25	proportional	proportional	ADJ
ap-1396	18	26	to	to	ADP
ap-1396	18	27	|ψ|2ψ	|ψ|2ψ	VERB
ap-1396	18	28	.	.	PUNCT
ap-1396	19	1	however	however	ADV
ap-1396	19	2	,	,	PUNCT
ap-1396	19	3	for	for	ADP
ap-1396	19	4	the	the	DET
ap-1396	19	5	purposes	purpose	NOUN
ap-1396	19	6	of	of	ADP
ap-1396	19	7	this	this	DET
ap-1396	19	8	paper	paper	NOUN
ap-1396	19	9	we	we	PRON
ap-1396	19	10	shall	shall	AUX
ap-1396	19	11	limit	limit	VERB
ap-1396	19	12	ourselves	ourselves	PRON
ap-1396	19	13	to	to	ADP
ap-1396	19	14	the	the	DET
ap-1396	19	15	linear	linear	ADJ
ap-1396	19	16	case	case	NOUN
ap-1396	19	17	.	.	PUNCT
ap-1396	20	1	a	a	DET
ap-1396	20	2	model	model	NOUN
ap-1396	20	3	system	system	NOUN
ap-1396	20	4	exemplifying	exemplify	VERB
ap-1396	20	5	some	some	PRON
ap-1396	20	6	of	of	ADP
ap-1396	20	7	the	the	DET
ap-1396	20	8	novel	novel	ADJ
ap-1396	20	9	features	feature	NOUN
ap-1396	20	10	of	of	ADP
ap-1396	20	11	beam	beam	ADJ
ap-1396	20	12	propagation	propagation	NOUN
ap-1396	20	13	in	in	ADP
ap-1396	20	14	pt	pt	NOUN
ap-1396	20	15	-symmetric	-symmetric	ADJ
ap-1396	20	16	optical	optical	ADJ
ap-1396	20	17	lattices	lattice	NOUN
ap-1396	20	18	uses	use	VERB
ap-1396	20	19	the	the	DET
ap-1396	20	20	sinusoidal	sinusoidal	ADJ
ap-1396	20	21	potential	potential	NOUN
ap-1396	20	22	v	v	NOUN
ap-1396	20	23	=	=	SYM
ap-1396	20	24	v0	v0	NOUN
ap-1396	20	25	[	[	X
ap-1396	20	26	cos(2πx	cos(2πx	NOUN
ap-1396	20	27	/	/	SYM
ap-1396	20	28	a	a	NOUN
ap-1396	20	29	)	)	PUNCT
ap-1396	20	30	+	+	NUM
ap-1396	20	31	iλ	iλ	PROPN
ap-1396	20	32	sin(2πx	sin(2πx	PROPN
ap-1396	20	33	/	/	SYM
ap-1396	20	34	a	a	NOUN
ap-1396	20	35	)	)	PUNCT
ap-1396	20	36	]	]	PUNCT
ap-1396	21	1	this	this	DET
ap-1396	21	2	model	model	NOUN
ap-1396	21	3	has	have	AUX
ap-1396	21	4	been	be	AUX
ap-1396	21	5	studied	study	VERB
ap-1396	21	6	numerically	numerically	ADV
ap-1396	21	7	and	and	CCONJ
ap-1396	21	8	theoretically	theoretically	ADV
ap-1396	21	9	in	in	ADP
ap-1396	21	10	refs	ref	NOUN
ap-1396	21	11	.	.	PUNCT
ap-1396	22	1	[	[	X
ap-1396	22	2	9	9	NUM
ap-1396	22	3	,	,	PUNCT
ap-1396	22	4	12	12	NUM
ap-1396	22	5	,	,	PUNCT
ap-1396	22	6	13	13	NUM
ap-1396	22	7	]	]	PUNCT
ap-1396	22	8	.	.	PUNCT
ap-1396	23	1	the	the	DET
ap-1396	23	2	propagation	propagation	NOUN
ap-1396	23	3	in	in	ADP
ap-1396	23	4	z	z	PROPN
ap-1396	23	5	of	of	ADP
ap-1396	23	6	the	the	DET
ap-1396	23	7	amplitude	amplitude	NOUN
ap-1396	23	8	ψ(x	ψ(x	NOUN
ap-1396	23	9	,	,	PUNCT
ap-1396	23	10	z	z	NOUN
ap-1396	23	11	)	)	PUNCT
ap-1396	23	12	is	be	AUX
ap-1396	23	13	governed	govern	VERB
ap-1396	23	14	by	by	ADP
ap-1396	23	15	the	the	DET
ap-1396	23	16	analogue	analogue	NOUN
ap-1396	23	17	schrödinger	schrödinger	NOUN
ap-1396	23	18	equation	equation	NOUN
ap-1396	23	19	(	(	PUNCT
ap-1396	23	20	1	1	NUM
ap-1396	23	21	)	)	PUNCT
ap-1396	23	22	,	,	PUNCT
ap-1396	23	23	which	which	PRON
ap-1396	23	24	for	for	ADP
ap-1396	23	25	an	an	DET
ap-1396	23	26	eigenstate	eigenstate	NOUN
ap-1396	23	27	of	of	ADP
ap-1396	23	28	h	h	NOUN
ap-1396	23	29	,	,	PUNCT
ap-1396	23	30	with	with	ADP
ap-1396	23	31	eigenvalue	eigenvalue	PROPN
ap-1396	23	32	β	β	X
ap-1396	23	33	and	and	CCONJ
ap-1396	23	34	z	z	NOUN
ap-1396	23	35	-	-	PUNCT
ap-1396	23	36	dependence	dependence	NOUN
ap-1396	23	37	ψ	ψ	NOUN
ap-1396	23	38	∝	∝	PROPN
ap-1396	23	39	e−iβz	e−iβz	NOUN
ap-1396	23	40	reduces	reduce	VERB
ap-1396	23	41	to	to	ADP
ap-1396	23	42	the	the	DET
ap-1396	23	43	eigenvalue	eigenvalue	ADJ
ap-1396	23	44	equation	equation	NOUN
ap-1396	23	45	−	−	NOUN
ap-1396	23	46	ψ′′	ψ′′	PROPN
ap-1396	23	47	−	−	PROPN
ap-1396	23	48	v0	v0	NOUN
ap-1396	23	49	[	[	X
ap-1396	23	50	cos(2πx	cos(2πx	NOUN
ap-1396	23	51	/	/	SYM
ap-1396	23	52	a	a	NOUN
ap-1396	23	53	)	)	PUNCT
ap-1396	23	54	+	+	NUM
ap-1396	23	55	iλ	iλ	PROPN
ap-1396	23	56	sin(2πx	sin(2πx	PROPN
ap-1396	23	57	/	/	SYM
ap-1396	23	58	a	a	NOUN
ap-1396	23	59	)	)	PUNCT
ap-1396	23	60	]	]	PUNCT
ap-1396	24	1	ψ	ψ	X
ap-1396	24	2	=	=	NOUN
ap-1396	24	3	βψ	βψ	X
ap-1396	24	4	.(2	.(2	PUNCT
ap-1396	24	5	)	)	PUNCT
ap-1396	25	1	it	it	PRON
ap-1396	25	2	turns	turn	VERB
ap-1396	25	3	out	out	ADP
ap-1396	25	4	that	that	SCONJ
ap-1396	25	5	these	these	DET
ap-1396	25	6	eigenvalues	eigenvalue	NOUN
ap-1396	25	7	are	be	AUX
ap-1396	25	8	real	real	ADJ
ap-1396	25	9	for	for	ADP
ap-1396	25	10	λ	λ	PROPN
ap-1396	25	11	≤	≤	NOUN
ap-1396	25	12	1	1	NUM
ap-1396	25	13	,	,	PUNCT
ap-1396	25	14	which	which	PRON
ap-1396	25	15	corresponds	correspond	VERB
ap-1396	25	16	to	to	ADP
ap-1396	25	17	unbroken	unbroken	ADJ
ap-1396	25	18	pt	pt	NOUN
ap-1396	25	19	symmetry	symmetry	NOUN
ap-1396	25	20	,	,	PUNCT
ap-1396	25	21	where	where	SCONJ
ap-1396	25	22	the	the	DET
ap-1396	25	23	eigenfunctions	eigenfunction	NOUN
ap-1396	25	24	respect	respect	VERB
ap-1396	25	25	the	the	DET
ap-1396	25	26	(	(	PUNCT
ap-1396	25	27	anti	anti	ADJ
ap-1396	25	28	-	-	ADJ
ap-1396	25	29	linear	linear	ADJ
ap-1396	25	30	)	)	PUNCT
ap-1396	25	31	symmetry	symmetry	NOUN
ap-1396	25	32	of	of	ADP
ap-1396	25	33	the	the	DET
ap-1396	25	34	hamiltonian	hamiltonian	NOUN
ap-1396	25	35	.	.	PUNCT
ap-1396	26	1	above	above	ADP
ap-1396	26	2	λ	λ	X
ap-1396	26	3	=	=	SYM
ap-1396	26	4	1	1	NUM
ap-1396	26	5	complex	complex	NOUN
ap-1396	26	6	eigenvalues	eigenvalue	NOUN
ap-1396	26	7	begin	begin	VERB
ap-1396	26	8	to	to	PART
ap-1396	26	9	appear	appear	VERB
ap-1396	26	10	,	,	PUNCT
ap-1396	26	11	and	and	CCONJ
ap-1396	26	12	indeed	indeed	ADV
ap-1396	26	13	above	above	ADP
ap-1396	26	14	λ	λ	PROPN
ap-1396	26	15	≈	≈	PROPN
ap-1396	26	16	1.776	1.776	NUM
ap-1396	26	17	87	87	NUM
ap-1396	26	18	all	all	DET
ap-1396	26	19	the	the	DET
ap-1396	26	20	eigenvalues	eigenvalue	NOUN
ap-1396	26	21	are	be	AUX
ap-1396	26	22	complex	complex	ADJ
ap-1396	27	1	[	[	X
ap-1396	27	2	16	16	NUM
ap-1396	27	3	]	]	PUNCT
ap-1396	27	4	.	.	PUNCT
ap-1396	28	1	clearly	clearly	ADV
ap-1396	28	2	one	one	PRON
ap-1396	28	3	would	would	AUX
ap-1396	28	4	expect	expect	VERB
ap-1396	28	5	oscillatory	oscillatory	ADJ
ap-1396	28	6	behaviour	behaviour	NOUN
ap-1396	28	7	of	of	ADP
ap-1396	28	8	the	the	DET
ap-1396	28	9	amplitude	amplitude	NOUN
ap-1396	28	10	below	below	ADP
ap-1396	28	11	the	the	DET
ap-1396	28	12	threshold	threshold	NOUN
ap-1396	28	13	at	at	ADP
ap-1396	28	14	λ	λ	X
ap-1396	28	15	=	=	SYM
ap-1396	28	16	1	1	NUM
ap-1396	28	17	and	and	CCONJ
ap-1396	28	18	exponential	exponential	ADJ
ap-1396	28	19	behaviour	behaviour	NOUN
ap-1396	28	20	above	above	ADP
ap-1396	28	21	the	the	DET
ap-1396	28	22	threshold	threshold	NOUN
ap-1396	28	23	,	,	PUNCT
ap-1396	28	24	but	but	CCONJ
ap-1396	28	25	the	the	DET
ap-1396	28	26	precise	precise	ADJ
ap-1396	28	27	form	form	NOUN
ap-1396	28	28	of	of	ADP
ap-1396	28	29	the	the	DET
ap-1396	28	30	evolution	evolution	NOUN
ap-1396	28	31	at	at	ADP
ap-1396	28	32	λ	λ	X
ap-1396	28	33	=	=	SYM
ap-1396	28	34	1	1	NUM
ap-1396	28	35	is	be	AUX
ap-1396	28	36	less	less	ADV
ap-1396	28	37	obvious	obvious	ADJ
ap-1396	28	38	.	.	PUNCT
ap-1396	29	1	at	at	ADP
ap-1396	29	2	first	first	ADJ
ap-1396	29	3	sight	sight	NOUN
ap-1396	29	4	one	one	PRON
ap-1396	29	5	would	would	AUX
ap-1396	29	6	expect	expect	VERB
ap-1396	29	7	linear	linear	ADJ
ap-1396	29	8	growth	growth	NOUN
ap-1396	29	9	because	because	SCONJ
ap-1396	29	10	of	of	ADP
ap-1396	29	11	the	the	DET
ap-1396	29	12	appearance	appearance	NOUN
ap-1396	29	13	of	of	ADP
ap-1396	29	14	jordan	jordan	PROPN
ap-1396	29	15	blocks	block	NOUN
ap-1396	29	16	associated	associate	VERB
ap-1396	29	17	with	with	ADP
ap-1396	29	18	the	the	DET
ap-1396	29	19	degenerate	degenerate	ADJ
ap-1396	29	20	eigenvalues	eigenvalue	NOUN
ap-1396	29	21	that	that	PRON
ap-1396	29	22	merge	merge	VERB
ap-1396	29	23	at	at	ADP
ap-1396	29	24	that	that	DET
ap-1396	29	25	value	value	NOUN
ap-1396	29	26	of	of	ADP
ap-1396	29	27	λ	λ	NOUN
ap-1396	29	28	,	,	PUNCT
ap-1396	29	29	but	but	CCONJ
ap-1396	29	30	,	,	PUNCT
ap-1396	29	31	as	as	SCONJ
ap-1396	29	32	longhi	longhi	PROPN
ap-1396	29	33	[	[	X
ap-1396	29	34	12	12	NUM
ap-1396	29	35	]	]	PUNCT
ap-1396	29	36	has	have	AUX
ap-1396	29	37	emphasized	emphasize	VERB
ap-1396	29	38	,	,	PUNCT
ap-1396	29	39	this	this	DET
ap-1396	29	40	behaviour	behaviour	NOUN
ap-1396	29	41	can	can	AUX
ap-1396	29	42	be	be	AUX
ap-1396	29	43	significantly	significantly	ADV
ap-1396	29	44	modified	modify	VERB
ap-1396	29	45	depending	depend	VERB
ap-1396	29	46	on	on	ADP
ap-1396	29	47	the	the	DET
ap-1396	29	48	nature	nature	NOUN
ap-1396	29	49	of	of	ADP
ap-1396	29	50	the	the	DET
ap-1396	29	51	initial	initial	ADJ
ap-1396	29	52	wave	wave	NOUN
ap-1396	29	53	packet	packet	NOUN
ap-1396	29	54	.	.	PUNCT
ap-1396	30	1	in	in	ADP
ap-1396	30	2	a	a	DET
ap-1396	30	3	previous	previous	ADJ
ap-1396	30	4	paper	paper	NOUN
ap-1396	30	5	[	[	X
ap-1396	30	6	17	17	NUM
ap-1396	30	7	]	]	PUNCT
ap-1396	30	8	we	we	PRON
ap-1396	30	9	approached	approach	VERB
ap-1396	30	10	this	this	DET
ap-1396	30	11	problem	problem	NOUN
ap-1396	30	12	by	by	ADP
ap-1396	30	13	explicitly	explicitly	ADV
ap-1396	30	14	constructing	construct	VERB
ap-1396	30	15	the	the	DET
ap-1396	30	16	bloch	bloch	PROPN
ap-1396	30	17	wavefunctions	wavefunction	NOUN
ap-1396	30	18	and	and	CCONJ
ap-1396	30	19	the	the	DET
ap-1396	30	20	associated	associated	PROPN
ap-1396	30	21	jordan	jordan	PROPN
ap-1396	30	22	functions	function	NOUN
ap-1396	30	23	corresponding	correspond	VERB
ap-1396	30	24	to	to	ADP
ap-1396	30	25	the	the	DET
ap-1396	30	26	degenerate	degenerate	ADJ
ap-1396	30	27	eigenvalues	eigenvalue	NOUN
ap-1396	30	28	and	and	CCONJ
ap-1396	30	29	then	then	ADV
ap-1396	30	30	using	use	VERB
ap-1396	30	31	the	the	DET
ap-1396	30	32	method	method	NOUN
ap-1396	30	33	of	of	ADP
ap-1396	30	34	stationary	stationary	ADJ
ap-1396	30	35	states	state	NOUN
ap-1396	30	36	to	to	PART
ap-1396	30	37	construct	construct	VERB
ap-1396	30	38	the	the	DET
ap-1396	30	39	z	z	NOUN
ap-1396	30	40	-	-	PUNCT
ap-1396	30	41	dependence	dependence	NOUN
ap-1396	30	42	.	.	PUNCT
ap-1396	31	1	we	we	PRON
ap-1396	31	2	found	find	VERB
ap-1396	31	3	that	that	SCONJ
ap-1396	31	4	the	the	DET
ap-1396	31	5	explicit	explicit	ADJ
ap-1396	31	6	linear	linear	ADJ
ap-1396	31	7	dependence	dependence	NOUN
ap-1396	31	8	arising	arise	VERB
ap-1396	31	9	from	from	ADP
ap-1396	31	10	the	the	DET
ap-1396	31	11	jordan	jordan	PROPN
ap-1396	31	12	associated	associate	VERB
ap-1396	31	13	21	21	NUM
ap-1396	31	14	acta	acta	PROPN
ap-1396	31	15	polytechnica	polytechnica	PROPN
ap-1396	31	16	vol	vol	NOUN
ap-1396	31	17	.	.	PUNCT
ap-1396	32	1	51	51	NUM
ap-1396	32	2	no	no	INTJ
ap-1396	32	3	.	.	PUNCT
ap-1396	33	1	4/2011	4/2011	NUM
ap-1396	33	2	functions	function	NOUN
ap-1396	33	3	is	be	AUX
ap-1396	33	4	indeed	indeed	ADV
ap-1396	33	5	cancelled	cancel	VERB
ap-1396	33	6	by	by	ADP
ap-1396	33	7	the	the	DET
ap-1396	33	8	combined	combine	VERB
ap-1396	33	9	contributions	contribution	NOUN
ap-1396	33	10	from	from	ADP
ap-1396	33	11	the	the	DET
ap-1396	33	12	non	non	ADJ
ap-1396	33	13	-	-	ADJ
ap-1396	33	14	degenerate	degenerate	ADJ
ap-1396	33	15	wave	wave	NOUN
ap-1396	33	16	-	-	PUNCT
ap-1396	33	17	functions	function	NOUN
ap-1396	33	18	and	and	CCONJ
ap-1396	33	19	were	be	AUX
ap-1396	33	20	able	able	ADJ
ap-1396	33	21	to	to	PART
ap-1396	33	22	understand	understand	VERB
ap-1396	33	23	how	how	SCONJ
ap-1396	33	24	this	this	DET
ap-1396	33	25	cancellation	cancellation	NOUN
ap-1396	33	26	came	come	VERB
ap-1396	33	27	about	about	ADP
ap-1396	33	28	.	.	PUNCT
ap-1396	34	1	in	in	ADP
ap-1396	34	2	the	the	DET
