id	sid	tid	token	lemma	pos
ap-2083	1	1	acta	acta	PROPN
ap-2083	1	2	polytechnica	polytechnica	PROPN
ap-2083	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2083	1	4	/	/	SYM
ap-2083	1	5	ap.2014.54.0116	ap.2014.54.0116	PROPN
ap-2083	1	6	acta	acta	PROPN
ap-2083	1	7	polytechnica	polytechnica	PROPN
ap-2083	1	8	54(2):116–121	54(2):116–121	NUM
ap-2083	1	9	,	,	PUNCT
ap-2083	1	10	2014	2014	NUM
ap-2083	1	11	©	©	PROPN
ap-2083	1	12	czech	czech	PROPN
ap-2083	1	13	technical	technical	PROPN
ap-2083	1	14	university	university	PROPN
ap-2083	1	15	in	in	ADP
ap-2083	1	16	prague	prague	PROPN
ap-2083	1	17	,	,	PUNCT
ap-2083	1	18	2014	2014	NUM
ap-2083	1	19	available	available	ADJ
ap-2083	1	20	online	online	ADV
ap-2083	1	21	at	at	ADP
ap-2083	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2083	1	23	a	a	DET
ap-2083	1	24	bose	bose	NOUN
ap-2083	1	25	-	-	PUNCT
ap-2083	1	26	einstein	einstein	NOUN
ap-2083	1	27	condensate	condensate	NOUN
ap-2083	1	28	with	with	ADP
ap-2083	1	29	pt	pt	ADJ
ap-2083	1	30	-	-	ADJ
ap-2083	1	31	symmetric	symmetric	ADJ
ap-2083	1	32	double	double	ADJ
ap-2083	1	33	-	-	PUNCT
ap-2083	1	34	delta	delta	NOUN
ap-2083	1	35	function	function	NOUN
ap-2083	1	36	loss	loss	NOUN
ap-2083	1	37	and	and	CCONJ
ap-2083	1	38	gain	gain	NOUN
ap-2083	1	39	in	in	ADP
ap-2083	1	40	a	a	DET
ap-2083	1	41	harmonic	harmonic	ADJ
ap-2083	1	42	trap	trap	NOUN
ap-2083	1	43	:	:	PUNCT
ap-2083	1	44	a	a	DET
ap-2083	1	45	test	test	NOUN
ap-2083	1	46	of	of	ADP
ap-2083	1	47	rigorous	rigorous	ADJ
ap-2083	1	48	estimates	estimate	NOUN
ap-2083	1	49	daniel	daniel	PROPN
ap-2083	1	50	haag	haag	PROPN
ap-2083	1	51	,	,	PUNCT
ap-2083	1	52	holger	holger	PROPN
ap-2083	1	53	cartarius	cartarius	NOUN
ap-2083	2	1	,	,	PUNCT
ap-2083	2	2	günter	günter	PROPN
ap-2083	2	3	wunner∗	wunner∗	VERB
ap-2083	2	4	institut	institut	PROPN
ap-2083	2	5	für	für	PROPN
ap-2083	2	6	theoretische	theoretische	PROPN
ap-2083	2	7	physik	physik	PROPN
ap-2083	2	8	1	1	NUM
ap-2083	2	9	,	,	PUNCT
ap-2083	2	10	universität	universität	PROPN
ap-2083	2	11	stuttgart	stuttgart	PROPN
ap-2083	2	12	,	,	PUNCT
ap-2083	2	13	70550	70550	NUM
ap-2083	2	14	stuttgart	stuttgart	PROPN
ap-2083	2	15	,	,	PUNCT
ap-2083	2	16	germany	germany	PROPN
ap-2083	2	17	∗	∗	NOUN
ap-2083	2	18	corresponding	correspond	VERB
ap-2083	2	19	author	author	NOUN
ap-2083	2	20	:	:	PUNCT
ap-2083	2	21	wunner@itp1.uni-stuttgart.de	wunner@itp1.uni-stuttgart.de	ADJ
ap-2083	2	22	abstract	abstract	NOUN
ap-2083	2	23	.	.	PUNCT
ap-2083	3	1	we	we	PRON
ap-2083	3	2	consider	consider	VERB
ap-2083	3	3	the	the	DET
ap-2083	3	4	linear	linear	ADJ
ap-2083	3	5	and	and	CCONJ
ap-2083	3	6	nonlinear	nonlinear	ADJ
ap-2083	3	7	schrödinger	schrödinger	ADJ
ap-2083	3	8	equation	equation	NOUN
ap-2083	3	9	for	for	ADP
ap-2083	3	10	a	a	DET
ap-2083	3	11	bose	bose	NOUN
ap-2083	3	12	-	-	PUNCT
ap-2083	3	13	einstein	einstein	NOUN
ap-2083	3	14	condensate	condensate	NOUN
ap-2083	3	15	in	in	ADP
ap-2083	3	16	a	a	DET
ap-2083	3	17	harmonic	harmonic	ADJ
ap-2083	3	18	trap	trap	NOUN
ap-2083	3	19	with	with	ADP
ap-2083	3	20	pt	pt	X
ap-2083	3	21	-symmetric	-symmetric	ADJ