ap-1396	34	3	present	present	ADJ
ap-1396	34	4	paper	paper	NOUN
ap-1396	34	5	we	we	PRON
ap-1396	34	6	approach	approach	VERB
ap-1396	34	7	the	the	DET
ap-1396	34	8	problem	problem	NOUN
ap-1396	34	9	from	from	ADP
ap-1396	34	10	a	a	DET
ap-1396	34	11	different	different	ADJ
ap-1396	34	12	point	point	NOUN
ap-1396	34	13	of	of	ADP
ap-1396	34	14	view	view	NOUN
ap-1396	34	15	by	by	ADP
ap-1396	34	16	revisiting	revisit	VERB
ap-1396	34	17	the	the	DET
ap-1396	34	18	complementary	complementary	ADJ
ap-1396	34	19	perturbative	perturbative	ADJ
ap-1396	34	20	calculation	calculation	NOUN
ap-1396	34	21	of	of	ADP
ap-1396	34	22	longhi	longhi	PROPN
ap-1396	35	1	[	[	X
ap-1396	35	2	12	12	NUM
ap-1396	35	3	]	]	PUNCT
ap-1396	35	4	.	.	PUNCT
ap-1396	36	1	in	in	ADP
ap-1396	36	2	section	section	NOUN
ap-1396	36	3	2	2	NUM
ap-1396	36	4	we	we	PRON
ap-1396	36	5	briefly	briefly	ADV
ap-1396	36	6	recapitulate	recapitulate	VERB
ap-1396	36	7	how	how	SCONJ
ap-1396	36	8	the	the	DET
ap-1396	36	9	spectrum	spectrum	NOUN
ap-1396	36	10	and	and	CCONJ
ap-1396	36	11	eigenfunctions	eigenfunction	NOUN
ap-1396	36	12	are	be	AUX
ap-1396	36	13	calculated	calculate	VERB
ap-1396	36	14	.	.	PUNCT
ap-1396	37	1	then	then	ADV
ap-1396	37	2	in	in	ADP
ap-1396	37	3	section	section	NOUN
ap-1396	37	4	3	3	NUM
ap-1396	37	5	,	,	PUNCT
ap-1396	37	6	which	which	PRON
ap-1396	37	7	forms	form	VERB
ap-1396	37	8	the	the	DET
ap-1396	37	9	main	main	ADJ
ap-1396	37	10	body	body	NOUN
ap-1396	37	11	of	of	ADP
ap-1396	37	12	the	the	DET
ap-1396	37	13	paper	paper	NOUN
ap-1396	37	14	,	,	PUNCT
ap-1396	37	15	we	we	PRON
ap-1396	37	16	give	give	VERB
ap-1396	37	17	an	an	DET
ap-1396	37	18	explicit	explicit	ADJ
ap-1396	37	19	expression	expression	NOUN
ap-1396	37	20	for	for	ADP
ap-1396	37	21	the	the	DET
ap-1396	37	22	first	first	ADJ
ap-1396	37	23	-	-	PUNCT
ap-1396	37	24	order	order	NOUN
ap-1396	37	25	contribution	contribution	NOUN
ap-1396	37	26	and	and	CCONJ
ap-1396	37	27	carry	carry	VERB
ap-1396	37	28	out	out	ADP
ap-1396	37	29	the	the	DET
ap-1396	37	30	second	second	ADJ
ap-1396	37	31	-	-	PUNCT
ap-1396	37	32	order	order	NOUN
ap-1396	37	33	calculation	calculation	NOUN
ap-1396	37	34	in	in	ADP
ap-1396	37	35	detail	detail	NOUN
ap-1396	37	36	.	.	PUNCT
ap-1396	38	1	this	this	PRON
ap-1396	38	2	enables	enable	VERB
ap-1396	38	3	us	we	PRON
ap-1396	38	4	to	to	PART
ap-1396	38	5	investigate	investigate	VERB
ap-1396	38	6	the	the	DET
ap-1396	38	7	saturation	saturation	NOUN
ap-1396	38	8	phenomenon	phenomenon	NOUN
ap-1396	38	9	for	for	ADP
ap-1396	38	10	a	a	DET
ap-1396	38	11	variety	variety	NOUN
ap-1396	38	12	of	of	ADP
ap-1396	38	13	different	different	ADJ
ap-1396	38	14	inputs	input	NOUN
ap-1396	38	15	.	.	PUNCT
ap-1396	39	1	finally	finally	ADV
ap-1396	39	2	,	,	PUNCT
ap-1396	39	3	in	in	ADP
ap-1396	39	4	section	section	NOUN
ap-1396	39	5	4	4	NUM
ap-1396	39	6	we	we	PRON
ap-1396	39	7	give	give	VERB
ap-1396	39	8	a	a	DET
ap-1396	39	9	brief	brief	ADJ
ap-1396	39	10	discussion	discussion	NOUN
ap-1396	39	11	of	of	ADP
ap-1396	39	12	our	our	PRON
ap-1396	39	13	results	result	NOUN
ap-1396	39	14	.	.	PUNCT
ap-1396	40	1	2	2	NUM
ap-1396	40	2	band	band	NOUN
ap-1396	40	3	structure	structure	NOUN
ap-1396	40	4	at	at	ADP
ap-1396	40	5	threshold	threshold	NOUN
ap-1396	40	6	at	at	ADP
ap-1396	40	7	the	the	DET
ap-1396	40	8	threshold	threshold	NOUN
ap-1396	40	9	λ	λ	X
ap-1396	40	10	=	=	SYM
ap-1396	40	11	1	1	NUM
ap-1396	40	12	,	,	PUNCT
ap-1396	40	13	the	the	DET
ap-1396	40	14	potential	potential	ADJ
ap-1396	40	15	v	v	NOUN
ap-1396	40	16	in	in	ADP
ap-1396	40	17	eq	eq	ADP
ap-1396	40	18	.	.	PUNCT
ap-1396	41	1	(	(	PUNCT
ap-1396	41	2	2	2	X
ap-1396	41	3	)	)	PUNCT
ap-1396	41	4	becomes	become	VERB
ap-1396	41	5	the	the	DET
ap-1396	41	6	complex	complex	ADJ
ap-1396	41	7	exponential	exponential	NOUN
ap-1396	41	8	v	v	NOUN
ap-1396	41	9	=	=	SYM
ap-1396	41	10	v0	v0	PROPN
ap-1396	41	11	exp(2iπx	exp(2iπx	PROPN
ap-1396	41	12	/	/	SYM
ap-1396	41	13	a	a	NOUN
ap-1396	41	14	)	)	PUNCT
ap-1396	41	15	,	,	PUNCT
ap-1396	41	16	for	for	ADP
ap-1396	41	17	which	which	PRON
ap-1396	41	18	the	the	DET
ap-1396	41	19	schrödinger	schrödinger	NOUN
ap-1396	41	20	equation	equation	NOUN
ap-1396	41	21	is	be	AUX
ap-1396	41	22	−	−	PROPN
ap-1396	41	23	ψ′′	ψ′′	PROPN
ap-1396	41	24	−	−	PROPN
ap-1396	41	25	v0	v0	PROPN
ap-1396	41	26	exp(2iπx	exp(2iπx	PROPN
ap-1396	41	27	/	/	SYM
ap-1396	41	28	a)ψ	a)ψ	NOUN
ap-1396	41	29	=	=	SYM
ap-1396	42	1	βψ	βψ	X
ap-1396	42	2	.	.	PUNCT
ap-1396	43	1	(	(	PUNCT
ap-1396	43	2	3	3	X
ap-1396	43	3	)	)	PUNCT
ap-1396	43	4	this	this	PRON
ap-1396	43	5	is	be	AUX
ap-1396	43	6	a	a	DET
ap-1396	43	7	form	form	NOUN
ap-1396	43	8	of	of	ADP
ap-1396	43	9	the	the	DET
ap-1396	43	10	bessel	bessel	ADJ
ap-1396	43	11	equation	equation	NOUN
ap-1396	43	12	,	,	PUNCT
ap-1396	43	13	as	as	SCONJ
ap-1396	43	14	is	be	AUX
ap-1396	43	15	seen	see	VERB
ap-1396	43	16	by	by	ADP
ap-1396	43	17	the	the	DET
ap-1396	43	18	substitution	substitution	NOUN
ap-1396	43	19	y	y	NOUN
ap-1396	43	20	=	=	SYM
ap-1396	43	21	y0	y0	PROPN
ap-1396	43	22	exp(iπx	exp(iπx	VERB
ap-1396	43	23	/	/	SYM
ap-1396	43	24	a	a	NOUN
ap-1396	43	25	)	)	PUNCT
ap-1396	43	26	,	,	PUNCT
ap-1396	43	27	where	where	SCONJ
ap-1396	43	28	y0	y0	NOUN
ap-1396	43	29	=	=	SYM
ap-1396	43	30	(	(	PUNCT
ap-1396	43	31	a	a	PRON
ap-1396	43	32	/	/	SYM
ap-1396	43	33	π	π	NOUN
ap-1396	43	34	)	)	PUNCT
ap-1396	43	35	√	√	NUM
ap-1396	43	36	v0	v0	NOUN
ap-1396	43	37	,	,	PUNCT
ap-1396	43	38	giving	give	VERB
ap-1396	43	39	y2	y2	PROPN
ap-1396	43	40	d2ψ	d2ψ	PROPN
ap-1396	43	41	dy2	dy2	PROPN
ap-1396	43	42	+	+	CCONJ
ap-1396	43	43	y	y	PROPN
ap-1396	43	44	dψ	dψ	X
ap-1396	43	45	dy	dy	NOUN
ap-1396	43	46	−	−	PROPN
ap-1396	44	1	(	(	PUNCT
ap-1396	44	2	y2	y2	PROPN
ap-1396	44	3	+	+	CCONJ
ap-1396	44	4	q2)ψ	q2)ψ	ADJ
ap-1396	44	5	=	=	SYM
ap-1396	44	6	0	0	NUM
ap-1396	44	7	,	,	PUNCT
ap-1396	44	8	(	(	PUNCT
ap-1396	44	9	4	4	X
ap-1396	44	10	)	)	PUNCT
ap-1396	44	11	�	�	NOUN
ap-1396	44	12	1	1	NUM
ap-1396	44	13	1	1	NUM
ap-1396	44	14	k.	k.	NOUN
ap-1396	44	15	a	a	DET
ap-1396	44	16	π	π	PROPN
ap-1396	44	17	2	2	NUM
ap-1396	44	18	4	4	NUM
ap-1396	44	19	9	9	NUM
ap-1396	44	20	16	16	NUM
ap-1396	44	21	β	β	NOUN
ap-1396	44	22	.	.	PUNCT
ap-1396	45	1	π2	π2	PROPN
ap-1396	45	2	a2	a2	PROPN
ap-1396	45	3	fig	fig	NOUN
ap-1396	45	4	.	.	PUNCT
ap-1396	46	1	1	1	NUM
ap-1396	46	2	:	:	PUNCT
ap-1396	46	3	band	band	NOUN
ap-1396	46	4	structure	structure	NOUN
ap-1396	46	5	for	for	ADP
ap-1396	46	6	λ	λ	NOUN
ap-1396	46	7	=	=	NOUN
ap-1396	46	8	1	1	NUM
ap-1396	46	9	in	in	ADP
ap-1396	46	10	the	the	DET
ap-1396	46	11	reduced	reduce	VERB
ap-1396	46	12	zone	zone	NOUN
ap-1396	46	13	scheme	scheme	NOUN
ap-1396	46	14	.	.	PUNCT
ap-1396	47	1	the	the	DET
ap-1396	47	2	bloch	bloch	PROPN
ap-1396	47	3	momentum	momentum	NOUN
ap-1396	47	4	k	k	PROPN
ap-1396	47	5	is	be	AUX
ap-1396	47	6	plotted	plot	VERB
ap-1396	47	7	in	in	ADP
ap-1396	47	8	units	unit	NOUN
ap-1396	47	9	of	of	ADP
ap-1396	47	10	π	π	PROPN
ap-1396	47	11	/	/	SYM
ap-1396	47	12	a	a	PROPN
ap-1396	47	13	and	and	CCONJ
ap-1396	47	14	the	the	DET
ap-1396	47	15	eigengvalue	eigengvalue	NOUN
ap-1396	47	16	β	β	X
ap-1396	47	17	in	in	ADP
ap-1396	47	18	units	unit	NOUN
ap-1396	47	19	of	of	ADP
ap-1396	47	20	(	(	PUNCT
ap-1396	47	21	a	a	PRON
ap-1396	47	22	/	/	SYM
ap-1396	47	23	π)2	π)2	PROPN
ap-1396	47	24	where	where	SCONJ
ap-1396	47	25	q2	q2	NOUN
ap-1396	47	26	=	=	SYM
ap-1396	47	27	β(a	β(a	PROPN
ap-1396	47	28	/	/	SYM
ap-1396	47	29	π)2	π)2	PROPN
ap-1396	47	30	.	.	PUNCT
ap-1396	48	1	thus	thus	ADV
ap-1396	48	2	the	the	DET
ap-1396	48	3	spectrum	spectrum	NOUN
ap-1396	48	4	is	be	AUX
ap-1396	48	5	that	that	PRON
ap-1396	48	6	of	of	ADP
ap-1396	48	7	a	a	DET
ap-1396	48	8	free	free	ADJ
ap-1396	48	9	massive	massive	ADJ
ap-1396	48	10	particle	particle	NOUN
ap-1396	48	11	,	,	PUNCT
ap-1396	48	12	shown	show	VERB
ap-1396	48	13	in	in	ADP
ap-1396	48	14	the	the	DET
ap-1396	48	15	reduced	reduce	VERB
ap-1396	48	16	zone	zone	NOUN
ap-1396	48	17	scheme	scheme	NOUN
ap-1396	48	18	in	in	ADP
ap-1396	48	19	fig	fig	NOUN
ap-1396	48	20	.	.	PUNCT
ap-1396	49	1	1	1	NUM
ap-1396	49	2	,	,	PUNCT
ap-1396	49	3	and	and	CCONJ
ap-1396	49	4	for	for	ADP
ap-1396	49	5	q	q	PROPN
ap-1396	49	6	≡	≡	PROPN
ap-1396	49	7	ka	ka	PROPN
ap-1396	49	8	/	/	SYM
ap-1396	49	9	π	π	PROPN
ap-1396	49	10	not	not	PART
ap-1396	49	11	an	an	DET
ap-1396	49	12	integer	integer	NOUN
ap-1396	49	13	the	the	DET
ap-1396	49	14	solutions	solution	NOUN
ap-1396	49	15	ψk(x	ψk(x	NOUN
ap-1396	49	16	)	)	PUNCT
ap-1396	50	1	=	=	SYM
ap-1396	50	2	iq(y	iq(y	X
ap-1396	50	3	)	)	PUNCT
ap-1396	50	4	and	and	CCONJ
ap-1396	50	5	ψ−k(x	ψ−k(x	ADJ
ap-1396	50	6	)	)	PUNCT
ap-1396	50	7	=	=	SYM
ap-1396	50	8	i−q(y	i−q(y	NOUN
ap-1396	50	9	)	)	PUNCT
ap-1396	50	10	are	be	AUX
ap-1396	50	11	linearly	linearly	ADV
ap-1396	50	12	independent	independent	ADJ
ap-1396	50	13	,	,	PUNCT
ap-1396	50	14	and	and	CCONJ
ap-1396	50	15	have	have	VERB
ap-1396	50	16	exactly	exactly	ADV
ap-1396	50	17	the	the	DET
ap-1396	50	18	correct	correct	ADJ
ap-1396	50	19	periodicity	periodicity	NOUN
ap-1396	50	20	,	,	PUNCT
ap-1396	50	21	ψk(x+a	ψk(x+a	NOUN
ap-1396	50	22	)	)	PUNCT
ap-1396	50	23	=	=	SYM
ap-1396	50	24	eikaψk(x	eikaψk(x	PROPN
ap-1396	50	25	)	)	PUNCT
ap-1396	50	26	,	,	PUNCT
ap-1396	50	27	to	to	PART
ap-1396	50	28	be	be	AUX
ap-1396	50	29	the	the	DET
ap-1396	50	30	bloch	bloch	PROPN
ap-1396	50	31	wavefunctions	wavefunction	NOUN
ap-1396	50	32	.	.	PUNCT
ap-1396	51	1	it	it	PRON
ap-1396	51	2	is	be	AUX
ap-1396	51	3	important	important	ADJ
ap-1396	51	4	to	to	PART
ap-1396	51	5	note	note	VERB
ap-1396	51	6	,	,	PUNCT
ap-1396	51	7	however	however	ADV
ap-1396	51	8	,	,	PUNCT
ap-1396	51	9	that	that	SCONJ
ap-1396	51	10	because	because	SCONJ
ap-1396	51	11	the	the	DET
ap-1396	51	12	original	original	ADJ
ap-1396	51	13	potential	potential	NOUN
ap-1396	51	14	is	be	AUX
ap-1396	51	15	pt	pt	X
ap-1396	51	16	-symmetric	-symmetric	NOUN
ap-1396	51	17	rather	rather	ADV
ap-1396	51	18	than	than	ADP
ap-1396	51	19	hermitian	hermitian	ADJ
ap-1396	51	20	,	,	PUNCT
ap-1396	51	21	these	these	DET
ap-1396	51	22	functions	function	NOUN
ap-1396	51	23	are	be	AUX
ap-1396	51	24	not	not	PART
ap-1396	51	25	orthogonal	orthogonal	ADJ
ap-1396	51	26	in	in	ADP
ap-1396	51	27	the	the	DET
ap-1396	51	28	usual	usual	ADJ
ap-1396	51	29	sense	sense	NOUN
ap-1396	51	30	,	,	PUNCT
ap-1396	51	31	but	but	CCONJ
ap-1396	51	32	rather	rather	ADV
ap-1396	51	33	with	with	ADP
ap-1396	51	34	respect	respect	NOUN
ap-1396	51	35	to	to	ADP
ap-1396	51	36	the	the	DET
ap-1396	51	37	pt	pt	PROPN
ap-1396	51	38	inner	inner	ADJ
ap-1396	51	39	product	product	NOUN
ap-1396	51	40	,	,	PUNCT
ap-1396	51	41	namely∫	namely∫	NOUN
ap-1396	51	42	dxψ−k(x)ψk′	dxψ−k(x)ψk′	NOUN
ap-1396	51	43	(	(	PUNCT
ap-1396	51	44	x	x	NOUN
ap-1396	51	45	)	)	PUNCT
ap-1396	51	46	=	=	SYM
ap-1396	51	47	δkk′	δkk′	NUM
ap-1396	51	48	∫	∫	PROPN
ap-1396	51	49	dxψ−k(x)ψk(x	dxψ−k(x)ψk(x	NOUN
ap-1396	51	50	)	)	PUNCT
ap-1396	51	51	(	(	PUNCT
ap-1396	51	52	5	5	X
ap-1396	51	53	)	)	PUNCT
ap-1396	51	54	however	however	ADV
ap-1396	51	55	,	,	PUNCT
ap-1396	51	56	for	for	ADP
ap-1396	51	57	q	q	NOUN
ap-1396	51	58	=	=	SYM
ap-1396	51	59	n	n	CCONJ
ap-1396	51	60	,	,	PUNCT
ap-1396	51	61	a	a	DET
ap-1396	51	62	non	non	ADJ
ap-1396	51	63	-	-	ADJ
ap-1396	51	64	zero	zero	NUM
ap-1396	51	65	integer	integer	NOUN
ap-1396	51	66	,	,	PUNCT
ap-1396	51	67	in(y	in(y	X
ap-1396	51	68	)	)	PUNCT
ap-1396	51	69	and	and	CCONJ
ap-1396	51	70	i−n(y	i−n(y	PROPN
ap-1396	51	71	)	)	PUNCT
ap-1396	51	72	are	be	AUX
ap-1396	51	73	no	no	ADV
ap-1396	51	74	longer	long	ADV
ap-1396	51	75	independent	independent	ADJ
ap-1396	51	76	.	.	PUNCT
ap-1396	52	1	in	in	ADP
ap-1396	52	2	that	that	DET
ap-1396	52	3	case	case	NOUN
ap-1396	52	4	the	the	DET
ap-1396	52	5	bloch	bloch	PROPN
ap-1396	52	6	eigenfunctions	eigenfunction	NOUN
ap-1396	52	7	do	do	AUX
ap-1396	52	8	not	not	PART
ap-1396	52	9	form	form	VERB
ap-1396	52	10	a	a	DET
ap-1396	52	11	complete	complete	ADJ
ap-1396	52	12	set	set	NOUN
ap-1396	52	13	,	,	PUNCT
ap-1396	52	14	and	and	CCONJ
ap-1396	52	15	we	we	PRON
ap-1396	52	16	must	must	AUX
ap-1396	52	17	search	search	VERB
ap-1396	52	18	for	for	ADP
ap-1396	52	19	other	other	ADJ
ap-1396	52	20	functions	function	NOUN
ap-1396	52	21	,	,	PUNCT
ap-1396	52	22	still	still	ADV
ap-1396	52	23	with	with	ADP
ap-1396	52	24	the	the	DET
ap-1396	52	25	same	same	ADJ
ap-1396	52	26	periodicity	periodicity	NOUN
ap-1396	52	27	,	,	PUNCT
ap-1396	52	28	to	to	PART
ap-1396	52	29	supplement	supplement	VERB
ap-1396	52	30	them	they	PRON
ap-1396	52	31	.	.	PUNCT
ap-1396	53	1	these	these	PRON
ap-1396	53	2	are	be	AUX
ap-1396	53	3	the	the	DET
ap-1396	53	4	jordan	jordan	PROPN
ap-1396	53	5	associated	associated	PROPN
ap-1396	53	6	functions	function	NOUN
ap-1396	53	7	,	,	PUNCT
ap-1396	53	8	which	which	PRON
ap-1396	53	9	we	we	PRON
ap-1396	53	10	denote	denote	VERB
ap-1396	53	11	by	by	ADP
ap-1396	53	12	ϕk(x	ϕk(x	NOUN
ap-1396	53	13	)	)	PUNCT
ap-1396	53	14	≡	≡	PROPN
ap-1396	53	15	χn(y	χn(y	NUM
ap-1396	53	16	)	)	PUNCT
ap-1396	53	17	.	.	PUNCT
ap-1396	54	1	they	they	PRON
ap-1396	54	2	may	may	AUX
ap-1396	54	3	be	be	AUX
ap-1396	54	4	defined	define	VERB
ap-1396	54	5	as	as	ADP
ap-1396	54	6	derivatives	derivative	NOUN
ap-1396	54	7	of	of	ADP
ap-1396	54	8	the	the	DET
ap-1396	54	9	eigenfunctions	eigenfunction	NOUN
ap-1396	54	10	with	with	ADP
ap-1396	54	11	respect	respect	NOUN
ap-1396	54	12	to	to	ADP
ap-1396	54	13	β	β	NOUN
ap-1396	54	14	,	,	PUNCT
ap-1396	54	15	and	and	CCONJ
ap-1396	54	16	satisfy	satisfy	VERB
ap-1396	54	17	the	the	DET
ap-1396	54	18	generalized	generalize	VERB
ap-1396	54	19	eigenvalue	eigenvalue	NOUN
ap-1396	54	20	equation	equation	NOUN
ap-1396	54	21	[	[	PUNCT
ap-1396	54	22	y2	y2	NOUN
ap-1396	54	23	d2	d2	PROPN
ap-1396	54	24	dy2	dy2	PROPN
ap-1396	54	25	+	+	CCONJ
ap-1396	54	26	y	y	PROPN
ap-1396	54	27	d	d	PROPN
ap-1396	54	28	dy	dy	NOUN
ap-1396	55	1	−	−	PROPN
ap-1396	55	2	(	(	PUNCT
ap-1396	55	3	y2	y2	NOUN
ap-1396	55	4	+	+	CCONJ
ap-1396	55	5	n2	n2	ADJ
ap-1396	55	6	)	)	PUNCT
ap-1396	55	7	]	]	PUNCT
ap-1396	56	1	χn(y	χn(y	PUNCT
ap-1396	56	2	)	)	PUNCT
ap-1396	56	3	=	=	SYM
ap-1396	56	4	in(y	in(y	X
ap-1396	56	5	)	)	PUNCT
ap-1396	56	6	(	(	PUNCT
ap-1396	56	7	6	6	X
ap-1396	56	8	)	)	PUNCT
ap-1396	56	9	the	the	DET
ap-1396	56	10	crucial	crucial	ADJ
ap-1396	56	11	feature	feature	NOUN
ap-1396	56	12	of	of	ADP
ap-1396	56	13	the	the	DET
ap-1396	56	14	jordan	jordan	PROPN
ap-1396	56	15	functions	function	NOUN
ap-1396	56	16	is	be	AUX
ap-1396	56	17	that	that	SCONJ
ap-1396	56	18	because	because	SCONJ
ap-1396	56	19	of	of	ADP
ap-1396	56	20	this	this	DET
ap-1396	56	21	latter	latter	ADJ
ap-1396	56	22	equation	equation	NOUN
ap-1396	56	23	they	they	PRON
ap-1396	56	24	naturally	naturally	ADV
ap-1396	56	25	give	give	VERB
ap-1396	56	26	rise	rise	NOUN
ap-1396	56	27	to	to	ADP
ap-1396	56	28	linear	linear	ADJ
ap-1396	56	29	growth	growth	NOUN
ap-1396	56	30	in	in	ADP
ap-1396	56	31	z	z	PROPN
ap-1396	56	32	,	,	PUNCT
ap-1396	56	33	provided	provide	VERB
ap-1396	56	34	that	that	SCONJ
ap-1396	56	35	they	they	PRON
ap-1396	56	36	are	be	AUX
ap-1396	56	37	excited	excited	ADJ
ap-1396	56	38	:	:	PUNCT
ap-1396	56	39	e−ihzϕr	e−ihzϕr	X
ap-1396	56	40	=	=	SYM
ap-1396	56	41	e−iβrze−i(h−βr)zϕr	e−iβrze−i(h−βr)zϕr	PROPN
ap-1396	56	42	=	=	PUNCT
ap-1396	56	43	e−iβrz(ϕr	e−iβrz(ϕr	ADV
ap-1396	56	44	−	−	NOUN
ap-1396	56	45	izψr	izψr	ADJ
ap-1396	56	46	)	)	PUNCT
ap-1396	56	47	.	.	PUNCT
ap-1396	57	1	(	(	PUNCT
ap-1396	57	2	7	7	X
ap-1396	57	3	)	)	PUNCT
ap-1396	57	4	however	however	ADV
ap-1396	57	5	,	,	PUNCT
ap-1396	57	6	as	as	SCONJ
ap-1396	57	7	was	be	AUX
ap-1396	57	8	found	find	VERB
ap-1396	57	9	numerically	numerically	ADV
ap-1396	57	10	in	in	ADP
ap-1396	57	11	ref	ref	NOUN
ap-1396	57	12	.	.	PUNCT
ap-1396	58	1	[	[	X
ap-1396	58	2	12	12	NUM
ap-1396	58	3	]	]	PUNCT
ap-1396	58	4	,	,	PUNCT
ap-1396	58	5	and	and	CCONJ
ap-1396	58	6	explored	explore	VERB
ap-1396	58	7	further	far	ADV
ap-1396	58	8	in	in	ADP
ap-1396	58	9	ref	ref	NOUN
ap-1396	58	10	.	.	PUNCT
ap-1396	59	1	[	[	X
ap-1396	59	2	17	17	NUM
ap-1396	59	3	]	]	PUNCT
ap-1396	59	4	,	,	PUNCT
ap-1396	59	5	this	this	DET
ap-1396	59	6	natural	natural	ADJ
ap-1396	59	7	linear	linear	NOUN
ap-1396	59	8	growth	growth	NOUN
ap-1396	59	9	may	may	AUX
ap-1396	59	10	become	become	VERB
ap-1396	59	11	saturated	saturated	ADJ
ap-1396	59	12	due	due	ADP
ap-1396	59	13	to	to	ADP
ap-1396	59	14	the	the	DET
ap-1396	59	15	contributions	contribution	NOUN
ap-1396	59	16	of	of	ADP
ap-1396	59	17	neighbouring	neighbouring	ADJ
ap-1396	59	18	bloch	bloch	NOUN
ap-1396	59	19	functions	function	NOUN
ap-1396	59	20	,	,	PUNCT
ap-1396	59	21	which	which	PRON
ap-1396	59	22	are	be	AUX
ap-1396	59	23	closely	closely	ADV
ap-1396	59	24	correlated	correlate	VERB
ap-1396	59	25	with	with	ADP
ap-1396	59	26	those	those	PRON
ap-1396	59	27	of	of	ADP
ap-1396	59	28	the	the	DET
ap-1396	59	29	jordan	jordan	PROPN
ap-1396	59	30	functions	function	NOUN
ap-1396	59	31	.	.	PUNCT
ap-1396	60	1	3	3	NUM
ap-1396	60	2	perturbation	perturbation	NOUN
ap-1396	60	3	theory	theory	NOUN
ap-1396	60	4	the	the	DET
ap-1396	60	5	analysis	analysis	NOUN
ap-1396	60	6	of	of	ADP
ap-1396	60	7	ref	ref	NOUN
ap-1396	60	8	.	.	PUNCT
ap-1396	61	1	[	[	X
ap-1396	61	2	17	17	NUM
ap-1396	61	3	]	]	PUNCT
ap-1396	61	4	approached	approach	VERB
ap-1396	61	5	the	the	DET
ap-1396	61	6	problem	problem	NOUN
ap-1396	61	7	from	from	ADP
ap-1396	61	8	one	one	NUM
ap-1396	61	9	point	point	NOUN
ap-1396	61	10	of	of	ADP
ap-1396	61	11	view	view	NOUN
ap-1396	61	12	,	,	PUNCT
ap-1396	61	13	in	in	ADP
ap-1396	61	14	which	which	PRON
ap-1396	61	15	the	the	DET
ap-1396	61	16	interplay	interplay	NOUN
ap-1396	61	17	between	between	ADP
ap-1396	61	18	the	the	DET
ap-1396	61	19	contributions	contribution	NOUN
ap-1396	61	20	of	of	ADP
ap-1396	61	21	the	the	DET
ap-1396	61	22	bloch	bloch	PROPN
ap-1396	61	23	eigenfunctions	eigenfunction	NOUN
ap-1396	61	24	and	and	CCONJ
ap-1396	61	25	the	the	DET
ap-1396	61	26	jordan	jordan	PROPN
ap-1396	61	27	associated	associated	PROPN
ap-1396	61	28	functions	function	NOUN
ap-1396	61	29	was	be	AUX
ap-1396	61	30	made	make	VERB
ap-1396	61	31	explicit	explicit	ADJ
ap-1396	61	32	.	.	PUNCT
ap-1396	62	1	a	a	DET
ap-1396	62	2	complementary	complementary	ADJ
ap-1396	62	3	way	way	NOUN
ap-1396	62	4	of	of	ADP
ap-1396	62	5	looking	look	VERB
ap-1396	62	6	at	at	ADP
ap-1396	62	7	things	thing	NOUN
ap-1396	62	8	,	,	PUNCT
ap-1396	62	9	which	which	PRON
ap-1396	62	10	does	do	AUX
ap-1396	62	11	not	not	PART
ap-1396	62	12	separate	separate	VERB
ap-1396	62	13	these	these	DET
ap-1396	62	14	two	two	NUM
ap-1396	62	15	contributions	contribution	NOUN
ap-1396	62	16	,	,	PUNCT
ap-1396	62	17	is	be	AUX
ap-1396	62	18	to	to	PART
ap-1396	62	19	use	use	VERB
ap-1396	62	20	the	the	DET
ap-1396	62	21	perturbative	perturbative	ADJ
ap-1396	62	22	expansion	expansion	NOUN
ap-1396	62	23	,	,	PUNCT
ap-1396	62	24	which	which	PRON
ap-1396	62	25	instead	instead	ADV
ap-1396	62	26	emphasizes	emphasize	VERB
ap-1396	62	27	the	the	DET
ap-1396	62	28	contributions	contribution	NOUN
ap-1396	62	29	of	of	ADP
ap-1396	62	30	the	the	DET
ap-1396	62	31	free	free	ADJ
ap-1396	62	32	propagation	propagation	NOUN
ap-1396	62	33	and	and	CCONJ
ap-1396	62	34	the	the	DET
ap-1396	62	35	corrections	correction	NOUN
ap-1396	62	36	brought	bring	VERB
ap-1396	62	37	about	about	ADP
ap-1396	62	38	by	by	ADP
ap-1396	62	39	the	the	DET
ap-1396	62	40	potential	potential	NOUN
ap-1396	62	41	.	.	PUNCT
ap-1396	63	1	the	the	DET
ap-1396	63	2	general	general	ADJ
ap-1396	63	3	framework	framework	NOUN
ap-1396	63	4	for	for	ADP
ap-1396	63	5	an	an	DET
ap-1396	63	6	expansion	expansion	NOUN
ap-1396	63	7	of	of	ADP
ap-1396	63	8	ψ(x	ψ(x	PROPN
ap-1396	63	9	,	,	PUNCT
ap-1396	63	10	z	z	NOUN
ap-1396	63	11	)	)	PUNCT
ap-1396	63	12	in	in	ADP
ap-1396	63	13	powers	power	NOUN
ap-1396	63	14	of	of	ADP
ap-1396	63	15	v0	v0	NOUN
ap-1396	63	16	,	,	PUNCT
ap-1396	63	17	namely	namely	ADV
ap-1396	63	18	ψ(x	ψ(x	NOUN
ap-1396	63	19	,	,	PUNCT
ap-1396	63	20	z	z	NOUN
ap-1396	63	21	)	)	PUNCT
ap-1396	63	22	=	=	PUNCT
ap-1396	64	1	∞∑	∞∑	NUM
ap-1396	64	2	r=0	r=0	NOUN
ap-1396	64	3	v	v	ADP
ap-1396	64	4	r	r	NOUN
ap-1396	64	5	0	0	NUM
ap-1396	64	6	ψr(x	ψr(x	PRON
ap-1396	64	7	,	,	PUNCT
ap-1396	64	8	z	z	NOUN
ap-1396	64	9	)	)	PUNCT
ap-1396	64	10	,	,	PUNCT
ap-1396	64	11	has	have	AUX
ap-1396	64	12	been	be	AUX
ap-1396	64	13	given	give	VERB
ap-1396	64	14	in	in	ADP
ap-1396	64	15	ref	ref	NOUN
ap-1396	64	16	.	.	PUNCT
ap-1396	65	1	[	[	X
ap-1396	65	2	12	12	NUM
ap-1396	65	3	]	]	X
ap-1396	65	4	,	,	PUNCT
ap-1396	65	5	along	along	ADP
ap-1396	65	6	with	with	ADP
ap-1396	65	7	an	an	DET
ap-1396	65	8	approximate	approximate	ADJ
ap-1396	65	9	form	form	NOUN
ap-1396	65	10	of	of	ADP
ap-1396	65	11	the	the	DET
ap-1396	65	12	first	first	ADJ
ap-1396	65	13	-	-	PUNCT
ap-1396	65	14	order	order	NOUN
ap-1396	65	15	term	term	NOUN
ap-1396	65	16	ψ1(x	ψ1(x	PROPN
ap-1396	65	17	,	,	PUNCT
ap-1396	65	18	z	z	NOUN
ap-1396	65	19	)	)	PUNCT
ap-1396	65	20	for	for	ADP
ap-1396	65	21	the	the	DET
ap-1396	65	22	case	case	NOUN
ap-1396	65	23	q0	q0	NOUN
ap-1396	65	24	=	=	PUNCT
ap-1396	65	25	−1	−1	NOUN
ap-1396	65	26	and	and	CCONJ
ap-1396	65	27	w	w	NOUN
ap-1396	65	28	large	large	ADJ
ap-1396	65	29	.	.	PUNCT
ap-1396	66	1	in	in	ADP
ap-1396	66	2	this	this	DET
ap-1396	66	3	section	section	NOUN
ap-1396	66	4	we	we	PRON
ap-1396	66	5	generalize	generalize	VERB
ap-1396	66	6	this	this	DET
ap-1396	66	7	calculation	calculation	NOUN
ap-1396	66	8	by	by	ADP
ap-1396	66	9	obtaining	obtain	VERB
ap-1396	66	10	analytic	analytic	ADJ
ap-1396	66	11	expressions	expression	NOUN
ap-1396	66	12	for	for	ADP
ap-1396	66	13	both	both	CCONJ
ap-1396	66	14	the	the	DET
ap-1396	66	15	firstand	firstand	NOUN
ap-1396	66	16	second	second	ADJ
ap-1396	66	17	-	-	PUNCT
ap-1396	66	18	order	order	NOUN
ap-1396	66	19	terms	term	NOUN
ap-1396	66	20	for	for	ADP
ap-1396	66	21	general	general	ADJ
ap-1396	66	22	q0	q0	NOUN
ap-1396	66	23	and	and	CCONJ
ap-1396	66	24	w.	w.	NOUN
ap-1396	66	25	of	of	ADP
ap-1396	66	26	course	course	NOUN
ap-1396	66	27	,	,	PUNCT
ap-1396	66	28	this	this	PRON
ap-1396	66	29	can	can	AUX
ap-1396	66	30	only	only	ADV
ap-1396	66	31	be	be	AUX
ap-1396	66	32	used	use	VERB
ap-1396	66	33	as	as	ADP
ap-1396	66	34	a	a	DET
ap-1396	66	35	guide	guide	NOUN
ap-1396	66	36	because	because	SCONJ
ap-1396	66	37	22	22	NUM
ap-1396	66	38	acta	acta	PROPN
ap-1396	66	39	polytechnica	polytechnica	PROPN
ap-1396	66	40	vol	vol	NOUN
ap-1396	66	41	.	.	PUNCT
ap-1396	67	1	51	51	NUM
ap-1396	67	2	no	no	NOUN
ap-1396	67	3	.	.	PUNCT
ap-1396	68	1	4/2011	4/2011	NUM
ap-1396	68	2	�	�	PROPN
ap-1396	68	3	400	400	NUM
ap-1396	68	4	�	�	NOUN
ap-1396	68	5	200	200	NUM
ap-1396	68	6	200	200	NUM
ap-1396	68	7	400	400	NUM
ap-1396	68	8	y	y	NOUN
ap-1396	68	9	0.5	0.5	NUM