ap-2083	3	22	double	double	ADJ
ap-2083	3	23	-	-	PUNCT
ap-2083	3	24	delta	delta	NOUN
ap-2083	3	25	function	function	NOUN
ap-2083	3	26	loss	loss	NOUN
ap-2083	3	27	and	and	CCONJ
ap-2083	3	28	gain	gain	VERB
ap-2083	3	29	terms	term	NOUN
ap-2083	3	30	.	.	PUNCT
ap-2083	4	1	we	we	PRON
ap-2083	4	2	verify	verify	VERB
ap-2083	4	3	that	that	SCONJ
ap-2083	4	4	the	the	DET
ap-2083	4	5	conditions	condition	NOUN
ap-2083	4	6	for	for	ADP
ap-2083	4	7	the	the	DET
ap-2083	4	8	applicability	applicability	NOUN
ap-2083	4	9	of	of	ADP
ap-2083	4	10	a	a	DET
ap-2083	4	11	recent	recent	ADJ
ap-2083	4	12	proposition	proposition	NOUN
ap-2083	4	13	by	by	ADP
ap-2083	4	14	mityagin	mityagin	NOUN
ap-2083	4	15	and	and	CCONJ
ap-2083	4	16	siegl	siegl	VERB
ap-2083	4	17	on	on	ADP
ap-2083	4	18	singular	singular	ADJ
ap-2083	4	19	perturbations	perturbation	NOUN
ap-2083	4	20	of	of	ADP
ap-2083	4	21	harmonic	harmonic	ADJ
ap-2083	4	22	oscillator	oscillator	NOUN
ap-2083	4	23	type	type	NOUN
ap-2083	4	24	self	self	NOUN
ap-2083	4	25	-	-	PUNCT
ap-2083	4	26	adjoint	adjoint	NOUN
ap-2083	4	27	operators	operator	NOUN
ap-2083	4	28	are	be	AUX
ap-2083	4	29	fulfilled	fulfil	VERB
ap-2083	4	30	.	.	PUNCT
ap-2083	5	1	in	in	ADP
ap-2083	5	2	both	both	CCONJ
ap-2083	5	3	the	the	DET
ap-2083	5	4	linear	linear	ADJ
ap-2083	5	5	and	and	CCONJ
ap-2083	5	6	nonlinear	nonlinear	ADJ
ap-2083	5	7	case	case	NOUN
ap-2083	5	8	we	we	PRON
ap-2083	5	9	calculate	calculate	VERB
ap-2083	5	10	numerically	numerically	ADV
ap-2083	5	11	the	the	DET
ap-2083	5	12	shifts	shift	NOUN
ap-2083	5	13	of	of	ADP
ap-2083	5	14	the	the	DET
ap-2083	5	15	unperturbed	unperturbed	ADJ
ap-2083	5	16	levels	level	NOUN
ap-2083	5	17	with	with	ADP
ap-2083	5	18	quantum	quantum	ADJ
ap-2083	5	19	numbers	number	NOUN
ap-2083	5	20	n	n	CCONJ
ap-2083	5	21	of	of	ADP
ap-2083	5	22	up	up	ADP
ap-2083	5	23	to	to	PART
ap-2083	5	24	89	89	NUM
ap-2083	5	25	in	in	ADP
ap-2083	5	26	dependence	dependence	NOUN
ap-2083	5	27	on	on	ADP
ap-2083	5	28	the	the	DET
ap-2083	5	29	strength	strength	NOUN
ap-2083	5	30	of	of	ADP
ap-2083	5	31	the	the	DET
ap-2083	5	32	non	non	ADJ
ap-2083	5	33	-	-	NOUN
ap-2083	5	34	hermiticity	hermiticity	NOUN
ap-2083	5	35	and	and	CCONJ
ap-2083	5	36	compare	compare	VERB
ap-2083	5	37	with	with	ADP
ap-2083	5	38	rigorous	rigorous	ADJ
ap-2083	5	39	estimates	estimate	NOUN
ap-2083	5	40	derived	derive	VERB
ap-2083	5	41	by	by	ADP
ap-2083	5	42	those	those	DET
ap-2083	5	43	authors	author	NOUN
ap-2083	5	44	.	.	PUNCT
ap-2083	6	1	we	we	PRON
ap-2083	6	2	confirm	confirm	VERB
ap-2083	6	3	that	that	SCONJ
ap-2083	6	4	the	the	DET
ap-2083	6	5	predicted	predict	VERB
ap-2083	6	6	1	1	NUM
ap-2083	6	7	/	/	SYM
ap-2083	6	8	n1/2	n1/2	NUM
ap-2083	6	9	estimate	estimate	NOUN
ap-2083	6	10	provides	provide	VERB
ap-2083	6	11	a	a	DET
ap-2083	6	12	valid	valid	ADJ
ap-2083	6	13	upper	upper	ADJ
ap-2083	6	14	bound	bind	VERB
ap-2083	6	15	on	on	ADP
ap-2083	6	16	the	the	DET
ap-2083	6	17	shrink	shrink	NOUN
ap-2083	6	18	rate	rate	NOUN
ap-2083	6	19	of	of	ADP
ap-2083	6	20	the	the	DET
ap-2083	6	21	numerical	numerical	ADJ
ap-2083	6	22	eigenvalues	eigenvalue	NOUN