ap-1396	68	10	1	1	NUM
ap-1396	68	11	1.5	1.5	NUM
ap-1396	68	12	2	2	NUM
ap-1396	68	13	�	�	PROPN
ap-1396	68	14	a	a	DET
ap-1396	68	15	�	�	PROPN
ap-1396	68	16	�	�	PROPN
ap-1396	68	17	400	400	NUM
ap-1396	68	18	�	�	NOUN
ap-1396	68	19	200	200	NUM
ap-1396	68	20	200	200	NUM
ap-1396	68	21	400	400	NUM
ap-1396	68	22	y	y	NOUN
ap-1396	68	23	0.1	0.1	NUM
ap-1396	68	24	0.2	0.2	NUM
ap-1396	68	25	0.3	0.3	NUM
ap-1396	68	26	0.4	0.4	NUM
ap-1396	68	27	0.5	0.5	NUM
ap-1396	68	28	�	�	PROPN
ap-1396	68	29	b	b	SYM
ap-1396	68	30	�	�	PROPN
ap-1396	68	31	fig	fig	NOUN
ap-1396	68	32	.	.	PUNCT
ap-1396	68	33	2	2	NUM
ap-1396	68	34	:	:	PUNCT
ap-1396	68	35	characteristic	characteristic	ADJ
ap-1396	68	36	behaviour	behaviour	NOUN
ap-1396	68	37	of	of	ADP
ap-1396	68	38	error	error	NOUN
ap-1396	68	39	functions	function	NOUN
ap-1396	68	40	whose	whose	DET
ap-1396	68	41	arguments	argument	NOUN
ap-1396	68	42	are	be	AUX
ap-1396	68	43	(	(	PUNCT
ap-1396	68	44	a	a	X
ap-1396	68	45	)	)	PUNCT
ap-1396	68	46	real	real	ADJ
ap-1396	68	47	or	or	CCONJ
ap-1396	68	48	(	(	PUNCT
ap-1396	68	49	b	b	X
ap-1396	68	50	)	)	PUNCT
ap-1396	68	51	have	have	VERB
ap-1396	68	52	a	a	DET
ap-1396	68	53	large	large	ADJ
ap-1396	68	54	imaginary	imaginary	ADJ
ap-1396	68	55	part	part	NOUN
ap-1396	68	56	.	.	PUNCT
ap-1396	69	1	in	in	ADP
ap-1396	69	2	(	(	PUNCT
ap-1396	69	3	a	a	X
ap-1396	69	4	)	)	PUNCT
ap-1396	69	5	we	we	PRON
ap-1396	69	6	plot	plot	VERB
ap-1396	69	7	erf(4	erf(4	NOUN
ap-1396	70	1	+	+	CCONJ
ap-1396	70	2	y	y	PROPN
ap-1396	70	3	/	/	SYM
ap-1396	70	4	w	w	PROPN
ap-1396	70	5	)	)	PUNCT
ap-1396	70	6	+	+	CCONJ
ap-1396	70	7	erf(4−	erf(4−	VERB
ap-1396	70	8	y	y	PROPN
ap-1396	70	9	/	/	SYM
ap-1396	70	10	w	w	PROPN
ap-1396	70	11	)	)	PUNCT
ap-1396	70	12	with	with	ADP
ap-1396	70	13	w	w	PROPN
ap-1396	70	14	=	=	NOUN
ap-1396	70	15	80	80	NUM
ap-1396	70	16	.	.	PUNCT
ap-1396	71	1	in	in	ADP
ap-1396	71	2	(	(	PUNCT
ap-1396	71	3	b	b	X
ap-1396	71	4	)	)	PUNCT
ap-1396	71	5	we	we	PRON
ap-1396	71	6	plot	plot	VERB
ap-1396	71	7	w	w	PROPN
ap-1396	71	8	e−w2	e−w2	X
ap-1396	71	9	|erf(4	|erf(4	PROPN
ap-1396	72	1	+	+	CCONJ
ap-1396	72	2	y	y	PROPN
ap-1396	72	3	/	/	SYM
ap-1396	72	4	w	w	PROPN
ap-1396	72	5	−	−	PROPN
ap-1396	72	6	iw	iw	PROPN
ap-1396	72	7	)	)	PUNCT
ap-1396	73	1	+	+	CCONJ
ap-1396	73	2	erf(4−	erf(4−	VERB
ap-1396	73	3	y	y	PROPN
ap-1396	73	4	/	/	SYM
ap-1396	73	5	w	w	PROPN
ap-1396	74	1	+	+	CCONJ
ap-1396	74	2	iw)|	iw)|	NOUN
ap-1396	74	3	there	there	PRON
ap-1396	74	4	is	be	VERB
ap-1396	74	5	no	no	DET
ap-1396	74	6	guarantee	guarantee	NOUN
ap-1396	74	7	that	that	SCONJ
ap-1396	74	8	the	the	DET
ap-1396	74	9	expansion	expansion	NOUN
ap-1396	74	10	converges	converge	VERB
ap-1396	74	11	,	,	PUNCT
ap-1396	74	12	nor	nor	CCONJ
ap-1396	74	13	that	that	SCONJ
ap-1396	74	14	the	the	DET
ap-1396	74	15	large	large	ADJ
ap-1396	74	16	-	-	PUNCT
ap-1396	74	17	z	z	NOUN
ap-1396	74	18	behaviour	behaviour	NOUN
ap-1396	74	19	of	of	ADP
ap-1396	74	20	the	the	DET
ap-1396	74	21	complete	complete	ADJ
ap-1396	74	22	amplitude	amplitude	NOUN
ap-1396	74	23	can	can	AUX
ap-1396	74	24	be	be	AUX
ap-1396	74	25	extracted	extract	VERB
ap-1396	74	26	from	from	ADP
ap-1396	74	27	the	the	DET
ap-1396	74	28	behaviour	behaviour	NOUN
ap-1396	74	29	of	of	ADP
ap-1396	74	30	the	the	DET
ap-1396	74	31	truncated	truncated	ADJ
ap-1396	74	32	series	series	NOUN
ap-1396	74	33	.	.	PUNCT
ap-1396	75	1	we	we	PRON
ap-1396	75	2	will	will	AUX
ap-1396	75	3	take	take	VERB
ap-1396	75	4	as	as	SCONJ
ap-1396	75	5	our	our	PRON
ap-1396	75	6	input	input	NOUN
ap-1396	75	7	a	a	DET
ap-1396	75	8	gaussian	gaussian	ADJ
ap-1396	75	9	profile	profile	NOUN
ap-1396	75	10	of	of	ADP
ap-1396	75	11	the	the	DET
ap-1396	75	12	form	form	NOUN
ap-1396	75	13	ψ(x	ψ(x	NOUN
ap-1396	75	14	,	,	PUNCT
ap-1396	75	15	0	0	NUM
ap-1396	75	16	)	)	PUNCT
ap-1396	75	17	=	=	SYM
ap-1396	75	18	f(x	f(x	PROPN
ap-1396	75	19	)	)	PUNCT
ap-1396	75	20	≡	≡	PROPN
ap-1396	75	21	e−(x	e−(x	PROPN
ap-1396	75	22	/	/	SYM
ap-1396	75	23	w)2+ik0x	w)2+ik0x	PROPN
ap-1396	75	24	,	,	PUNCT
ap-1396	75	25	(	(	PUNCT
ap-1396	75	26	8)	8)	NUM
ap-1396	75	27	with	with	ADP
ap-1396	75	28	offset	offset	ADJ
ap-1396	75	29	k0	k0	PROPN
ap-1396	75	30	and	and	CCONJ
ap-1396	75	31	width	width	VERB
ap-1396	75	32	w.	w.	PROPN
ap-1396	75	33	the	the	DET
ap-1396	75	34	zeroth	zeroth	ADJ
ap-1396	75	35	-	-	PUNCT
ap-1396	75	36	order	order	NOUN
ap-1396	75	37	term	term	NOUN
ap-1396	75	38	,	,	PUNCT
ap-1396	75	39	ψ0(x	ψ0(x	NOUN
ap-1396	75	40	,	,	PUNCT
ap-1396	75	41	z	z	NOUN
ap-1396	75	42	)	)	PUNCT
ap-1396	75	43	,	,	PUNCT
ap-1396	75	44	is	be	AUX
ap-1396	75	45	just	just	ADV
ap-1396	75	46	the	the	DET
ap-1396	75	47	freely	freely	ADV
ap-1396	75	48	-	-	PUNCT
ap-1396	75	49	propagating	propagate	VERB
ap-1396	75	50	wave	wave	NOUN
ap-1396	75	51	-	-	PUNCT
ap-1396	75	52	packet	packet	NOUN
ap-1396	75	53	ψ0(x	ψ0(x	NOUN
ap-1396	75	54	,	,	PUNCT
ap-1396	75	55	z	z	NOUN
ap-1396	75	56	)	)	PUNCT
ap-1396	75	57	=	=	SYM
ap-1396	75	58	w√	w√	X
ap-1396	75	59	(	(	PUNCT
ap-1396	75	60	w2	w2	NOUN
ap-1396	75	61	+	+	CCONJ
ap-1396	75	62	4iz	4iz	NOUN
ap-1396	75	63	)	)	PUNCT
ap-1396	75	64	·	·	PUNCT
ap-1396	75	65	eik0(x−k0z)e−(x−2k0z	eik0(x−k0z)e−(x−2k0z	VERB
ap-1396	75	66	)	)	PUNCT
ap-1396	75	67	2/(w2	2/(w2	NUM
ap-1396	75	68	+	+	NOUN
ap-1396	75	69	4iz	4iz	NOUN
ap-1396	75	70	)	)	PUNCT
ap-1396	75	71	,	,	PUNCT
ap-1396	75	72	(	(	PUNCT
ap-1396	75	73	9	9	X
ap-1396	75	74	)	)	PUNCT
ap-1396	75	75	while	while	SCONJ
ap-1396	75	76	the	the	DET
ap-1396	75	77	first	first	ADJ
ap-1396	75	78	-	-	PUNCT
ap-1396	75	79	order	order	NOUN
ap-1396	75	80	term	term	NOUN
ap-1396	75	81	,	,	PUNCT
ap-1396	75	82	ψ1(x	ψ1(x	PROPN
ap-1396	75	83	,	,	PUNCT
ap-1396	75	84	z	z	NOUN
ap-1396	75	85	)	)	PUNCT
ap-1396	75	86	,	,	PUNCT
ap-1396	75	87	is	be	AUX
ap-1396	75	88	given	give	VERB
ap-1396	75	89	by	by	ADP
ap-1396	75	90	ψ1(x	ψ1(x	PROPN
ap-1396	75	91	,	,	PUNCT
ap-1396	75	92	z	z	NOUN
ap-1396	75	93	)	)	PUNCT
ap-1396	76	1	=	=	NUM
ap-1396	76	2	−i	−i	ADJ
ap-1396	76	3	∫	∫	PROPN
ap-1396	76	4	dkf̃(k)ei(k+kb	dkf̃(k)ei(k+kb	NOUN
ap-1396	76	5	)	)	PUNCT
ap-1396	76	6	x	x	SYM
ap-1396	76	7	·	·	PUNCT
ap-1396	76	8	[	[	PUNCT
ap-1396	76	9	−i	−i	ADJ
ap-1396	76	10	∫	∫	PROPN
ap-1396	76	11	z	z	NOUN
ap-1396	76	12	0	0	NUM
ap-1396	76	13	dy	dy	NOUN
ap-1396	76	14	e−ik2yei(k+kb	e−ik2yei(k+kb	PROPN
ap-1396	76	15	)	)	PUNCT
ap-1396	76	16	2(y−z	2(y−z	NUM
ap-1396	76	17	)	)	PUNCT
ap-1396	76	18	]	]	PUNCT
ap-1396	76	19	,	,	PUNCT
ap-1396	76	20	(	(	PUNCT
ap-1396	76	21	10	10	NUM
ap-1396	76	22	)	)	PUNCT
ap-1396	76	23	where	where	SCONJ
ap-1396	76	24	f̃(k	f̃(k	VERB
ap-1396	76	25	)	)	PUNCT
ap-1396	76	26	=	=	SYM
ap-1396	77	1	w	w	PROPN
ap-1396	77	2	2	2	NUM
ap-1396	77	3	√	√	PROPN
ap-1396	77	4	π	π	PROPN
ap-1396	77	5	e−(k−k0	e−(k−k0	PROPN
ap-1396	77	6	)	)	PUNCT
ap-1396	77	7	2w2/4	2w2/4	NUM
ap-1396	77	8	(	(	PUNCT
ap-1396	77	9	11	11	NUM
ap-1396	77	10	)	)	PUNCT
ap-1396	77	11	is	be	AUX
ap-1396	77	12	the	the	DET
ap-1396	77	13	fourier	fourier	ADJ
ap-1396	77	14	transform	transform	NOUN
ap-1396	77	15	of	of	ADP
ap-1396	77	16	f(x	f(x	PROPN
ap-1396	77	17	)	)	PUNCT
ap-1396	77	18	of	of	ADP
ap-1396	77	19	eq	eq	PROPN
ap-1396	77	20	.	.	PUNCT
ap-1396	78	1	(	(	PUNCT
ap-1396	78	2	8)	8)	NUM
ap-1396	78	3	and	and	CCONJ
ap-1396	78	4	kb	kb	NOUN
ap-1396	78	5	=	=	PUNCT
ap-1396	79	1	2π	2π	NOUN
ap-1396	79	2	/	/	SYM
ap-1396	79	3	a	a	PRON
ap-1396	79	4	is	be	AUX
ap-1396	79	5	the	the	DET
ap-1396	79	6	width	width	NOUN
ap-1396	79	7	of	of	ADP
ap-1396	79	8	the	the	DET
ap-1396	79	9	first	first	ADJ
ap-1396	79	10	brillouin	brillouin	NOUN
ap-1396	79	11	zone	zone	NOUN
ap-1396	79	12	.	.	PUNCT
ap-1396	80	1	we	we	PRON
ap-1396	80	2	can	can	AUX
ap-1396	80	3	reverse	reverse	VERB
ap-1396	80	4	the	the	DET
ap-1396	80	5	order	order	NOUN
ap-1396	80	6	of	of	ADP
ap-1396	80	7	integration	integration	NOUN
ap-1396	80	8	in	in	ADP
ap-1396	80	9	the	the	DET
ap-1396	80	10	expression	expression	NOUN
ap-1396	80	11	for	for	ADP
ap-1396	80	12	ψ1	ψ1	NOUN
ap-1396	80	13	,	,	PUNCT
ap-1396	80	14	performing	perform	VERB
ap-1396	80	15	the	the	DET
ap-1396	80	16	(	(	PUNCT
ap-1396	80	17	gaussian	gaussian	ADJ
ap-1396	80	18	)	)	PUNCT
ap-1396	80	19	k	k	NOUN
ap-1396	80	20	integration	integration	NOUN
ap-1396	80	21	first	first	ADV
ap-1396	80	22	,	,	PUNCT
ap-1396	80	23	to	to	PART
ap-1396	80	24	obtain	obtain	VERB
ap-1396	80	25	ψ1(x	ψ1(x	PROPN
ap-1396	80	26	,	,	PUNCT
ap-1396	80	27	z	z	NOUN
ap-1396	80	28	)	)	PUNCT
ap-1396	81	1	=	=	SYM
ap-1396	81	2	−i	−i	ADJ
ap-1396	81	3	w√	w√	PROPN
ap-1396	81	4	(	(	PUNCT
ap-1396	81	5	w2	w2	NOUN
ap-1396	81	6	+	+	CCONJ
ap-1396	81	7	4iz	4iz	NOUN
ap-1396	81	8	)	)	PUNCT
ap-1396	81	9	e	e	NOUN
ap-1396	81	10	1	1	NUM
ap-1396	81	11	2	2	NUM
ap-1396	81	12	ikbx−	ikbx−	NOUN
ap-1396	81	13	1	1	NUM
ap-1396	81	14	4	4	NUM
ap-1396	81	15	ik2bz−	ik2bz−	NOUN
ap-1396	81	16	1	1	NUM
ap-1396	81	17	4	4	NUM
ap-1396	81	18	(	(	PUNCT
ap-1396	81	19	k0	k0	PROPN
ap-1396	81	20	+	+	PROPN
ap-1396	81	21	1	1	NUM
ap-1396	81	22	2	2	NUM
ap-1396	81	23	kb	kb	PROPN
ap-1396	81	24	)	)	PUNCT
ap-1396	81	25	2w2	2w2	NUM
ap-1396	81	26	×	×	NOUN
ap-1396	81	27	(	(	PUNCT
ap-1396	81	28	12)∫	12)∫	NUM
ap-1396	81	29	z	z	NOUN
ap-1396	81	30	0	0	PUNCT
ap-1396	81	31	dy	dy	NOUN
ap-1396	81	32	e−(2kby−(x+kbz)+	e−(2kby−(x+kbz)+	NOUN
ap-1396	81	33	12	12	NUM
ap-1396	81	34	iw2(k0	iw2(k0	NOUN
ap-1396	81	35	+	+	X
ap-1396	81	36	12kb))2/(w2	12kb))2/(w2	NUM
ap-1396	81	37	+	+	NOUN
ap-1396	81	38	4iz	4iz	NOUN
ap-1396	81	39	)	)	PUNCT
ap-1396	81	40	.	.	PUNCT
ap-1396	82	1	the	the	DET
ap-1396	82	2	y	y	PROPN
ap-1396	82	3	integration	integration	NOUN
ap-1396	82	4	is	be	AUX
ap-1396	82	5	then	then	ADV
ap-1396	82	6	also	also	ADV
ap-1396	82	7	a	a	DET
ap-1396	82	8	gaussian	gaussian	ADJ
ap-1396	82	9	integration	integration	NOUN
ap-1396	82	10	over	over	ADP
ap-1396	82	11	a	a	DET
ap-1396	82	12	finite	finite	ADJ
ap-1396	82	13	range	range	NOUN
ap-1396	82	14	,	,	PUNCT
ap-1396	82	15	giving	give	VERB
ap-1396	82	16	the	the	DET
ap-1396	82	17	result	result	NOUN
ap-1396	82	18	ψ1(x	ψ1(x	PROPN
ap-1396	82	19	,	,	PUNCT
ap-1396	82	20	z	z	NOUN
ap-1396	82	21	)	)	PUNCT
ap-1396	83	1	=	=	SYM
ap-1396	84	1	−i	−i	ADJ
ap-1396	84	2	w	w	NOUN
ap-1396	84	3	√	√	PROPN
ap-1396	84	4	π	π	PROPN
ap-1396	84	5	4	4	NUM
ap-1396	84	6	kb	kb	X
ap-1396	84	7	·	·	PUNCT
ap-1396	84	8	e	e	NOUN
ap-1396	84	9	1	1	NUM
ap-1396	84	10	2	2	NUM
ap-1396	84	11	ikbx−	ikbx−	NOUN
ap-1396	84	12	1	1	NUM
ap-1396	84	13	4	4	NUM
ap-1396	84	14	ik2bz−	ik2bz−	NOUN
ap-1396	84	15	1	1	NUM
ap-1396	84	16	4	4	NUM
ap-1396	84	17	(	(	PUNCT
ap-1396	84	18	k0	k0	PROPN
ap-1396	84	19	+	+	CCONJ
ap-1396	84	20	1	1	NUM
ap-1396	84	21	2	2	NUM
ap-1396	84	22	kb	kb	PROPN
ap-1396	84	23	)	)	PUNCT
ap-1396	84	24	2w2	2w2	NUM
ap-1396	84	25	(	(	PUNCT
ap-1396	84	26	erf(η1	erf(η1	PROPN
ap-1396	84	27	)	)	PUNCT
ap-1396	85	1	+	+	CCONJ
ap-1396	85	2	erf(η2	erf(η2	PROPN
ap-1396	85	3	)	)	PUNCT
ap-1396	85	4	)	)	PUNCT
ap-1396	85	5	,	,	PUNCT
ap-1396	85	6	(	(	PUNCT
ap-1396	85	7	13	13	NUM
ap-1396	85	8	)	)	PUNCT
ap-1396	85	9	where	where	SCONJ
ap-1396	85	10	η1	η1	NOUN
ap-1396	85	11	=	=	SYM
ap-1396	85	12	kbz	kbz	PROPN
ap-1396	86	1	+	+	NOUN
ap-1396	86	2	x	x	SYM
ap-1396	86	3	−	−	NOUN
ap-1396	86	4	1	1	NUM
ap-1396	86	5	2	2	NUM
ap-1396	86	6	iw	iw	PROPN
ap-1396	86	7	2(k0	2(k0	NUM
ap-1396	86	8	+	+	CCONJ
ap-1396	86	9	1	1	NUM
ap-1396	86	10	2kb)√	2kb)√	NUM
ap-1396	86	11	(	(	PUNCT
ap-1396	86	12	w2	w2	NOUN
ap-1396	86	13	+	+	CCONJ
ap-1396	86	14	4iz	4iz	NOUN