ap-2083	6	23	.	.	PUNCT
ap-2083	7	1	moreover	moreover	ADV
ap-2083	7	2	,	,	PUNCT
ap-2083	7	3	we	we	PRON
ap-2083	7	4	find	find	VERB
ap-2083	7	5	that	that	SCONJ
ap-2083	7	6	a	a	DET
ap-2083	7	7	more	more	ADV
ap-2083	7	8	recent	recent	ADJ
ap-2083	7	9	estimate	estimate	NOUN
ap-2083	7	10	of	of	ADP
ap-2083	7	11	log(n)/n3/2	log(n)/n3/2	PROPN
ap-2083	7	12	is	be	AUX
ap-2083	7	13	in	in	ADP
ap-2083	7	14	excellent	excellent	ADJ
ap-2083	7	15	agreement	agreement	NOUN
ap-2083	7	16	with	with	ADP
ap-2083	7	17	the	the	DET
ap-2083	7	18	numerical	numerical	ADJ
ap-2083	7	19	results	result	NOUN
ap-2083	7	20	.	.	PUNCT
ap-2083	8	1	with	with	ADP
ap-2083	8	2	nonlinearity	nonlinearity	NOUN
ap-2083	8	3	the	the	DET
ap-2083	8	4	shrink	shrink	NOUN
ap-2083	8	5	rates	rate	NOUN
ap-2083	8	6	are	be	AUX
ap-2083	8	7	found	find	VERB
ap-2083	8	8	to	to	PART
ap-2083	8	9	be	be	AUX
ap-2083	8	10	smaller	small	ADJ
ap-2083	8	11	than	than	ADP
ap-2083	8	12	without	without	ADP
ap-2083	8	13	nonlinearity	nonlinearity	NOUN
ap-2083	8	14	,	,	PUNCT
ap-2083	8	15	and	and	CCONJ
ap-2083	8	16	the	the	DET
ap-2083	8	17	rigorous	rigorous	ADJ
ap-2083	8	18	estimates	estimate	NOUN
ap-2083	8	19	,	,	PUNCT
ap-2083	8	20	derived	derive	VERB
ap-2083	8	21	only	only	ADV
ap-2083	8	22	for	for	ADP
ap-2083	8	23	the	the	DET
ap-2083	8	24	linear	linear	ADJ
ap-2083	8	25	case	case	NOUN
ap-2083	8	26	,	,	PUNCT
ap-2083	8	27	are	be	AUX
ap-2083	8	28	no	no	ADV
ap-2083	8	29	longer	long	ADV
ap-2083	8	30	applicable	applicable	ADJ
ap-2083	8	31	.	.	PUNCT
ap-2083	9	1	keywords	keyword	NOUN
ap-2083	9	2	:	:	PUNCT
ap-2083	9	3	pt	pt	PROPN
ap-2083	9	4	symmetry	symmetry	NOUN
ap-2083	9	5	,	,	PUNCT
ap-2083	9	6	bose	bose	NOUN
ap-2083	9	7	-	-	PUNCT
ap-2083	9	8	einstein	einstein	NOUN
ap-2083	9	9	condensates	condensate	NOUN
ap-2083	9	10	,	,	PUNCT
ap-2083	9	11	perturbed	perturb	VERB
ap-2083	9	12	harmonic	harmonic	ADJ
ap-2083	9	13	oscillator	oscillator	NOUN
ap-2083	9	14	.	.	PUNCT
ap-2083	10	1	1	1	NUM
ap-2083	10	2	.	.	X
ap-2083	10	3	introduction	introduction	NOUN
ap-2083	10	4	bose	bose	NOUN
ap-2083	10	5	-	-	PUNCT
ap-2083	10	6	einstein	einstein	NOUN
ap-2083	10	7	condensates	condensate	NOUN
ap-2083	10	8	with	with	ADP
ap-2083	10	9	pt	pt	NOUN
ap-2083	10	10	-symmetric	-symmetric	ADJ
ap-2083	10	11	loss	loss	NOUN
ap-2083	10	12	and	and	CCONJ
ap-2083	10	13	gain	gain	NOUN
ap-2083	10	14	have	have	AUX
ap-2083	10	15	been	be	AUX
ap-2083	10	16	proposed	propose	VERB
ap-2083	10	17	[	[	X
ap-2083	10	18	1	1	NUM
ap-2083	10	19	]	]	PUNCT
ap-2083	10	20	as	as	ADP
ap-2083	10	21	a	a	DET
ap-2083	10	22	first	first	ADJ
ap-2083	10	23	experimental	experimental	ADJ
ap-2083	10	24	realisation	realisation	NOUN
ap-2083	10	25	of	of	ADP
ap-2083	10	26	pt	pt	NOUN
ap-2083	10	27	symmetry	symmetry	NOUN
ap-2083	10	28	in	in	ADP
ap-2083	10	29	a	a	DET
ap-2083	10	30	real	real	ADJ
ap-2083	10	31	quantum	quantum	ADJ
ap-2083	10	32	system	system	NOUN
ap-2083	10	33	.	.	PUNCT
ap-2083	11	1	the	the	DET
ap-2083	11	2	idea	idea	NOUN
ap-2083	11	3	is	be	AUX
ap-2083	11	4	to	to	PART
ap-2083	11	5	confine	confine	VERB
ap-2083	11	6	the	the	DET
ap-2083	11	7	condensate	condensate	NOUN
ap-2083	11	8	in	in	ADP
ap-2083	11	9	a	a	DET
ap-2083	11	10	double	double	ADJ
ap-2083	11	11	well	well	NOUN
ap-2083	11	12	potential	potential	NOUN
ap-2083	11	13	,	,	PUNCT
ap-2083	11	14	and	and	CCONJ
ap-2083	11	15	to	to	PART
ap-2083	11	16	create	create	VERB
ap-2083	11	17	a	a	DET
ap-2083	11	18	pt	pt	NOUN
ap-2083	11	19	-symmetric	-symmetric	ADJ
ap-2083	11	20	situation	situation	NOUN
ap-2083	11	21	by	by	ADP
ap-2083	11	22	coherently	coherently	ADV
ap-2083	11	23	injecting	inject	VERB
ap-2083	11	24	atoms	atom	NOUN
ap-2083	11	25	into	into	ADP
ap-2083	11	26	one	one	NUM
ap-2083	11	27	well	well	ADV
ap-2083	11	28	and	and	CCONJ
ap-2083	11	29	removing	remove	VERB
ap-2083	11	30	them	they	PRON
ap-2083	11	31	from	from	ADP
ap-2083	11	32	the	the	DET
ap-2083	11	33	other	other	ADJ
ap-2083	11	34	.	.	PUNCT
ap-2083	12	1	a	a	DET
ap-2083	12	2	particular	particular	ADJ
ap-2083	12	3	difficulty	difficulty	NOUN
ap-2083	12	4	in	in	ADP
ap-2083	12	5	the	the	DET
ap-2083	12	6	theoretical	theoretical	ADJ
ap-2083	12	7	treatment	treatment	NOUN
ap-2083	12	8	is	be	AUX
ap-2083	12	9	that	that	SCONJ
ap-2083	12	10	,	,	PUNCT
ap-2083	12	11	on	on	ADP
ap-2083	12	12	account	account	NOUN
ap-2083	12	13	of	of	ADP
ap-2083	12	14	the	the	DET
ap-2083	12	15	swave	swave	NOUN
ap-2083	12	16	scattering	scattering	NOUN
ap-2083	12	17	of	of	ADP
ap-2083	12	18	the	the	DET
ap-2083	12	19	atoms	atom	NOUN
ap-2083	12	20	,	,	PUNCT
ap-2083	12	21	the	the	DET
ap-2083	12	22	gross	gross	ADJ
ap-2083	12	23	-	-	PUNCT
ap-2083	12	24	pitaevskii	pitaevskii	ADJ
ap-2083	12	25	equation	equation	NOUN
ap-2083	12	26	,	,	PUNCT
ap-2083	12	27	which	which	PRON
ap-2083	12	28	describes	describe	VERB
ap-2083	12	29	the	the	DET
ap-2083	12	30	condensates	condensate	NOUN
ap-2083	12	31	,	,	PUNCT
ap-2083	12	32	contains	contain	VERB
ap-2083	12	33	a	a	DET
ap-2083	12	34	term	term	NOUN
ap-2083	12	35	g|ψ|2	g|ψ|2	NOUN
ap-2083	12	36	,	,	PUNCT
ap-2083	12	37	and	and	CCONJ
ap-2083	12	38	is	be	AUX
ap-2083	12	39	-shell	-shell	NOUN
ap-2083	12	40	-	-	PUNCT
ap-2083	12	41	escapebthus	escapebthus	NOUN
ap-2083	12	42	nonlinear	nonlinear	NOUN
ap-2083	12	43	in	in	ADP
ap-2083	12	44	the	the	DET
ap-2083	12	45	wanted	want	VERB
ap-2083	12	46	wave	wave	NOUN
ap-2083	12	47	function	function	NOUN
ap-2083	12	48	.	.	PUNCT
ap-2083	13	1	in	in	ADP
ap-2083	13	2	a	a	DET
ap-2083	13	3	series	series	NOUN
ap-2083	13	4	of	of	ADP
ap-2083	13	5	papers	paper	NOUN
ap-2083	13	6	both	both	CCONJ
ap-2083	13	7	for	for	ADP
ap-2083	13	8	realistic	realistic	ADJ
ap-2083	13	9	set	set	NOUN
ap-2083	13	10	-	-	PUNCT
ap-2083	13	11	ups	up	NOUN
ap-2083	13	12	as	as	ADV
ap-2083	13	13	well	well	ADV
ap-2083	13	14	as	as	ADP
ap-2083	13	15	for	for	ADP
ap-2083	13	16	delta	delta	NOUN
ap-2083	13	17	-	-	PUNCT
ap-2083	13	18	function	function	NOUN
ap-2083	13	19	models	model	NOUN
ap-2083	13	20	of	of	ADP
ap-2083	13	21	the	the	DET
ap-2083	13	22	double	double	ADJ
ap-2083	13	23	wells	well	NOUN
ap-2083	13	24	we	we	PRON
ap-2083	13	25	have	have	AUX
ap-2083	13	26	shown	show	VERB
ap-2083	13	27	[	[	X
ap-2083	13	28	2–7	2–7	X
ap-2083	13	29	]	]	X
ap-2083	13	30	that	that	SCONJ