ap-1396	86	15	)	)	PUNCT
ap-1396	86	16	(	(	PUNCT
ap-1396	86	17	14	14	NUM
ap-1396	86	18	)	)	PUNCT
ap-1396	86	19	η2	η2	PROPN
ap-1396	86	20	=	=	PUNCT
ap-1396	86	21	kbz	kbz	PROPN
ap-1396	86	22	−	−	NOUN
ap-1396	86	23	x	x	SYM
ap-1396	87	1	+	+	CCONJ
ap-1396	87	2	1	1	NUM
ap-1396	87	3	2	2	NUM
ap-1396	87	4	iw	iw	PROPN
ap-1396	87	5	2(k0	2(k0	NUM
ap-1396	87	6	+	+	CCONJ
ap-1396	87	7	1	1	NUM
ap-1396	87	8	2kb)√	2kb)√	NUM
ap-1396	87	9	(	(	PUNCT
ap-1396	87	10	w2	w2	NOUN
ap-1396	87	11	+	+	CCONJ
ap-1396	87	12	4iz	4iz	NOUN
ap-1396	87	13	)	)	PUNCT
ap-1396	87	14	.	.	PUNCT
ap-1396	88	1	(	(	PUNCT
ap-1396	88	2	15	15	NUM
ap-1396	88	3	)	)	PUNCT
ap-1396	88	4	for	for	ADP
ap-1396	88	5	the	the	DET
ap-1396	88	6	purposes	purpose	NOUN
ap-1396	88	7	of	of	ADP
ap-1396	88	8	considering	consider	VERB
ap-1396	88	9	large	large	ADJ
ap-1396	88	10	w	w	NOUN
ap-1396	88	11	,	,	PUNCT
ap-1396	88	12	it	it	PRON
ap-1396	88	13	is	be	AUX
ap-1396	88	14	convenient	convenient	ADJ
ap-1396	88	15	to	to	PART
ap-1396	88	16	rewrite	rewrite	VERB
ap-1396	88	17	these	these	PRON
ap-1396	88	18	in	in	ADP
ap-1396	88	19	the	the	DET
ap-1396	88	20	form	form	NOUN
ap-1396	88	21	η1	η1	NOUN
ap-1396	89	1	=	=	PUNCT
ap-1396	89	2	x	x	SYM
ap-1396	89	3	−	−	PROPN
ap-1396	89	4	2k0z√	2k0z√	PROPN
ap-1396	89	5	(	(	PUNCT
ap-1396	89	6	w2	w2	NOUN
ap-1396	89	7	+	+	CCONJ
ap-1396	89	8	4iz	4iz	NOUN
ap-1396	89	9	)	)	PUNCT
ap-1396	89	10	−	−	NOUN
ap-1396	89	11	1	1	NUM
ap-1396	89	12	2	2	NUM
ap-1396	89	13	i(k0	i(k0	NOUN
ap-1396	89	14	+	+	SYM
ap-1396	89	15	1	1	NUM
ap-1396	89	16	2	2	NUM
ap-1396	89	17	kb	kb	PROPN
ap-1396	89	18	)	)	PUNCT
ap-1396	89	19	√	√	PROPN
ap-1396	89	20	(	(	PUNCT
ap-1396	89	21	w2	w2	NOUN
ap-1396	89	22	+	+	CCONJ
ap-1396	89	23	4iz	4iz	NOUN
ap-1396	89	24	)	)	PUNCT
ap-1396	89	25	(	(	PUNCT
ap-1396	89	26	16	16	X
ap-1396	89	27	)	)	PUNCT
ap-1396	89	28	η2	η2	NOUN
ap-1396	89	29	=	=	SYM
ap-1396	89	30	2z(kb	2z(kb	NUM
ap-1396	89	31	+	+	CCONJ
ap-1396	89	32	k0	k0	PROPN
ap-1396	89	33	)	)	PUNCT
ap-1396	89	34	−	−	PROPN
ap-1396	89	35	x√	x√	PROPN
ap-1396	89	36	(	(	PUNCT
ap-1396	89	37	w2	w2	NOUN
ap-1396	89	38	+	+	CCONJ
ap-1396	89	39	4iz	4iz	NOUN
ap-1396	89	40	)	)	PUNCT
ap-1396	90	1	+	+	CCONJ
ap-1396	90	2	1	1	NUM
ap-1396	90	3	2	2	NUM
ap-1396	90	4	i(k0	i(k0	NOUN
ap-1396	90	5	+	+	SYM
ap-1396	90	6	1	1	NUM
ap-1396	90	7	2	2	NUM
ap-1396	90	8	kb	kb	PROPN
ap-1396	90	9	)	)	PUNCT
ap-1396	90	10	√	√	PROPN
ap-1396	90	11	(	(	PUNCT
ap-1396	90	12	w2	w2	NOUN
ap-1396	90	13	+	+	CCONJ
ap-1396	90	14	4iz	4iz	NOUN
ap-1396	90	15	)	)	PUNCT
ap-1396	90	16	.	.	PUNCT
ap-1396	91	1	(	(	PUNCT
ap-1396	91	2	17	17	NUM
ap-1396	91	3	)	)	PUNCT
ap-1396	91	4	the	the	DET
ap-1396	91	5	case	case	NOUN
ap-1396	91	6	k0	k0	PROPN
ap-1396	91	7	=	=	PROPN
ap-1396	91	8	−1	−1	NOUN
ap-1396	91	9	2	2	NUM
ap-1396	91	10	kb	kb	PROPN
ap-1396	91	11	,	,	PUNCT
ap-1396	91	12	i.e.	i.e.	X
ap-1396	91	13	q0	q0	PROPN
ap-1396	91	14	=	=	SYM
ap-1396	91	15	−1	−1	NOUN
ap-1396	91	16	,	,	PUNCT
ap-1396	91	17	is	be	AUX
ap-1396	91	18	clearly	clearly	ADV
ap-1396	91	19	very	very	ADV
ap-1396	91	20	special	special	ADJ
ap-1396	91	21	,	,	PUNCT
ap-1396	91	22	since	since	SCONJ
ap-1396	91	23	in	in	ADP
ap-1396	91	24	this	this	DET
ap-1396	91	25	case	case	NOUN
ap-1396	91	26	the	the	DET
ap-1396	91	27	second	second	ADJ
ap-1396	91	28	terms	term	NOUN
ap-1396	91	29	in	in	ADP
ap-1396	91	30	the	the	DET
ap-1396	91	31	contributions	contribution	NOUN
ap-1396	91	32	to	to	ADP
ap-1396	91	33	η1	η1	NOUN
ap-1396	91	34	and	and	CCONJ
ap-1396	91	35	η2	η2	NOUN
ap-1396	91	36	vanish	vanish	VERB
ap-1396	91	37	,	,	PUNCT
ap-1396	91	38	so	so	SCONJ
ap-1396	91	39	that	that	SCONJ
ap-1396	91	40	we	we	PRON
ap-1396	91	41	get	get	VERB
ap-1396	91	42	the	the	DET
ap-1396	91	43	simple	simple	ADJ
ap-1396	91	44	expressions	expression	NOUN
ap-1396	91	45	η1	η1	NOUN
ap-1396	91	46	=	=	SYM
ap-1396	91	47	(	(	PUNCT
ap-1396	91	48	x	x	SYM
ap-1396	91	49	+	+	X
ap-1396	91	50	kbz)/	kbz)/	ADJ
ap-1396	91	51	√	√	ADJ
ap-1396	91	52	(	(	PUNCT
ap-1396	91	53	w2	w2	NOUN
ap-1396	91	54	+	+	CCONJ
ap-1396	91	55	4iz	4iz	NOUN
ap-1396	91	56	)	)	PUNCT
ap-1396	91	57	and	and	CCONJ
ap-1396	91	58	η2	η2	ADJ
ap-1396	91	59	=	=	PUNCT
ap-1396	91	60	−(x	−(x	NOUN
ap-1396	92	1	−	−	PROPN
ap-1396	92	2	kbz)/	kbz)/	ADJ
ap-1396	92	3	√	√	PROPN
ap-1396	92	4	(	(	PUNCT
ap-1396	92	5	w2	w2	NOUN
ap-1396	92	6	+	+	CCONJ
ap-1396	92	7	4iz	4iz	NOUN
ap-1396	92	8	)	)	PUNCT
ap-1396	92	9	.	.	PUNCT
ap-1396	93	1	in	in	ADP
ap-1396	93	2	that	that	DET
ap-1396	93	3	case	case	NOUN
ap-1396	93	4	,	,	PUNCT
ap-1396	93	5	as	as	ADV
ap-1396	93	6	long	long	ADV
ap-1396	93	7	as	as	SCONJ
ap-1396	93	8	w2	w2	PROPN
ap-1396	93	9	�	�	PROPN
ap-1396	93	10	4z	4z	PROPN
ap-1396	93	11	the	the	DET
ap-1396	93	12	arguments	argument	NOUN
ap-1396	93	13	may	may	AUX
ap-1396	93	14	be	be	AUX
ap-1396	93	15	treated	treat	VERB
ap-1396	93	16	as	as	ADP
ap-1396	93	17	effectively	effectively	ADV
ap-1396	93	18	real	real	ADJ
ap-1396	93	19	,	,	PUNCT
ap-1396	93	20	and	and	CCONJ
ap-1396	93	21	each	each	DET
ap-1396	93	22	error	error	NOUN
ap-1396	93	23	function	function	NOUN
ap-1396	93	24	behaves	behave	VERB
ap-1396	93	25	like	like	ADP
ap-1396	93	26	a	a	DET
ap-1396	93	27	sign	sign	NOUN
ap-1396	93	28	function	function	NOUN
ap-1396	93	29	of	of	ADP
ap-1396	93	30	its	its	PRON
ap-1396	93	31	argument	argument	NOUN
ap-1396	93	32	(	(	PUNCT
ap-1396	93	33	see	see	VERB
ap-1396	93	34	figure	figure	NOUN
ap-1396	93	35	2(a	2(a	NUM
ap-1396	93	36	)	)	PUNCT
ap-1396	93	37	)	)	PUNCT
ap-1396	93	38	,	,	PUNCT
ap-1396	93	39	so	so	SCONJ
ap-1396	93	40	that	that	SCONJ
ap-1396	93	41	the	the	DET
ap-1396	93	42	sum	sum	NOUN
ap-1396	93	43	of	of	ADP
ap-1396	93	44	the	the	DET
ap-1396	93	45	two	two	NUM
ap-1396	93	46	behaves	behave	NOUN
ap-1396	93	47	like	like	ADP
ap-1396	93	48	the	the	DET
ap-1396	93	49	step	step	NOUN
ap-1396	93	50	function	function	NOUN
ap-1396	93	51	θ(kbz−	θ(kbz−	ADJ
ap-1396	93	52	|x|	|x|	PROPN
ap-1396	93	53	)	)	PUNCT
ap-1396	93	54	.	.	PUNCT
ap-1396	94	1	this	this	PRON
ap-1396	94	2	is	be	AUX
ap-1396	94	3	the	the	DET
ap-1396	94	4	function	function	NOUN
ap-1396	94	5	φ(x/(kbz	φ(x/(kbz	NOUN
ap-1396	94	6	)	)	PUNCT
ap-1396	94	7	)	)	PUNCT
ap-1396	94	8	of	of	ADP
ap-1396	94	9	ref	ref	NOUN
ap-1396	94	10	.	.	PUNCT
ap-1396	95	1	[	[	X
ap-1396	95	2	12	12	NUM
ap-1396	95	3	]	]	PUNCT
ap-1396	95	4	.	.	PUNCT
ap-1396	96	1	in	in	ADP
ap-1396	96	2	this	this	DET
ap-1396	96	3	case	case	NOUN
ap-1396	96	4	the	the	DET
ap-1396	96	5	qualitative	qualitative	ADJ
ap-1396	96	6	features	feature	NOUN
ap-1396	96	7	of	of	ADP
ap-1396	96	8	the	the	DET
ap-1396	96	9	perturbative	perturbative	ADJ
ap-1396	96	10	calculation	calculation	NOUN
ap-1396	96	11	are	be	AUX
ap-1396	96	12	in	in	ADP
ap-1396	96	13	complete	complete	ADJ
ap-1396	96	14	agreement	agreement	NOUN
ap-1396	96	15	with	with	ADP
ap-1396	96	16	the	the	DET
ap-1396	96	17	spreading	spreading	NOUN
ap-1396	96	18	of	of	ADP
ap-1396	96	19	the	the	DET
ap-1396	96	20	wave	wave	NOUN
ap-1396	96	21	-	-	PUNCT
ap-1396	96	22	function	function	NOUN
ap-1396	96	23	in	in	ADP
ap-1396	96	24	figure	figure	NOUN
ap-1396	96	25	3	3	NUM
ap-1396	96	26	of	of	ADP
ap-1396	96	27	that	that	DET
ap-1396	96	28	paper	paper	NOUN
ap-1396	96	29	,	,	PUNCT
ap-1396	96	30	and	and	CCONJ
ap-1396	96	31	the	the	DET
ap-1396	96	32	saturation1	saturation1	NOUN
ap-1396	96	33	of	of	ADP
ap-1396	96	34	ψmax	ψmax	NOUN
ap-1396	96	35	.	.	PUNCT
ap-1396	97	1	however	however	ADV
ap-1396	97	2	,	,	PUNCT
ap-1396	97	3	in	in	ADP
ap-1396	97	4	this	this	DET
ap-1396	97	5	treatment	treatment	NOUN
ap-1396	97	6	there	there	PRON
ap-1396	97	7	is	be	VERB
ap-1396	97	8	of	of	ADP
ap-1396	97	9	course	course	NOUN
ap-1396	97	10	no	no	DET
ap-1396	97	11	mention	mention	NOUN
ap-1396	97	12	of	of	ADP
ap-1396	97	13	whether	whether	SCONJ
ap-1396	97	14	or	or	CCONJ
ap-1396	97	15	not	not	PART
ap-1396	97	16	any	any	DET
ap-1396	97	17	jordan	jordan	PROPN
ap-1396	97	18	functions	function	NOUN
ap-1396	97	19	are	be	AUX
ap-1396	97	20	excited	excited	ADJ
ap-1396	97	21	.	.	PUNCT
ap-1396	98	1	1ψ1(x	1ψ1(x	NUM
ap-1396	98	2	,	,	PUNCT
ap-1396	98	3	z	z	NOUN
ap-1396	98	4	)	)	PUNCT
ap-1396	98	5	grows	grow	VERB
ap-1396	98	6	initially	initially	ADV
ap-1396	98	7	like	like	ADP
ap-1396	98	8	z	z	NOUN
ap-1396	98	9	for	for	ADP
ap-1396	98	10	small	small	ADJ
ap-1396	98	11	z.	z.	PROPN
ap-1396	98	12	23	23	NUM
ap-1396	98	13	acta	acta	PROPN
ap-1396	98	14	polytechnica	polytechnica	PROPN
ap-1396	98	15	vol	vol	NOUN
ap-1396	98	16	.	.	PUNCT
ap-1396	99	1	51	51	NUM
ap-1396	99	2	no	no	INTJ
ap-1396	99	3	.	.	PUNCT
ap-1396	100	1	4/2011	4/2011	NUM
ap-1396	101	1	-400	-400	NUM
ap-1396	102	1	-200	-200	NUM
ap-1396	103	1	200	200	NUM
ap-1396	103	2	400	400	NUM
ap-1396	103	3	0.2	0.2	NUM
ap-1396	103	4	0.4	0.4	NUM
ap-1396	103	5	0.6	0.6	NUM
ap-1396	103	6	0.8	0.8	NUM
ap-1396	103	7	1	1	NUM
ap-1396	103	8	-400	-400	NUM
ap-1396	103	9	-200	-200	NUM
ap-1396	104	1	200	200	NUM
ap-1396	104	2	400	400	NUM
ap-1396	104	3	0.002	0.002	NUM
ap-1396	104	4	0.004	0.004	NUM
ap-1396	104	5	0.006	0.006	NUM
ap-1396	104	6	0.008	0.008	NUM
ap-1396	104	7	0.01	0.01	NUM
ap-1396	104	8	0.012	0.012	NUM
ap-1396	104	9	0.014	0.014	NUM
ap-1396	104	10	fig	fig	NOUN
ap-1396	104	11	.	.	PUNCT
ap-1396	105	1	3	3	NUM
ap-1396	105	2	:	:	PUNCT
ap-1396	105	3	|ψ2(x	|ψ2(x	NUM
ap-1396	105	4	,	,	PUNCT
ap-1396	105	5	z)|	z)|	NOUN
ap-1396	105	6	versus	versus	X
ap-1396	105	7	x	x	PUNCT
ap-1396	105	8	for	for	ADP
ap-1396	105	9	z	z	NOUN
ap-1396	105	10	=	=	SYM
ap-1396	105	11	50	50	NUM
ap-1396	105	12	.	.	PUNCT
ap-1396	106	1	(	(	PUNCT
ap-1396	106	2	a	a	X
ap-1396	106	3	)	)	PUNCT
ap-1396	106	4	q0	q0	NOUN
ap-1396	106	5	=	=	SYM
ap-1396	106	6	−1	−1	NOUN
ap-1396	106	7	,	,	PUNCT
ap-1396	106	8	(	(	PUNCT
ap-1396	106	9	b	b	X
ap-1396	106	10	)	)	PUNCT
ap-1396	106	11	q0	q0	NOUN
ap-1396	106	12	=	=	NOUN
ap-1396	106	13	0	0	PROPN
ap-1396	106	14	.	.	PUNCT
ap-1396	107	1	the	the	DET
ap-1396	107	2	parameters	parameter	NOUN
ap-1396	107	3	are	be	AUX
ap-1396	107	4	:	:	PUNCT
ap-1396	107	5	a	a	DET
ap-1396	107	6	=	=	SYM
ap-1396	107	7	1	1	NUM
ap-1396	107	8	,	,	PUNCT
ap-1396	107	9	v0	v0	NOUN
ap-1396	107	10	=	=	SYM
ap-1396	107	11	2	2	NUM
ap-1396	107	12	and	and	CCONJ
ap-1396	107	13	w	w	NOUN
ap-1396	107	14	=	=	NOUN
ap-1396	107	15	6π	6π	NOUN
ap-1396	107	16	the	the	DET
ap-1396	107	17	same	same	ADJ
ap-1396	107	18	expressions	expression	NOUN
ap-1396	107	19	in	in	ADP
ap-1396	107	20	eqs	eqs	PROPN
ap-1396	107	21	.	.	PUNCT
ap-1396	108	1	(	(	PUNCT
ap-1396	108	2	13	13	NUM
ap-1396	108	3	)	)	PUNCT
ap-1396	108	4	and	and	CCONJ
ap-1396	108	5	(	(	PUNCT
ap-1396	108	6	16	16	NUM
ap-1396	108	7	)	)	PUNCT
ap-1396	108	8	can	can	AUX
ap-1396	108	9	also	also	ADV
ap-1396	108	10	be	be	AUX
ap-1396	108	11	used	use	VERB
ap-1396	108	12	for	for	ADP
ap-1396	108	13	the	the	DET
ap-1396	108	14	cases	case	NOUN
ap-1396	108	15	q0	q0	VERB
ap-1396	108	16	=	=	SYM
ap-1396	108	17	0	0	NUM
ap-1396	108	18	and	and	CCONJ
ap-1396	108	19	q0	q0	VERB
ap-1396	108	20	=	=	NOUN
ap-1396	108	21	1	1	NUM
ap-1396	108	22	in	in	ADP
ap-1396	108	23	the	the	DET
ap-1396	108	24	limit	limit	NOUN
ap-1396	108	25	of	of	ADP
ap-1396	108	26	large	large	ADJ
ap-1396	108	27	w.	w.	NOUN
ap-1396	108	28	in	in	ADP
ap-1396	108	29	each	each	DET
ap-1396	108	30	case	case	NOUN
ap-1396	108	31	the	the	DET
ap-1396	108	32	arguments	argument	NOUN
ap-1396	108	33	η1	η1	NOUN
ap-1396	108	34	and	and	CCONJ
ap-1396	108	35	η2	η2	PROPN
ap-1396	108	36	now	now	ADV