ap-2083	13	31	the	the	DET
ap-2083	13	32	nonlinearity	nonlinearity	NOUN
ap-2083	13	33	introduces	introduce	VERB
ap-2083	13	34	new	new	ADJ
ap-2083	13	35	features	feature	NOUN
ap-2083	13	36	in	in	ADP
ap-2083	13	37	the	the	DET
ap-2083	13	38	evolution	evolution	NOUN
ap-2083	13	39	of	of	ADP
ap-2083	13	40	the	the	DET
ap-2083	13	41	eigenvalue	eigenvalue	NOUN
ap-2083	13	42	spectrum	spectrum	NOUN
ap-2083	13	43	as	as	SCONJ
ap-2083	13	44	the	the	DET
ap-2083	13	45	non	non	NOUN
ap-2083	13	46	-	-	NOUN
ap-2083	13	47	hermiticity	hermiticity	NOUN
ap-2083	13	48	is	be	AUX
ap-2083	13	49	increased	increase	VERB
ap-2083	13	50	but	but	CCONJ
ap-2083	13	51	yet	yet	ADV
ap-2083	13	52	pt	pt	PROPN
ap-2083	13	53	symmetry	symmetry	NOUN
ap-2083	13	54	of	of	ADP
ap-2083	13	55	the	the	DET
ap-2083	13	56	wave	wave	NOUN
ap-2083	13	57	function	function	NOUN
ap-2083	13	58	is	be	AUX
ap-2083	13	59	preserved	preserve	VERB
ap-2083	13	60	if	if	SCONJ
ap-2083	13	61	both	both	CCONJ
ap-2083	13	62	nonlinearity	nonlinearity	NOUN
ap-2083	13	63	and	and	CCONJ
ap-2083	13	64	non	non	ADJ
ap-2083	13	65	-	-	ADJ
ap-2083	13	66	hermiticity	hermiticity	NOUN
ap-2083	13	67	are	be	AUX
ap-2083	13	68	not	not	PART
ap-2083	13	69	too	too	ADV
ap-2083	13	70	strong	strong	ADJ
ap-2083	13	71	.	.	PUNCT
ap-2083	14	1	bose	bose	NOUN
ap-2083	14	2	-	-	PUNCT
ap-2083	14	3	einstein	einstein	NOUN
ap-2083	14	4	condensates	condensate	NOUN
ap-2083	14	5	are	be	AUX
ap-2083	14	6	usually	usually	ADV
ap-2083	14	7	trapped	trap	VERB
ap-2083	14	8	in	in	ADP
ap-2083	14	9	harmonic	harmonic	ADJ
ap-2083	14	10	potentials	potential	NOUN
ap-2083	14	11	produced	produce	VERB
ap-2083	14	12	by	by	ADP
ap-2083	14	13	counterpropagating	counterpropagate	VERB
ap-2083	14	14	laser	laser	NOUN
ap-2083	14	15	beams	beam	NOUN
ap-2083	14	16	.	.	PUNCT
ap-2083	15	1	therefore	therefore	ADV
ap-2083	15	2	condensates	condensate	NOUN
ap-2083	15	3	with	with	ADP
ap-2083	15	4	an	an	DET
ap-2083	15	5	additional	additional	ADJ
ap-2083	15	6	pt	pt	NOUN
ap-2083	15	7	-symmetric	-symmetric	ADJ
ap-2083	15	8	double	double	ADJ
ap-2083	15	9	well	well	NOUN
ap-2083	15	10	potential	potential	NOUN
ap-2083	15	11	can	can	AUX
ap-2083	15	12	be	be	AUX
ap-2083	15	13	regarded	regard	VERB
ap-2083	15	14	as	as	ADP
ap-2083	15	15	a	a	DET
ap-2083	15	16	“	"	PUNCT
ap-2083	15	17	perturbation	perturbation	NOUN
ap-2083	15	18	”	"	PUNCT
ap-2083	15	19	of	of	ADP
ap-2083	15	20	the	the	DET
ap-2083	15	21	harmonic	harmonic	ADJ
ap-2083	15	22	oscillator	oscillator	NOUN
ap-2083	15	23	.	.	PUNCT
ap-2083	16	1	aducci	aducci	PROPN
ap-2083	16	2	and	and	CCONJ
ap-2083	16	3	mityagin	mityagin	VERB
ap-2083	16	4	[	[	X
ap-2083	16	5	8	8	NUM
ap-2083	16	6	]	]	PUNCT
ap-2083	16	7	and	and	CCONJ
ap-2083	16	8	siegl	siegl	VERB
ap-2083	16	9	and	and	CCONJ
ap-2083	16	10	mityagin	mityagin	VERB
ap-2083	16	11	[	[	X
ap-2083	16	12	9	9	NUM
ap-2083	16	13	]	]	PUNCT
ap-2083	16	14	have	have	AUX
ap-2083	16	15	recently	recently	ADV
ap-2083	16	16	analysed	analyse	VERB
ap-2083	16	17	perturbations	perturbation	NOUN
ap-2083	16	18	of	of	ADP
ap-2083	16	19	harmoniclike	harmoniclike	PROPN
ap-2083	16	20	operators	operator	NOUN
ap-2083	16	21	from	from	ADP
ap-2083	16	22	a	a	DET
ap-2083	16	23	mathematical	mathematical	ADJ
ap-2083	16	24	point	point	NOUN
ap-2083	16	25	of	of	ADP
ap-2083	16	26	view	view	NOUN
ap-2083	16	27	.	.	PUNCT
ap-2083	17	1	the	the	DET
ap-2083	17	2	second	second	ADJ
ap-2083	17	3	paper	paper	NOUN
ap-2083	17	4	in	in	ADP
ap-2083	17	5	particular	particular	ADJ
ap-2083	17	6	also	also	ADV
ap-2083	17	7	allows	allow	VERB
ap-2083	17	8	for	for	ADP
ap-2083	17	9	singular	singular	ADJ
ap-2083	17	10	perturbations	perturbation	NOUN
ap-2083	17	11	,	,	PUNCT
ap-2083	17	12	such	such	ADJ
ap-2083	17	13	as	as	ADP
ap-2083	17	14	delta	delta	NOUN
ap-2083	17	15	-	-	PUNCT
ap-2083	17	16	functions	function	NOUN
ap-2083	17	17	.	.	PUNCT
ap-2083	18	1	these	these	DET
ap-2083	18	2	authors	author	NOUN
ap-2083	18	3	have	have	AUX
ap-2083	18	4	proved	prove	VERB
ap-2083	18	5	that	that	SCONJ
ap-2083	18	6	the	the	DET
ap-2083	18	7	eigenvalues	eigenvalue	NOUN
ap-2083	18	8	of	of	ADP
ap-2083	18	9	the	the	DET
ap-2083	18	10	perturbed	perturb	VERB
ap-2083	18	11	operator	operator	NOUN
ap-2083	18	12	eventually	eventually	ADV
ap-2083	18	13	become	become	VERB
ap-2083	18	14	simple	simple	ADJ
ap-2083	18	15	and	and	CCONJ
ap-2083	18	16	the	the	DET
ap-2083	18	17	root	root	NOUN
ap-2083	18	18	system	system	NOUN
ap-2083	18	19	forms	form	VERB
ap-2083	18	20	a	a	DET
ap-2083	18	21	riesz	riesz	NOUN
ap-2083	18	22	basis	basis	NOUN
ap-2083	18	23	.	.	PUNCT
ap-2083	19	1	their	their	PRON
ap-2083	19	2	results	result	NOUN
ap-2083	19	3	are	be	AUX
ap-2083	19	4	valid	valid	ADJ
ap-2083	19	5	if	if	SCONJ
ap-2083	19	6	the	the	DET
ap-2083	19	7	following	follow	VERB
ap-2083	19	8	criterion	criterion	NOUN
ap-2083	19	9	is	be	AUX
ap-2083	19	10	fulfilled	fulfil	VERB
ap-2083	19	11	:	:	PUNCT
ap-2083	19	12	∀m	∀m	NUM
ap-2083	19	13	,	,	PUNCT
ap-2083	19	14	n	n	SYM
ap-2083	19	15	∈	∈	PROPN
ap-2083	19	16	n	n	CCONJ
ap-2083	19	17	∣∣〈ψm|b̂|ψn〉∣∣	∣∣〈ψm|b̂|ψn〉∣∣	PROPN
ap-2083	19	18	≤	≤	PROPN
ap-2083	19	19	m	m	VERB
ap-2083	19	20	mαnα	mαnα	NOUN
ap-2083	19	21	,	,	PUNCT
ap-2083	19	22	α	α	PROPN
ap-2083	19	23	>	>	X
ap-2083	19	24	0	0	PROPN
ap-2083	19	25	,	,	PUNCT
ap-2083	19	26	m	m	VERB
ap-2083	19	27	>	>	X
ap-2083	19	28	0	0	NUM
ap-2083	19	29	,	,	PUNCT
ap-2083	19	30	(	(	PUNCT
ap-2083	19	31	1	1	X
ap-2083	19	32	)	)	PUNCT
ap-2083	19	33	where	where	SCONJ
ap-2083	19	34	b̂	b̂	NOUN
ap-2083	19	35	is	be	AUX
ap-2083	19	36	the	the	DET
ap-2083	19	37	perturbation	perturbation	NOUN
ap-2083	19	38	operator	operator	NOUN
ap-2083	19	39	,	,	PUNCT
ap-2083	19	40	m	m	VERB
ap-2083	19	41	is	be	AUX
ap-2083	19	42	a	a	DET
ap-2083	19	43	constant	constant	ADJ
ap-2083	19	44	that	that	PRON
ap-2083	19	45	depends	depend	VERB
ap-2083	19	46	on	on	ADP
ap-2083	19	47	the	the	DET
ap-2083	19	48	type	type	NOUN
ap-2083	19	49	of	of	ADP
ap-2083	19	50	the	the	DET
ap-2083	19	51	perturbation	perturbation	NOUN
ap-2083	19	52	,	,	PUNCT
ap-2083	19	53	and	and	CCONJ
ap-2083	19	54	the	the	DET
ap-2083	19	55	ψm	ψm	PROPN
ap-2083	19	56	are	be	AUX
ap-2083	19	57	the	the	DET
ap-2083	19	58	harmonic	harmonic	ADJ