ap-1396	108	37	have	have	VERB
ap-1396	108	38	a	a	DET
ap-1396	108	39	large	large	ADJ
ap-1396	108	40	imaginary	imaginary	ADJ
ap-1396	108	41	part	part	NOUN
ap-1396	108	42	.	.	PUNCT
ap-1396	109	1	in	in	ADP
ap-1396	109	2	that	that	DET
ap-1396	109	3	situation	situation	NOUN
ap-1396	109	4	the	the	DET
ap-1396	109	5	modulus	modulus	NOUN
ap-1396	109	6	of	of	ADP
ap-1396	109	7	the	the	DET
ap-1396	109	8	erf	erf	NOUN
ap-1396	109	9	has	have	VERB
ap-1396	109	10	a	a	DET
ap-1396	109	11	narrow	narrow	ADJ
ap-1396	109	12	peak	peak	NOUN
ap-1396	109	13	where	where	SCONJ
ap-1396	109	14	the	the	DET
ap-1396	109	15	real	real	ADJ
ap-1396	109	16	part	part	NOUN
ap-1396	109	17	vanishes	vanish	VERB
ap-1396	109	18	(	(	PUNCT
ap-1396	109	19	see	see	VERB
ap-1396	109	20	figure	figure	NOUN
ap-1396	109	21	2(b	2(b	NUM
ap-1396	109	22	)	)	PUNCT
ap-1396	109	23	)	)	PUNCT
ap-1396	109	24	.	.	PUNCT
ap-1396	110	1	thus	thus	ADV
ap-1396	110	2	the	the	DET
ap-1396	110	3	result	result	NOUN
ap-1396	110	4	consists	consist	VERB
ap-1396	110	5	of	of	ADP
ap-1396	110	6	two	two	NUM
ap-1396	110	7	narrow	narrow	ADJ
ap-1396	110	8	rays	ray	NOUN
ap-1396	110	9	,	,	PUNCT
ap-1396	110	10	which	which	PRON
ap-1396	110	11	are	be	AUX
ap-1396	110	12	centered	center	VERB
ap-1396	110	13	on	on	ADP
ap-1396	110	14	x	x	X
ap-1396	110	15	=	=	PUNCT
ap-1396	110	16	2k0z	2k0z	NOUN
ap-1396	110	17	and	and	CCONJ
ap-1396	110	18	x	x	SYM
ap-1396	110	19	=	=	SYM
ap-1396	110	20	2(kb	2(kb	PROPN
ap-1396	110	21	+	+	NUM
ap-1396	110	22	k0)z	k0)z	NOUN
ap-1396	110	23	.	.	PUNCT
ap-1396	111	1	here	here	ADV
ap-1396	111	2	we	we	PRON
ap-1396	111	3	have	have	VERB
ap-1396	111	4	the	the	DET
ap-1396	111	5	seeds	seed	NOUN
ap-1396	111	6	of	of	ADP
ap-1396	111	7	the	the	DET
ap-1396	111	8	birefringence	birefringence	NOUN
ap-1396	111	9	first	first	ADV
ap-1396	111	10	observed	observe	VERB
ap-1396	111	11	in	in	ADP
ap-1396	111	12	ref	ref	NOUN
ap-1396	111	13	.	.	PUNCT
ap-1396	112	1	[	[	X
ap-1396	112	2	7	7	NUM
ap-1396	112	3	]	]	PUNCT
ap-1396	112	4	.	.	PUNCT
ap-1396	113	1	for	for	ADP
ap-1396	113	2	the	the	DET
ap-1396	113	3	case	case	NOUN
ap-1396	113	4	k0	k0	PROPN
ap-1396	113	5	=	=	PUNCT
ap-1396	113	6	q0	q0	PROPN
ap-1396	113	7	=	=	SYM
ap-1396	113	8	0	0	PROPN
ap-1396	113	9	,	,	PUNCT
ap-1396	113	10	the	the	DET
ap-1396	113	11	two	two	NUM
ap-1396	113	12	rays	ray	NOUN
ap-1396	113	13	are	be	AUX
ap-1396	113	14	centered	center	VERB
ap-1396	113	15	on	on	ADP
ap-1396	113	16	x	x	X
ap-1396	113	17	=	=	SYM
ap-1396	113	18	0	0	NUM
ap-1396	113	19	and	and	CCONJ
ap-1396	113	20	x	x	SYM
ap-1396	113	21	=	=	SYM
ap-1396	113	22	2kbz	2kbz	NUM
ap-1396	113	23	,	,	PUNCT
ap-1396	113	24	while	while	SCONJ
ap-1396	113	25	for	for	SCONJ
ap-1396	113	26	the	the	DET
ap-1396	113	27	case	case	NOUN
ap-1396	113	28	q0	q0	NOUN
ap-1396	113	29	=	=	SYM
ap-1396	113	30	1	1	NUM
ap-1396	113	31	,	,	PUNCT
ap-1396	113	32	or	or	CCONJ
ap-1396	113	33	k0	k0	PROPN
ap-1396	113	34	=	=	NOUN
ap-1396	113	35	1	1	NUM
ap-1396	113	36	2	2	NUM
ap-1396	113	37	kb	kb	PROPN
ap-1396	113	38	,	,	PUNCT
ap-1396	113	39	the	the	DET
ap-1396	113	40	two	two	NUM
ap-1396	113	41	rays	ray	NOUN
ap-1396	113	42	are	be	AUX
ap-1396	113	43	centered	center	VERB
ap-1396	113	44	on	on	ADP
ap-1396	113	45	x	x	X
ap-1396	113	46	=	=	PUNCT
ap-1396	113	47	kbz	kbz	PROPN
ap-1396	113	48	and	and	CCONJ
ap-1396	113	49	x	x	SYM
ap-1396	113	50	=	=	SYM
ap-1396	113	51	3kbz	3kbz	NUM
ap-1396	113	52	.	.	PUNCT
ap-1396	114	1	we	we	PRON
ap-1396	114	2	now	now	ADV
ap-1396	114	3	go	go	VERB
ap-1396	114	4	on	on	ADP
ap-1396	114	5	to	to	ADP
ap-1396	114	6	second	second	ADJ
ap-1396	114	7	-	-	PUNCT
ap-1396	114	8	order	order	NOUN
ap-1396	114	9	perturbation	perturbation	NOUN
ap-1396	114	10	theory	theory	NOUN
ap-1396	114	11	to	to	PART
ap-1396	114	12	investigate	investigate	VERB
ap-1396	114	13	the	the	DET
ap-1396	114	14	behaviour	behaviour	NOUN
ap-1396	114	15	of	of	ADP
ap-1396	114	16	ψ2(x	ψ2(x	PROPN
ap-1396	114	17	,	,	PUNCT
ap-1396	114	18	z	z	NOUN
ap-1396	114	19	)	)	PUNCT
ap-1396	114	20	,	,	PUNCT
ap-1396	114	21	which	which	PRON
ap-1396	114	22	is	be	AUX
ap-1396	114	23	given	give	VERB
ap-1396	114	24	by	by	ADP
ap-1396	114	25	[	[	X
ap-1396	114	26	12	12	NUM
ap-1396	114	27	]	]	PUNCT
ap-1396	114	28	ψ2(x	ψ2(x	PROPN
ap-1396	114	29	,	,	PUNCT
ap-1396	114	30	z	z	NOUN
ap-1396	114	31	)	)	PUNCT
ap-1396	114	32	=	=	SYM
ap-1396	115	1	−	−	PROPN
ap-1396	115	2	∫	∫	PROPN
ap-1396	115	3	dkf̃(k)ei(k+2	dkf̃(k)ei(k+2	PROPN
ap-1396	115	4	kb	kb	PROPN
ap-1396	115	5	)	)	PUNCT
ap-1396	115	6	∫	∫	PROPN
ap-1396	115	7	z	z	NOUN
ap-1396	115	8	0	0	NUM
ap-1396	115	9	dη	dη	NOUN
ap-1396	115	10	·	·	PUNCT
ap-1396	115	11	(	(	PUNCT
ap-1396	115	12	18)∫	18)∫	PROPN
ap-1396	115	13	z−η	z−η	NUM
ap-1396	115	14	0	0	NUM
ap-1396	115	15	dξ	dξ	PROPN
ap-1396	115	16	e−ik2z−4ikb(k+kb)η+ikb(kb+2k)ξ	e−ik2z−4ikb(k+kb)η+ikb(kb+2k)ξ	VERB
ap-1396	115	17	again	again	ADV
ap-1396	115	18	the	the	DET
ap-1396	115	19	k	k	PROPN
ap-1396	115	20	integration	integration	NOUN
ap-1396	115	21	is	be	AUX
ap-1396	115	22	a	a	DET
ap-1396	115	23	gaussian	gaussian	NOUN
ap-1396	115	24	,	,	PUNCT
ap-1396	115	25	which	which	PRON
ap-1396	115	26	leaves	leave	VERB
ap-1396	115	27	finite	finite	ADJ
ap-1396	115	28	-	-	ADJ
ap-1396	115	29	range	range	ADJ
ap-1396	115	30	gaussian	gaussian	ADJ
ap-1396	115	31	integrations	integration	NOUN
ap-1396	115	32	over	over	ADP
ap-1396	115	33	ξ	ξ	PROPN
ap-1396	115	34	and	and	CCONJ
ap-1396	115	35	η	η	PROPN
ap-1396	115	36	.	.	PROPN
ap-1396	116	1	it	it	PRON
ap-1396	116	2	is	be	AUX
ap-1396	116	3	convenient	convenient	ADJ
ap-1396	116	4	to	to	PART
ap-1396	116	5	change	change	VERB
ap-1396	116	6	the	the	DET
ap-1396	116	7	integration	integration	NOUN
ap-1396	116	8	variable	variable	NOUN
ap-1396	116	9	ξ	ξ	PROPN
ap-1396	116	10	to	to	ADP
ap-1396	116	11	y	y	PROPN
ap-1396	116	12	≡	≡	PROPN
ap-1396	116	13	2η	2η	PROPN
ap-1396	117	1	−	−	PROPN
ap-1396	117	2	ξ	ξ	X
ap-1396	117	3	.	.	PUNCT
ap-1396	118	1	the	the	DET
ap-1396	118	2	integration	integration	NOUN
ap-1396	118	3	over	over	ADP
ap-1396	118	4	y	y	PROPN
ap-1396	118	5	then	then	ADV
ap-1396	118	6	yields	yield	VERB
ap-1396	118	7	the	the	DET
ap-1396	118	8	expression	expression	NOUN
ap-1396	118	9	ψ2(x	ψ2(x	PROPN
ap-1396	118	10	,	,	PUNCT
ap-1396	118	11	z	z	NOUN
ap-1396	118	12	)	)	PUNCT
ap-1396	118	13	=	=	SYM
ap-1396	119	1	−	−	PROPN
ap-1396	119	2	w	w	NOUN
ap-1396	119	3	2	2	NUM
ap-1396	119	4	kb	kb	PROPN
ap-1396	119	5	∫	∫	PROPN
ap-1396	119	6	z	z	NOUN
ap-1396	119	7	0	0	NUM
ap-1396	119	8	dη	dη	NOUN
ap-1396	119	9	√	√	PROPN
ap-1396	119	10	π	π	SYM
ap-1396	119	11	2	2	NUM
ap-1396	119	12	(	(	PUNCT
ap-1396	119	13	erf(a	erf(a	PROPN
ap-1396	119	14	)	)	PUNCT
ap-1396	119	15	−	−	PRON
ap-1396	119	16	erf(b	erf(b	PROPN
ap-1396	119	17	)	)	PUNCT
ap-1396	119	18	)	)	PUNCT
ap-1396	119	19	·	·	PUNCT
ap-1396	120	1	(	(	PUNCT
ap-1396	120	2	19	19	NUM
ap-1396	120	3	)	)	PUNCT
ap-1396	120	4	e−2ik	e−2ik	NOUN
ap-1396	120	5	2	2	NUM
ap-1396	120	6	bηe	bηe	NOUN
ap-1396	120	7	3	3	NUM
ap-1396	120	8	2	2	NUM
ap-1396	120	9	ikbx−	ikbx−	NOUN
ap-1396	120	10	1	1	NUM
ap-1396	120	11	4	4	NUM
ap-1396	120	12	ik2bt−	ik2bt−	ADJ
ap-1396	120	13	1	1	NUM
ap-1396	120	14	4w2δ2	4w2δ2	NOUN
ap-1396	120	15	,	,	PUNCT
ap-1396	120	16	where	where	SCONJ
ap-1396	120	17	we	we	PRON
ap-1396	120	18	have	have	AUX
ap-1396	120	19	written	write	VERB
ap-1396	120	20	k0	k0	PROPN
ap-1396	120	21	=	=	PUNCT
ap-1396	120	22	−	−	PROPN
ap-1396	120	23	(	(	PUNCT
ap-1396	120	24	1	1	NUM
ap-1396	120	25	2	2	NUM
ap-1396	120	26	kb	kb	NOUN
ap-1396	120	27	+	+	PROPN
ap-1396	120	28	δ	δ	PROPN
ap-1396	120	29	)	)	PUNCT
ap-1396	120	30	,	,	PUNCT
ap-1396	120	31	and	and	CCONJ
ap-1396	120	32	a	a	PRON
ap-1396	120	33	and	and	CCONJ
ap-1396	120	34	b	b	NOUN
ap-1396	120	35	are	be	AUX
ap-1396	120	36	given	give	VERB
ap-1396	120	37	by	by	ADP
ap-1396	120	38	b	b	NOUN
ap-1396	120	39	=	=	SYM
ap-1396	120	40	4kbη	4kbη	NUM
ap-1396	120	41	−	−	NOUN
ap-1396	120	42	x	x	SYM
ap-1396	120	43	−	−	PROPN
ap-1396	120	44	kbz	kbz	NOUN
ap-1396	120	45	−	−	NOUN
ap-1396	120	46	1	1	NUM
ap-1396	120	47	2	2	NUM
ap-1396	120	48	iw	iw	PROPN
ap-1396	120	49	2δ√	2δ√	NOUN
ap-1396	120	50	(	(	PUNCT
ap-1396	120	51	w2	w2	NOUN
ap-1396	120	52	+	+	CCONJ
ap-1396	120	53	4iz	4iz	NOUN
ap-1396	120	54	)	)	PUNCT
ap-1396	120	55	a	a	DET
ap-1396	120	56	=	=	SYM
ap-1396	120	57	3kb(2η	3kb(2η	NUM
ap-1396	120	58	−	−	PROPN
ap-1396	120	59	z	z	NOUN
ap-1396	120	60	)	)	PUNCT
ap-1396	121	1	−	−	NOUN
ap-1396	122	1	x	x	SYM
ap-1396	123	1	−	−	NOUN
ap-1396	123	2	1	1	NUM
ap-1396	123	3	2	2	NUM
ap-1396	123	4	iw	iw	PROPN
ap-1396	123	5	2δ√	2δ√	NOUN
ap-1396	123	6	(	(	PUNCT
ap-1396	123	7	w2	w2	NOUN
ap-1396	123	8	+	+	CCONJ
ap-1396	123	9	4iz	4iz	NOUN
ap-1396	123	10	)	)	PUNCT
ap-1396	123	11	.	.	PUNCT
ap-1396	124	1	(	(	PUNCT
ap-1396	124	2	20	20	NUM
ap-1396	124	3	)	)	PUNCT
ap-1396	124	4	the	the	DET
ap-1396	124	5	final	final	PROPN
ap-1396	124	6	η	η	PROPN
ap-1396	124	7	integrations	integration	NOUN
ap-1396	124	8	are	be	AUX
ap-1396	124	9	then	then	ADV
ap-1396	124	10	of	of	ADP
ap-1396	124	11	the	the	DET
ap-1396	124	12	form	form	NOUN
ap-1396	124	13	iη	iη	VERB
ap-1396	124	14	≡	≡	PROPN
ap-1396	124	15	∫	∫	PROPN
ap-1396	125	1	dη	dη	X
ap-1396	125	2	erf(c1η	erf(c1η	PROPN
ap-1396	126	1	+	+	NUM
ap-1396	126	2	c2)ec3η	c2)ec3η	ADJ
ap-1396	126	3	=	=	SYM
ap-1396	126	4	1	1	NUM
ap-1396	126	5	c3	c3	NOUN
ap-1396	126	6	[	[	PUNCT
ap-1396	126	7	ec3ηerf(c1η	ec3ηerf(c1η	PROPN
ap-1396	126	8	+	+	CCONJ
ap-1396	126	9	c2	c2	PROPN
ap-1396	126	10	)	)	PUNCT
ap-1396	126	11	−	−	PROPN
ap-1396	126	12	(	(	PUNCT
ap-1396	126	13	21	21	NUM
ap-1396	126	14	)	)	PUNCT
ap-1396	126	15	ec3(c3−4c1c2)/(4c21)erf	ec3(c3−4c1c2)/(4c21)erf	NOUN
ap-1396	126	16	(	(	PUNCT
ap-1396	126	17	c1η	c1η	NOUN
ap-1396	126	18	+	+	NUM
ap-1396	126	19	c2	c2	PROPN
ap-1396	126	20	−	−	PROPN
ap-1396	126	21	c3/(2c1	c3/(2c1	PROPN
ap-1396	126	22	)	)	PUNCT
ap-1396	126	23	)	)	PUNCT
ap-1396	126	24	]	]	PUNCT
ap-1396	126	25	.	.	PUNCT
ap-1396	127	1	thus	thus	ADV
ap-1396	127	2	in	in	ADP
ap-1396	127	3	principle	principle	ADJ
ap-1396	127	4	ψ2	ψ2	NOUN
ap-1396	127	5	is	be	AUX
ap-1396	127	6	expressible	expressible	ADJ
ap-1396	127	7	in	in	ADP
ap-1396	127	8	terms	term	NOUN
ap-1396	127	9	of	of	ADP
ap-1396	127	10	eight	eight	NUM
ap-1396	127	11	error	error	NOUN
ap-1396	127	12	functions	function	NOUN
ap-1396	127	13	.	.	PUNCT
ap-1396	128	1	however	however	ADV
ap-1396	128	2	,	,	PUNCT
ap-1396	128	3	it	it	PRON
ap-1396	128	4	turns	turn	VERB
ap-1396	128	5	out	out	ADP
ap-1396	128	6	in	in	ADP
ap-1396	128	7	practice	practice	NOUN
ap-1396	128	8	that	that	SCONJ
ap-1396	128	9	only	only	ADV
ap-1396	128	10	six	six	NUM
ap-1396	128	11	are	be	AUX
ap-1396	128	12	involved	involve	VERB
ap-1396	128	13	.	.	PUNCT
ap-1396	129	1	in	in	ADP
ap-1396	129	2	the	the	DET
ap-1396	129	3	case	case	NOUN
ap-1396	129	4	k0	k0	PROPN
ap-1396	129	5	=	=	SYM
ap-1396	129	6	−kb/2	−kb/2	PROPN
ap-1396	129	7	,	,	PUNCT
ap-1396	129	8	or	or	CCONJ
ap-1396	129	9	q0	q0	PROPN
ap-1396	129	10	=	=	SYM
ap-1396	129	11	−1	−1	NOUN
ap-1396	129	12	,	,	PUNCT
ap-1396	129	13	when	when	SCONJ
ap-1396	129	14	δ	δ	PROPN
ap-1396	129	15	=	=	SYM
ap-1396	129	16	0	0	PROPN
ap-1396	129	17	,	,	PUNCT
ap-1396	129	18	the	the	DET
ap-1396	129	19	arguments	argument	NOUN
ap-1396	129	20	of	of	ADP
ap-1396	129	21	the	the	DET
ap-1396	129	22	error	error	NOUN
ap-1396	129	23	functions	function	NOUN
ap-1396	129	24	are	be	AUX
ap-1396	129	25	such	such	ADJ