ap-2083	19	59	oscillator	oscillator	NOUN
ap-2083	19	60	eigenfunctions	eigenfunction	NOUN
ap-2083	19	61	.	.	PUNCT
ap-2083	20	1	a	a	DET
ap-2083	20	2	further	further	ADJ
ap-2083	20	3	prediction	prediction	NOUN
ap-2083	20	4	is	be	AUX
ap-2083	20	5	that	that	SCONJ
ap-2083	20	6	the	the	DET
ap-2083	20	7	shrink	shrink	ADJ
ap-2083	20	8	rate	rate	NOUN
ap-2083	20	9	of	of	ADP
ap-2083	20	10	the	the	DET
ap-2083	20	11	disks	disk	NOUN
ap-2083	20	12	into	into	ADP
ap-2083	20	13	which	which	PRON
ap-2083	20	14	the	the	DET
ap-2083	20	15	eigenvalues	eigenvalue	NOUN
ap-2083	20	16	can	can	AUX
ap-2083	20	17	be	be	AUX
ap-2083	20	18	shifted	shift	VERB
ap-2083	20	19	is	be	AUX
ap-2083	20	20	proportional	proportional	ADJ
ap-2083	20	21	to	to	ADP
ap-2083	20	22	1	1	NUM
ap-2083	20	23	/	/	SYM
ap-2083	20	24	n2α	n2α	PROPN
ap-2083	20	25	,	,	PUNCT
ap-2083	20	26	with	with	ADP
ap-2083	20	27	α	α	PRON
ap-2083	20	28	the	the	DET
ap-2083	20	29	exponent	exponent	NOUN
ap-2083	20	30	appearing	appear	VERB
ap-2083	20	31	in	in	ADP
ap-2083	20	32	(	(	PUNCT
ap-2083	20	33	1	1	NUM
ap-2083	20	34	)	)	PUNCT
ap-2083	20	35	.	.	PUNCT
ap-2083	21	1	it	it	PRON
ap-2083	21	2	is	be	AUX
ap-2083	21	3	the	the	DET
ap-2083	21	4	purpose	purpose	NOUN
ap-2083	21	5	of	of	ADP
ap-2083	21	6	this	this	DET
ap-2083	21	7	paper	paper	NOUN
ap-2083	21	8	to	to	PART
ap-2083	21	9	test	test	VERB
ap-2083	21	10	the	the	DET
ap-2083	21	11	estimates	estimate	NOUN
ap-2083	21	12	numerically	numerically	ADV
ap-2083	21	13	for	for	ADP
ap-2083	21	14	the	the	DET
ap-2083	21	15	example	example	NOUN
ap-2083	21	16	of	of	ADP
ap-2083	21	17	a	a	DET
ap-2083	21	18	bose	bose	NOUN
ap-2083	21	19	-	-	PUNCT
ap-2083	21	20	einstein	einstein	NOUN
ap-2083	21	21	condensate	condensate	NOUN
ap-2083	21	22	in	in	ADP
ap-2083	21	23	a	a	DET
ap-2083	21	24	double	double	ADJ
ap-2083	21	25	well	well	ADV
ap-2083	21	26	potential	potential	NOUN
ap-2083	21	27	confined	confine	VERB
ap-2083	21	28	by	by	ADP
ap-2083	21	29	a	a	DET
ap-2083	21	30	harmonic	harmonic	ADJ
ap-2083	21	31	trap	trap	NOUN
ap-2083	21	32	.	.	PUNCT
ap-2083	22	1	to	to	ADP
ap-2083	22	2	this	this	DET
ap-2083	22	3	end	end	NOUN
ap-2083	22	4	we	we	PRON
ap-2083	22	5	consider	consider	VERB
ap-2083	22	6	the	the	DET
ap-2083	22	7	model	model	NOUN
ap-2083	22	8	of	of	ADP
ap-2083	22	9	two	two	NUM
ap-2083	22	10	pt	pt	NOUN
ap-2083	22	11	-symmetric	-symmetric	ADJ
ap-2083	22	12	delta	delta	NOUN
ap-2083	22	13	-	-	PUNCT
ap-2083	22	14	function	function	NOUN
ap-2083	22	15	wells	well	NOUN
ap-2083	22	16	,	,	PUNCT
ap-2083	22	17	since	since	SCONJ
ap-2083	22	18	in	in	ADP
ap-2083	22	19	this	this	DET
ap-2083	22	20	case	case	NOUN
ap-2083	22	21	simple	simple	ADJ
ap-2083	22	22	analytical	analytical	ADJ
ap-2083	22	23	estimates	estimate	NOUN
ap-2083	22	24	can	can	AUX
ap-2083	22	25	be	be	AUX
ap-2083	22	26	obtained	obtain	VERB
ap-2083	22	27	,	,	PUNCT
ap-2083	22	28	whereas	whereas	SCONJ
ap-2083	22	29	in	in	ADP
ap-2083	22	30	the	the	DET
ap-2083	22	31	case	case	NOUN
ap-2083	22	32	of	of	ADP
ap-2083	22	33	the	the	DET
ap-2083	22	34	realistic	realistic	ADJ
ap-2083	22	35	double	double	ADJ
ap-2083	22	36	well	well	INTJ