ap-1396	129	26	as	as	ADP
ap-1396	129	27	to	to	PART
ap-1396	129	28	give	give	VERB
ap-1396	129	29	a	a	DET
ap-1396	129	30	plateau	plateau	NOUN
ap-1396	129	31	in	in	ADP
ap-1396	129	32	|ψ2|	|ψ2|	NOUN
ap-1396	129	33	between	between	ADP
ap-1396	129	34	x	x	X
ap-1396	129	35	=	=	X
ap-1396	129	36	−3kbz	−3kbz	PROPN
ap-1396	129	37	and	and	CCONJ
ap-1396	129	38	x	x	X
ap-1396	129	39	=	=	PUNCT
ap-1396	129	40	−kbz	−kbz	NUM
ap-1396	129	41	,	,	PUNCT
ap-1396	129	42	i.e.	i.e.	X
ap-1396	129	43	a	a	DET
ap-1396	129	44	widening	widening	NOUN
ap-1396	129	45	of	of	ADP
ap-1396	129	46	the	the	DET
ap-1396	129	47	beam	beam	NOUN
ap-1396	129	48	to	to	ADP
ap-1396	129	49	the	the	DET
ap-1396	129	50	left	left	NOUN
ap-1396	129	51	of	of	ADP
ap-1396	129	52	ψ0	ψ0	PROPN
ap-1396	129	53	,	,	PUNCT
ap-1396	129	54	and	and	CCONJ
ap-1396	129	55	a	a	DET
ap-1396	129	56	much	much	ADV
ap-1396	129	57	smaller	small	ADJ
ap-1396	129	58	peak	peak	NOUN
ap-1396	129	59	,	,	PUNCT
ap-1396	129	60	centered	center	VERB
ap-1396	129	61	around	around	ADV
ap-1396	129	62	x	x	X
ap-1396	130	1	=	=	SYM
ap-1396	130	2	3kbz	3kbz	NUM
ap-1396	130	3	,	,	PUNCT
ap-1396	130	4	that	that	ADV
ap-1396	130	5	is	is	ADV
ap-1396	130	6	,	,	PUNCT
ap-1396	130	7	a	a	DET
ap-1396	130	8	second	second	ADJ
ap-1396	130	9	weak	weak	ADJ
ap-1396	130	10	beam	beam	NOUN
ap-1396	130	11	to	to	ADP
ap-1396	130	12	the	the	DET
ap-1396	130	13	right	right	NOUN
ap-1396	130	14	.	.	PUNCT
ap-1396	131	1	more	more	ADV
ap-1396	131	2	importantly	importantly	ADV
ap-1396	131	3	,	,	PUNCT
ap-1396	131	4	the	the	DET
ap-1396	131	5	second	second	ADJ
ap-1396	131	6	-	-	PUNCT
ap-1396	131	7	order	order	NOUN
ap-1396	131	8	contribution	contribution	NOUN
ap-1396	131	9	again	again	ADV
ap-1396	131	10	shows	show	VERB
ap-1396	131	11	no	no	DET
ap-1396	131	12	sign	sign	NOUN
ap-1396	131	13	of	of	ADP
ap-1396	131	14	the	the	DET
ap-1396	131	15	linear	linear	PROPN
ap-1396	131	16	growth2	growth2	PROPN
ap-1396	131	17	in	in	ADP
ap-1396	131	18	z	z	PROPN
ap-1396	131	19	näıvely	näıvely	ADV
ap-1396	131	20	expected	expect	VERB
ap-1396	131	21	from	from	ADP
ap-1396	131	22	the	the	DET
ap-1396	131	23	excitation	excitation	NOUN
ap-1396	131	24	of	of	ADP
ap-1396	131	25	jordan	jordan	PROPN
ap-1396	131	26	associated	associated	PROPN
ap-1396	131	27	functions	function	NOUN
ap-1396	131	28	.	.	PUNCT
ap-1396	132	1	in	in	ADP
ap-1396	132	2	the	the	DET
ap-1396	132	3	other	other	ADJ
ap-1396	132	4	case	case	NOUN
ap-1396	132	5	,	,	PUNCT
ap-1396	132	6	q0	q0	PROPN
ap-1396	132	7	=	=	SYM
ap-1396	132	8	0	0	PROPN
ap-1396	132	9	,	,	PUNCT
ap-1396	132	10	corresponding	correspond	VERB
ap-1396	132	11	to	to	ADP
ap-1396	132	12	δ	δ	X
ap-1396	132	13	=	=	SYM
ap-1396	133	1	−kb/2	−kb/2	NUM
ap-1396	133	2	,	,	PUNCT
ap-1396	133	3	there	there	PRON
ap-1396	133	4	are	be	VERB
ap-1396	133	5	three	three	NUM
ap-1396	133	6	peaks	peak	NOUN
ap-1396	133	7	,	,	PUNCT
ap-1396	133	8	centered	center	VERB
ap-1396	133	9	around	around	ADV
ap-1396	133	10	x	x	PUNCT
ap-1396	133	11	=	=	SYM
ap-1396	133	12	0	0	NUM
ap-1396	133	13	,	,	PUNCT
ap-1396	133	14	x	x	PUNCT
ap-1396	133	15	=	=	PUNCT
ap-1396	133	16	−2kbz	−2kbz	PROPN
ap-1396	133	17	and	and	CCONJ
ap-1396	133	18	x	x	X
ap-1396	133	19	=	=	SYM
ap-1396	133	20	4kbz	4kbz	PROPN
ap-1396	133	21	,	,	PUNCT
ap-1396	133	22	representing	represent	VERB
ap-1396	133	23	a	a	DET
ap-1396	133	24	further	further	ADJ
ap-1396	133	25	splitting	splitting	NOUN
ap-1396	133	26	of	of	ADP
ap-1396	133	27	the	the	DET
ap-1396	133	28	initial	initial	ADJ
ap-1396	133	29	beam	beam	NOUN
ap-1396	133	30	.	.	PUNCT
ap-1396	134	1	both	both	DET
ap-1396	134	2	cases	case	NOUN
ap-1396	134	3	are	be	AUX
ap-1396	134	4	illustrated	illustrate	VERB
ap-1396	134	5	in	in	ADP
ap-1396	134	6	figure	figure	NOUN
ap-1396	134	7	3	3	NUM
ap-1396	134	8	.	.	NOUN
ap-1396	134	9	4	4	NUM
ap-1396	134	10	discussion	discussion	NOUN
ap-1396	134	11	of	of	ADP
ap-1396	134	12	course	course	NOUN
ap-1396	134	13	one	one	NUM
ap-1396	134	14	needs	need	VERB
ap-1396	134	15	to	to	PART
ap-1396	134	16	treat	treat	VERB
ap-1396	134	17	the	the	DET
ap-1396	134	18	results	result	NOUN
ap-1396	134	19	of	of	ADP
ap-1396	134	20	perturbation	perturbation	NOUN
ap-1396	134	21	theory	theory	NOUN
ap-1396	134	22	with	with	ADP
ap-1396	134	23	caution	caution	NOUN
ap-1396	134	24	.	.	PUNCT
ap-1396	135	1	in	in	ADP
ap-1396	135	2	general	general	ADJ
ap-1396	135	3	terms	term	NOUN
ap-1396	135	4	we	we	PRON
ap-1396	135	5	have	have	VERB
ap-1396	135	6	no	no	DET
ap-1396	135	7	proof	proof	NOUN
ap-1396	135	8	that	that	SCONJ
ap-1396	135	9	the	the	DET
ap-1396	135	10	perturbation	perturbation	NOUN
ap-1396	135	11	series	series	NOUN
ap-1396	135	12	converges	converge	VERB
ap-1396	135	13	,	,	PUNCT
ap-1396	135	14	and	and	CCONJ
ap-1396	135	15	in	in	ADP
ap-1396	135	16	particular	particular	ADJ
ap-1396	135	17	the	the	DET
ap-1396	135	18	asymptotic	asymptotic	ADJ
ap-1396	135	19	behaviour	behaviour	NOUN
ap-1396	135	20	in	in	ADP
ap-1396	135	21	z	z	PROPN
ap-1396	135	22	of	of	ADP
ap-1396	135	23	a	a	DET
ap-1396	135	24	few	few	ADJ
ap-1396	135	25	terms	term	NOUN
ap-1396	135	26	of	of	ADP
ap-1396	135	27	the	the	DET
ap-1396	135	28	series	series	NOUN
ap-1396	135	29	does	do	AUX
ap-1396	135	30	not	not	PART
ap-1396	135	31	necessarily	necessarily	ADV
ap-1396	135	32	give	give	VERB
ap-1396	135	33	the	the	DET
ap-1396	135	34	correct	correct	ADJ
ap-1396	135	35	asymptotic	asymptotic	ADJ
ap-1396	135	36	behaviour	behaviour	NOUN
ap-1396	135	37	of	of	ADP
ap-1396	135	38	the	the	DET
ap-1396	135	39	entire	entire	ADJ
ap-1396	135	40	sum	sum	NOUN
ap-1396	135	41	.	.	PUNCT
ap-1396	136	1	nonetheless	nonetheless	ADV
ap-1396	136	2	this	this	DET
ap-1396	136	3	series	series	NOUN
ap-1396	136	4	does	do	AUX
ap-1396	136	5	appear	appear	VERB
ap-1396	136	6	to	to	PART
ap-1396	136	7	give	give	VERB
ap-1396	136	8	reliable	reliable	ADJ
ap-1396	136	9	results	result	NOUN
ap-1396	136	10	.	.	PUNCT
ap-1396	137	1	for	for	ADP
ap-1396	137	2	the	the	DET
ap-1396	137	3	parameters	parameter	NOUN
ap-1396	137	4	used	use	VERB
ap-1396	137	5	by	by	ADP
ap-1396	137	6	longhi	longhi	PROPN
ap-1396	137	7	in	in	ADP
ap-1396	137	8	ref	ref	NOUN
ap-1396	137	9	.	.	PUNCT
ap-1396	138	1	[	[	X
ap-1396	138	2	12	12	NUM
ap-1396	138	3	]	]	PUNCT
ap-1396	138	4	,	,	PUNCT
ap-1396	138	5	with	with	ADP
ap-1396	138	6	v0	v0	NOUN
ap-1396	138	7	=	=	SYM
ap-1396	138	8	0.2	0.2	NUM
ap-1396	138	9	,	,	PUNCT
ap-1396	138	10	first	first	ADJ
ap-1396	138	11	-	-	PUNCT
ap-1396	138	12	order	order	NOUN
ap-1396	138	13	perturbation	perturbation	NOUN
ap-1396	138	14	theory	theory	NOUN
ap-1396	138	15	already	already	ADV
ap-1396	138	16	reproduces	reproduce	VERB
ap-1396	138	17	the	the	DET
ap-1396	138	18	numerical	numerical	ADJ
ap-1396	138	19	results	result	NOUN
ap-1396	138	20	very	very	ADV
ap-1396	138	21	well	well	ADV
ap-1396	138	22	,	,	PUNCT
ap-1396	138	23	and	and	CCONJ
ap-1396	138	24	the	the	DET
ap-1396	138	25	second	second	ADJ
ap-1396	138	26	-	-	PUNCT
ap-1396	138	27	order	order	NOUN
ap-1396	138	28	term	term	NOUN
ap-1396	138	29	gives	give	VERB
ap-1396	138	30	only	only	ADV
ap-1396	138	31	an	an	DET
ap-1396	138	32	extremely	extremely	ADV
ap-1396	138	33	small	small	ADJ
ap-1396	138	34	correction	correction	NOUN
ap-1396	138	35	.	.	PUNCT
ap-1396	139	1	2	2	NUM
ap-1396	139	2	in	in	ADP
ap-1396	139	3	fact	fact	NOUN
ap-1396	139	4	ψ2(x	ψ2(x	PROPN
ap-1396	139	5	,	,	PUNCT
ap-1396	139	6	z	z	NOUN
ap-1396	139	7	)	)	PUNCT
ap-1396	139	8	is	be	AUX
ap-1396	139	9	proportional	proportional	ADJ
ap-1396	139	10	to	to	ADP
ap-1396	139	11	z2	z2	PROPN
ap-1396	139	12	for	for	ADP
ap-1396	139	13	small	small	ADJ
ap-1396	139	14	z.	z.	PROPN
ap-1396	139	15	24	24	NUM
ap-1396	139	16	acta	acta	PROPN
ap-1396	139	17	polytechnica	polytechnica	PROPN
ap-1396	139	18	vol	vol	NOUN
ap-1396	139	19	.	.	PUNCT
ap-1396	140	1	51	51	NUM
ap-1396	140	2	no	no	INTJ
ap-1396	140	3	.	.	PUNCT
ap-1396	141	1	4/2011	4/2011	NUM
ap-1396	141	2	in	in	ADP
ap-1396	141	3	all	all	PRON
ap-1396	141	4	of	of	ADP
ap-1396	141	5	our	our	PRON
ap-1396	141	6	calculations	calculation	NOUN
ap-1396	141	7	we	we	PRON
ap-1396	141	8	have	have	AUX
ap-1396	141	9	not	not	PART
ap-1396	141	10	allowed	allow	VERB
ap-1396	141	11	z	z	NOUN
ap-1396	141	12	to	to	PART
ap-1396	141	13	become	become	VERB
ap-1396	141	14	too	too	ADV
ap-1396	141	15	large	large	ADJ
ap-1396	141	16	,	,	PUNCT
ap-1396	141	17	restricting	restrict	VERB
ap-1396	141	18	it	it	PRON
ap-1396	141	19	by	by	ADP
ap-1396	141	20	the	the	DET
ap-1396	141	21	condition	condition	NOUN
ap-1396	141	22	z	z	PROPN
ap-1396	141	23	�	�	PROPN
ap-1396	141	24	w2/4	w2/4	PROPN
ap-1396	141	25	,	,	PUNCT
ap-1396	141	26	in	in	ADP
ap-1396	141	27	which	which	DET
ap-1396	141	28	case	case	NOUN
ap-1396	141	29	saturation	saturation	NOUN
ap-1396	141	30	is	be	AUX
ap-1396	141	31	an	an	DET
ap-1396	141	32	inbuilt	inbuilt	ADJ
ap-1396	141	33	feature	feature	NOUN
ap-1396	141	34	of	of	ADP
ap-1396	141	35	perturbation	perturbation	NOUN
ap-1396	141	36	theory	theory	NOUN
ap-1396	141	37	.	.	PUNCT
ap-1396	142	1	in	in	ADP
ap-1396	142	2	fact	fact	NOUN
ap-1396	142	3	it	it	PRON
ap-1396	142	4	was	be	AUX
ap-1396	142	5	shown	show	VERB
ap-1396	142	6	in	in	ADP
ap-1396	142	7	ref	ref	NOUN
ap-1396	142	8	.	.	PUNCT
ap-1396	143	1	[	[	X
ap-1396	143	2	17	17	NUM
ap-1396	143	3	]	]	PUNCT
ap-1396	143	4	using	use	VERB
ap-1396	143	5	the	the	DET
ap-1396	143	6	method	method	NOUN
ap-1396	143	7	of	of	ADP
ap-1396	143	8	stationary	stationary	ADJ
ap-1396	143	9	states	state	NOUN
ap-1396	143	10	that	that	SCONJ
ap-1396	143	11	if	if	SCONJ
ap-1396	143	12	one	one	PRON
ap-1396	143	13	goes	go	VERB
ap-1396	143	14	to	to	ADP
ap-1396	143	15	much	much	ADV
ap-1396	143	16	larger	large	ADJ
ap-1396	143	17	values	value	NOUN
ap-1396	143	18	of	of	ADP
ap-1396	143	19	z	z	NOUN
ap-1396	143	20	the	the	DET
ap-1396	143	21	amplitude	amplitude	NOUN
ap-1396	143	22	so	so	ADV
ap-1396	143	23	calculated	calculate	VERB
ap-1396	143	24	begins	begin	VERB
ap-1396	143	25	to	to	PART
ap-1396	143	26	grow	grow	VERB
ap-1396	143	27	again	again	ADV
ap-1396	143	28	but	but	CCONJ
ap-1396	143	29	this	this	DET
ap-1396	143	30	ultimate	ultimate	ADJ
ap-1396	143	31	resumption	resumption	NOUN
ap-1396	143	32	of	of	ADP
ap-1396	143	33	linear	linear	ADJ
ap-1396	143	34	growth	growth	NOUN
ap-1396	143	35	is	be	AUX
ap-1396	143	36	not	not	PART
ap-1396	143	37	physical	physical	ADJ
ap-1396	143	38	,	,	PUNCT
ap-1396	143	39	because	because	SCONJ
ap-1396	143	40	it	it	PRON
ap-1396	143	41	corresponds	correspond	VERB
ap-1396	143	42	to	to	ADP
ap-1396	143	43	the	the	DET
ap-1396	143	44	situation	situation	NOUN
ap-1396	143	45	where	where	SCONJ
ap-1396	143	46	the	the	DET
ap-1396	143	47	beam	beam	NOUN
ap-1396	143	48	has	have	AUX
ap-1396	143	49	widened	widen	VERB
ap-1396	143	50	beyond	beyond	ADP
ap-1396	143	51	lateral	lateral	ADJ
ap-1396	143	52	limits	limit	NOUN
ap-1396	143	53	of	of	ADP
ap-1396	143	54	the	the	DET
ap-1396	143	55	optical	optical	ADJ
ap-1396	143	56	lattice	lattice	NOUN
ap-1396	143	57	.	.	PUNCT
ap-1396	144	1	it	it	PRON
ap-1396	144	2	is	be	AUX
ap-1396	144	3	an	an	DET
ap-1396	144	4	elegant	elegant	ADJ
ap-1396	144	5	feature	feature	NOUN
ap-1396	144	6	of	of	ADP
ap-1396	144	7	the	the	DET
ap-1396	144	8	perturbative	perturbative	ADJ
ap-1396	144	9	expansion	expansion	NOUN
ap-1396	144	10	that	that	PRON
ap-1396	144	11	the	the	DET
ap-1396	144	12	different	different	ADJ
ap-1396	144	13	types	type	NOUN
ap-1396	144	14	of	of	ADP
ap-1396	144	15	possible	possible	ADJ
ap-1396	144	16	behaviour	behaviour	NOUN
ap-1396	144	17	of	of	ADP
ap-1396	144	18	the	the	DET
ap-1396	144	19	beam	beam	NOUN
ap-1396	144	20	—	—	PUNCT
ap-1396	144	21	spreading	spread	VERB
ap-1396	144	22	or	or	CCONJ
ap-1396	144	23	splitting	splitting	NOUN
ap-1396	144	24	into	into	ADP
ap-1396	144	25	two	two	NUM
ap-1396	144	26	or	or	CCONJ
ap-1396	144	27	more	more	ADJ
ap-1396	144	28	beams	beam	NOUN
ap-1396	144	29	—	—	PUNCT
ap-1396	144	30	arise	arise	VERB
ap-1396	144	31	from	from	ADP
ap-1396	144	32	very	very	ADV
ap-1396	144	33	simple	simple	ADJ
ap-1396	144	34	properties	property	NOUN
ap-1396	144	35	of	of	ADP
ap-1396	144	36	the	the	DET
ap-1396	144	37	error	error	NOUN
ap-1396	144	38	function	function	NOUN
ap-1396	144	39	depending	depend	VERB
ap-1396	144	40	crucially	crucially	ADV
ap-1396	144	41	on	on	ADP
ap-1396	144	42	the	the	DET
ap-1396	144	43	offset	offset	ADJ
ap-1396	144	44	k0	k0	PROPN
ap-1396	144	45	.	.	PUNCT
ap-1396	145	1	in	in	ADP
ap-1396	145	2	the	the	DET
ap-1396	145	3	first	first	ADJ
ap-1396	145	4	case	case	NOUN
ap-1396	145	5	the	the	DET
ap-1396	145	6	arguments	argument	NOUN
ap-1396	145	7	are	be	AUX
ap-1396	145	8	essentially	essentially	ADV
ap-1396	145	9	real	real	ADJ
ap-1396	145	10	,	,	PUNCT
ap-1396	145	11	and	and	CCONJ
ap-1396	145	12	the	the	DET
ap-1396	145	13	error	error	NOUN
ap-1396	145	14	functions	function	NOUN
ap-1396	145	15	behave	behave	VERB
ap-1396	145	16	like	like	ADP
ap-1396	145	17	sign	sign	NOUN
ap-1396	145	18	functions	function	NOUN
ap-1396	145	19	,	,	PUNCT
ap-1396	145	20	while	while	SCONJ
ap-1396	145	21	in	in	ADP
ap-1396	145	22	the	the	DET
ap-1396	145	23	second	second	ADJ
ap-1396	145	24	case	case	NOUN
ap-1396	145	25	there	there	PRON
ap-1396	145	26	is	be	VERB
ap-1396	145	27	a	a	DET
ap-1396	145	28	large	large	ADJ
ap-1396	145	29	imaginary	imaginary	ADJ
ap-1396	145	30	part	part	NOUN
ap-1396	145	31	,	,	PUNCT
ap-1396	145	32	and	and	CCONJ
ap-1396	145	33	the	the	DET
ap-1396	145	34	moduli	modulus	NOUN
ap-1396	145	35	of	of	ADP
ap-1396	145	36	the	the	DET
ap-1396	145	37	error	error	NOUN
ap-1396	145	38	functions	function	NOUN
ap-1396	145	39	behave	behave	VERB
ap-1396	145	40	instead	instead	ADV
ap-1396	145	41	like	like	ADP
ap-1396	145	42	narrow	narrow	ADJ
ap-1396	145	43	peaks	peak	NOUN
ap-1396	145	44	.	.	PUNCT
ap-1396	146	1	references	reference	NOUN
ap-1396	146	2	[	[	X
ap-1396	146	3	1	1	NUM
ap-1396	146	4	]	]	X
ap-1396	146	5	bender	bender	NOUN
ap-1396	146	6	,	,	PUNCT
ap-1396	146	7	c.	c.	PROPN
ap-1396	146	8	m.	m.	PROPN
ap-1396	146	9	,	,	PUNCT
ap-1396	146	10	boettcher	boettcher	PROPN
ap-1396	146	11	,	,	PUNCT
ap-1396	146	12	s.	s.	PROPN
ap-1396	146	13	:	:	PUNCT
ap-1396	146	14	phys	phy	NOUN
ap-1396	146	15	.	.	PUNCT
ap-1396	147	1	rev	rev	PROPN
ap-1396	147	2	.	.	PROPN
ap-1396	147	3	lett	lett	PROPN
ap-1396	147	4	.	.	PROPN
ap-1396	147	5	80	80	NUM
ap-1396	147	6	,	,	PUNCT
ap-1396	147	7	5243	5243	NUM
ap-1396	147	8	(	(	PUNCT
ap-1396	147	9	1998	1998	NUM
ap-1396	147	10	)	)	PUNCT
ap-1396	147	11	.	.	PUNCT
ap-1396	148	1	[	[	X
ap-1396	148	2	2	2	NUM
ap-1396	148	3	]	]	X
ap-1396	148	4	bender	bender	NOUN
ap-1396	148	5	,	,	PUNCT
ap-1396	148	6	c.	c.	PROPN
ap-1396	148	7	m.	m.	NOUN
ap-1396	148	8	:	:	PUNCT
ap-1396	148	9	contemp	contemp	NOUN
ap-1396	148	10	.	.	PUNCT
ap-1396	149	1	phys	phy	NOUN
ap-1396	149	2	.	.	PUNCT
ap-1396	150	1	46	46	NUM
ap-1396	150	2	,	,	PUNCT
ap-1396	150	3	277	277	NUM
ap-1396	150	4	(	(	PUNCT
ap-1396	150	5	2005	2005	NUM
ap-1396	150	6	)	)	PUNCT
ap-1396	150	7	;	;	PUNCT
ap-1396	150	8	rep	rep	PROPN
ap-1396	150	9	.	.	PROPN
ap-1396	150	10	prog	prog	PROPN
ap-1396	150	11	.	.	PUNCT
ap-1396	151	1	phys	phy	NOUN
ap-1396	151	2	.	.	PUNCT
ap-1396	152	1	70	70	NUM
ap-1396	152	2	,	,	PUNCT
ap-1396	152	3	947	947	NUM
ap-1396	152	4	(	(	PUNCT
ap-1396	152	5	2007	2007	NUM
ap-1396	152	6	)	)	PUNCT
ap-1396	152	7	.	.	PUNCT
ap-1396	153	1	[	[	X
ap-1396	153	2	3	3	NUM
ap-1396	153	3	]	]	X
ap-1396	153	4	mostafazadeh	mostafazadeh	NOUN
ap-1396	153	5	,	,	PUNCT
ap-1396	153	6	a.	a.	NOUN
ap-1396	153	7	:	:	PUNCT
ap-1396	153	8	arxiv:0810.5643	arxiv:0810.5643	NOUN
ap-1396	153	9	.	.	PUNCT
ap-1396	154	1	[	[	X
ap-1396	154	2	4	4	NUM
ap-1396	154	3	]	]	X
ap-1396	154	4	bender	bender	NOUN
ap-1396	154	5	,	,	PUNCT
ap-1396	154	6	c.	c.	PROPN
ap-1396	154	7	m.	m.	PROPN
ap-1396	154	8	,	,	PUNCT
ap-1396	154	9	brody	brody	PROPN
ap-1396	154	10	,	,	PUNCT
ap-1396	154	11	d.	d.	PROPN
ap-1396	154	12	c.	c.	PROPN
ap-1396	154	13	,	,	PUNCT
ap-1396	154	14	jones	jones	PROPN
ap-1396	154	15	,	,	PUNCT
ap-1396	154	16	h.	h.	PROPN
ap-1396	154	17	f.	f.	PROPN
ap-1396	154	18	:	:	PUNCT
ap-1396	154	19	phys	phy	NOUN
ap-1396	154	20	.	.	PUNCT
ap-1396	155	1	rev	rev	PROPN
ap-1396	155	2	.	.	PROPN
ap-1396	155	3	lett	lett	PROPN
ap-1396	155	4	.	.	PROPN
ap-1396	155	5	89	89	NUM
ap-1396	155	6	,	,	PUNCT
ap-1396	155	7	270401	270401	NUM
ap-1396	155	8	(	(	PUNCT
ap-1396	155	9	2002	2002	NUM
ap-1396	155	10	)	)	PUNCT
ap-1396	155	11	;	;	PUNCT
ap-1396	155	12	92	92	NUM
ap-1396	155	13	,	,	PUNCT
ap-1396	155	14	119902(e	119902(e	NUM
ap-1396	155	15	)	)	PUNCT
ap-1396	155	16	(	(	PUNCT
ap-1396	155	17	2004	2004	NUM
ap-1396	155	18	)	)	PUNCT
ap-1396	155	19	.	.	PUNCT
ap-1396	156	1	[	[	X
ap-1396	156	2	5	5	NUM
ap-1396	156	3	]	]	X
ap-1396	156	4	bender	bender	NOUN
ap-1396	156	5	,	,	PUNCT
ap-1396	156	6	c.	c.	PROPN
ap-1396	156	7	m.	m.	PROPN
ap-1396	156	8	,	,	PUNCT
ap-1396	156	9	brody	brody	PROPN
ap-1396	156	10	,	,	PUNCT
ap-1396	156	11	d.	d.	PROPN
ap-1396	156	12	c.	c.	PROPN
ap-1396	156	13	,	,	PUNCT
ap-1396	156	14	jones	jones	PROPN
ap-1396	156	15	,	,	PUNCT
ap-1396	156	16	h.	h.	PROPN
ap-1396	156	17	f.	f.	PROPN
ap-1396	156	18	:	:	PUNCT
ap-1396	156	19	phys	phy	NOUN
ap-1396	156	20	.	.	PUNCT
ap-1396	157	1	rev	rev	PROPN
ap-1396	157	2	.	.	PUNCT
ap-1396	158	1	d	d	PROPN
ap-1396	158	2	70	70	NUM
ap-1396	158	3	,	,	PUNCT
ap-1396	158	4	025001	025001	NUM
ap-1396	158	5	(	(	PUNCT
ap-1396	158	6	2004	2004	NUM
ap-1396	158	7	)	)	PUNCT
ap-1396	158	8	;	;	PUNCT
ap-1396	158	9	71	71	NUM
ap-1396	158	10	,	,	PUNCT
ap-1396	158	11	049901(e	049901(e	PUNCT
ap-1396	158	12	)	)	PUNCT
ap-1396	158	13	(	(	PUNCT
ap-1396	158	14	2005	2005	NUM
ap-1396	158	15	)	)	PUNCT
ap-1396	158	16	.	.	PUNCT
ap-1396	159	1	[	[	X
ap-1396	159	2	6	6	NUM
ap-1396	159	3	]	]	X
ap-1396	159	4	mostafazadeh	mostafazadeh	NOUN
ap-1396	159	5	,	,	PUNCT
ap-1396	159	6	a.	a.	NOUN
ap-1396	159	7	:	:	PUNCT
ap-1396	159	8	j.	j.	PROPN
ap-1396	159	9	math	math	PROPN
ap-1396	159	10	.	.	PUNCT
ap-1396	160	1	phys	phy	NOUN
ap-1396	160	2	.	.	PUNCT
ap-1396	161	1	43	43	NUM
ap-1396	161	2	,	,	PUNCT
ap-1396	161	3	205	205	NUM
ap-1396	161	4	(	(	PUNCT
ap-1396	161	5	2002	2002	NUM
ap-1396	161	6	)	)	PUNCT
ap-1396	161	7	;	;	PUNCT
ap-1396	161	8	j.	j.	PROPN
ap-1396	161	9	phys	phys	PROPN
ap-1396	161	10	.	.	PUNCT
ap-1396	162	1	a	a	DET
ap-1396	162	2	36	36	NUM
ap-1396	162	3	,	,	PUNCT
ap-1396	162	4	7081	7081	NUM
ap-1396	162	5	(	(	PUNCT
ap-1396	162	6	2003	2003	NUM
ap-1396	162	7	)	)	PUNCT
ap-1396	162	8	.	.	PUNCT
ap-1396	163	1	[	[	X
ap-1396	163	2	7	7	X
ap-1396	163	3	]	]	X
ap-1396	163	4	el	el	PROPN
ap-1396	163	5	-	-	PUNCT
ap-1396	163	6	ganainy	ganainy	PROPN
ap-1396	163	7	,	,	PUNCT
ap-1396	163	8	r.	r.	PROPN
ap-1396	163	9	et	et	PROPN
ap-1396	163	10	al	al	PROPN
ap-1396	163	11	.	.	PROPN
ap-1396	163	12	:	:	PUNCT
ap-1396	164	1	optics	optic	NOUN
ap-1396	164	2	letters	letter	NOUN
ap-1396	164	3	32	32	NUM
ap-1396	164	4	,	,	PUNCT
ap-1396	164	5	2632	2632	NUM
ap-1396	164	6	(	(	PUNCT
ap-1396	164	7	2007	2007	NUM
ap-1396	164	8	)	)	PUNCT
ap-1396	164	9	.	.	PUNCT
ap-1396	165	1	[	[	X
ap-1396	165	2	8	8	NUM
ap-1396	165	3	]	]	X
ap-1396	165	4	musslimani	musslimani	NOUN
ap-1396	165	5	,	,	PUNCT
ap-1396	165	6	z.	z.	PROPN
ap-1396	165	7	et	et	PROPN
ap-1396	165	8	al	al	PROPN
ap-1396	165	9	.	.	PROPN
ap-1396	165	10	:	:	PUNCT
ap-1396	166	1	phy	phy	AUX
ap-1396	166	2	.	.	PUNCT
ap-1396	166	3	rev	rev	PROPN
ap-1396	166	4	.	.	PROPN
ap-1396	166	5	lett	lett	PROPN
ap-1396	166	6	.	.	PROPN
ap-1396	167	1	100	100	NUM
ap-1396	167	2	,	,	PUNCT
ap-1396	167	3	030402	030402	NUM
ap-1396	167	4	(	(	PUNCT
ap-1396	167	5	2008	2008	NUM
ap-1396	167	6	)	)	PUNCT
ap-1396	167	7	.	.	PUNCT
ap-1396	168	1	[	[	X
ap-1396	168	2	9	9	NUM
ap-1396	168	3	]	]	SYM
ap-1396	168	4	makris	makris	X
ap-1396	168	5	,	,	PUNCT
ap-1396	168	6	k.	k.	PROPN
ap-1396	168	7	et	et	PROPN
ap-1396	168	8	al	al	PROPN
ap-1396	168	9	.	.	PROPN
ap-1396	168	10	:	:	PUNCT
ap-1396	168	11	phy	phy	AUX
ap-1396	168	12	.	.	PUNCT
ap-1396	168	13	rev	rev	PROPN
ap-1396	168	14	.	.	PROPN
ap-1396	168	15	lett	lett	PROPN
ap-1396	168	16	.	.	PROPN
ap-1396	169	1	100	100	NUM
ap-1396	169	2	,	,	PUNCT
ap-1396	169	3	103904	103904	NUM
ap-1396	169	4	(	(	PUNCT
ap-1396	169	5	2008	2008	NUM
ap-1396	169	6	)	)	PUNCT
ap-1396	169	7	.	.	PUNCT
ap-1396	170	1	[	[	X
ap-1396	170	2	10	10	NUM
ap-1396	170	3	]	]	X
ap-1396	170	4	klaiman	klaiman	NOUN
ap-1396	170	5	,	,	PUNCT
ap-1396	170	6	s.	s.	PROPN
ap-1396	170	7	,	,	PUNCT
ap-1396	170	8	günther	günther	PROPN
ap-1396	170	9	,	,	PUNCT
ap-1396	170	10	u.	u.	PROPN
ap-1396	170	11	,	,	PUNCT
ap-1396	170	12	moiseyev	moiseyev	PROPN
ap-1396	170	13	,	,	PUNCT
ap-1396	170	14	n.	n.	NOUN
ap-1396	170	15	:	:	PUNCT
ap-1396	170	16	phys	phy	NOUN
ap-1396	170	17	.	.	PUNCT
ap-1396	170	18	rev	rev	PROPN
ap-1396	170	19	.	.	PROPN
ap-1396	170	20	lett	lett	PROPN
ap-1396	170	21	.	.	PUNCT
ap-1396	171	1	101	101	NUM
ap-1396	171	2	080402	080402	NUM
ap-1396	171	3	(	(	PUNCT
ap-1396	171	4	2008	2008	NUM
ap-1396	171	5	)	)	PUNCT
ap-1396	171	6	.	.	PUNCT
ap-1396	172	1	[	[	X
ap-1396	172	2	11	11	NUM
ap-1396	172	3	]	]	X
ap-1396	172	4	guo	guo	PROPN
ap-1396	172	5	,	,	PUNCT
ap-1396	172	6	a.	a.	PROPN
ap-1396	172	7	et	et	PROPN
ap-1396	172	8	al	al	PROPN
ap-1396	172	9	.	.	PROPN
ap-1396	172	10	:	:	PUNCT
ap-1396	172	11	phy	phy	AUX
ap-1396	172	12	.	.	PUNCT
ap-1396	172	13	rev	rev	PROPN
ap-1396	172	14	.	.	PROPN
ap-1396	172	15	lett	lett	PROPN
ap-1396	172	16	.	.	PROPN
ap-1396	173	1	103	103	NUM
ap-1396	173	2	,	,	PUNCT
ap-1396	173	3	093902	093902	NUM
ap-1396	173	4	(	(	PUNCT
ap-1396	173	5	2009	2009	NUM
ap-1396	173	6	)	)	PUNCT
ap-1396	173	7	.	.	PUNCT
ap-1396	174	1	[	[	X
ap-1396	174	2	12	12	NUM
ap-1396	174	3	]	]	PUNCT
ap-1396	174	4	longhi	longhi	PROPN
ap-1396	174	5	,	,	PUNCT
ap-1396	174	6	s.	s.	PROPN
ap-1396	174	7	:	:	PUNCT
ap-1396	174	8	phys	phy	NOUN
ap-1396	174	9	.	.	PUNCT
ap-1396	174	10	rev	rev	PROPN
ap-1396	174	11	.	.	PUNCT
ap-1396	175	1	a	a	DET
ap-1396	175	2	81	81	NUM
ap-1396	175	3	,	,	PUNCT
ap-1396	175	4	022102	022102	NUM
ap-1396	175	5	(	(	PUNCT
ap-1396	175	6	2010	2010	NUM
ap-1396	175	7	)	)	PUNCT
ap-1396	175	8	.	.	PUNCT
ap-1396	176	1	[	[	X
ap-1396	176	2	13	13	NUM
ap-1396	176	3	]	]	SYM
ap-1396	176	4	makris	makris	X
ap-1396	176	5	,	,	PUNCT
ap-1396	176	6	k.	k.	PROPN
ap-1396	176	7	et	et	PROPN
ap-1396	176	8	al	al	PROPN
ap-1396	176	9	.	.	PROPN
ap-1396	176	10	:	:	PUNCT
ap-1396	176	11	phy	phy	PROPN
ap-1396	176	12	.	.	PUNCT
ap-1396	177	1	rev	rev	PROPN
ap-1396	177	2	.	.	PUNCT
ap-1396	178	1	a	a	DET
ap-1396	178	2	81	81	NUM
ap-1396	178	3	,	,	PUNCT
ap-1396	178	4	063807	063807	NUM
ap-1396	178	5	(	(	PUNCT
ap-1396	178	6	2010	2010	NUM
ap-1396	178	7	)	)	PUNCT
ap-1396	178	8	.	.	PUNCT
ap-1396	179	1	[	[	X
ap-1396	179	2	14	14	NUM
ap-1396	179	3	]	]	X
ap-1396	179	4	rüter	rüter	PROPN
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