ap-2083	22	37	discussed	discuss	VERB
ap-2083	22	38	in	in	ADP
ap-2083	22	39	refs	ref	NOUN
ap-2083	22	40	.	.	PUNCT
ap-2083	23	1	[	[	X
ap-2083	23	2	4	4	NUM
ap-2083	23	3	,	,	PUNCT
ap-2083	23	4	5	5	NUM
ap-2083	23	5	]	]	PUNCT
ap-2083	23	6	complicated	complicated	ADJ
ap-2083	23	7	estimates	estimate	NOUN
ap-2083	23	8	in	in	ADP
ap-2083	23	9	terms	term	NOUN
ap-2083	23	10	of	of	ADP
ap-2083	23	11	hypergeometric	hypergeometric	ADJ
ap-2083	23	12	functions	function	NOUN
ap-2083	23	13	result	result	VERB
ap-2083	23	14	.	.	PUNCT
ap-2083	24	1	it	it	PRON
ap-2083	24	2	should	should	AUX
ap-2083	24	3	be	be	AUX
ap-2083	24	4	mentioned	mention	VERB
ap-2083	24	5	that	that	PRON
ap-2083	24	6	of	of	ADP
ap-2083	24	7	course	course	NOUN
ap-2083	24	8	because	because	SCONJ
ap-2083	24	9	of	of	ADP
ap-2083	24	10	their	their	PRON
ap-2083	24	11	simplicity	simplicity	NOUN
ap-2083	24	12	delta	delta	NOUN
ap-2083	24	13	functions	function	NOUN
ap-2083	24	14	have	have	AUX
ap-2083	24	15	been	be	AUX
ap-2083	24	16	widely	widely	ADV
ap-2083	24	17	used	use	VERB
ap-2083	24	18	in	in	ADP
ap-2083	24	19	the	the	DET
ap-2083	24	20	literature	literature	NOUN
ap-2083	24	21	in	in	ADP
ap-2083	24	22	the	the	DET
ap-2083	24	23	context	context	NOUN
ap-2083	24	24	of	of	ADP
ap-2083	24	25	pt	pt	NOUN
ap-2083	24	26	symmetry	symmetry	NOUN
ap-2083	24	27	.	.	PUNCT
ap-2083	25	1	spectral	spectral	ADJ
ap-2083	25	2	properties	property	NOUN
ap-2083	25	3	of	of	ADP
ap-2083	25	4	scattering	scatter	VERB
ap-2083	25	5	and	and	CCONJ
ap-2083	25	6	bound	bound	ADJ
ap-2083	25	7	states	state	NOUN
ap-2083	25	8	in	in	ADP
ap-2083	25	9	pt	pt	PROPN
ap-2083	25	10	symmetric	symmetric	ADJ
ap-2083	25	11	doubleand	doubleand	NOUN
ap-2083	25	12	multiple	multiple	ADJ
ap-2083	25	13	-	-	PUNCT
ap-2083	25	14	delta	delta	NOUN
ap-2083	25	15	function	function	NOUN
ap-2083	25	16	potentials	potential	NOUN
ap-2083	25	17	have	have	AUX
ap-2083	25	18	been	be	AUX
ap-2083	25	19	investigated	investigate	VERB
ap-2083	25	20	e.g.	e.g.	ADV
ap-2083	25	21	in	in	ADP
ap-2083	25	22	refs	ref	NOUN
ap-2083	25	23	.	.	PUNCT
ap-2083	26	1	[	[	X
ap-2083	26	2	2	2	NUM
ap-2083	26	3	,	,	PUNCT
ap-2083	26	4	3	3	NUM
ap-2083	26	5	,	,	PUNCT
ap-2083	26	6	11–18	11–18	NUM
ap-2083	26	7	]	]	PUNCT
ap-2083	26	8	.	.	PUNCT
ap-2083	27	1	in	in	ADP
ap-2083	27	2	all	all	DET
ap-2083	27	3	these	these	DET
ap-2083	27	4	papers	paper	NOUN
ap-2083	27	5	no	no	DET
ap-2083	27	6	external	external	ADJ
ap-2083	27	7	potential	potential	NOUN
ap-2083	27	8	was	be	AUX
ap-2083	27	9	present	present	ADJ
ap-2083	27	10	,	,	PUNCT
ap-2083	27	11	in	in	ADP
ap-2083	27	12	addition	addition	NOUN
ap-2083	27	13	to	to	ADP
ap-2083	27	14	the	the	DET
ap-2083	27	15	delta	delta	NOUN
ap-2083	27	16	potentials	potential	VERB
ap-2083	27	17	.	.	PUNCT
ap-2083	28	1	a	a	DET
ap-2083	28	2	paper	paper	NOUN
ap-2083	28	3	in	in	ADP
ap-2083	28	4	which	which	PRON
ap-2083	28	5	pt	pt	X
ap-2083	28	6	-symmetric	-symmetric	ADJ
ap-2083	28	7	point	point	NOUN
ap-2083	28	8	interactions	interaction	NOUN
ap-2083	28	9	were	be	AUX
ap-2083	28	10	studied	study	VERB
ap-2083	28	11	embedded	embed	VERB
ap-2083	28	12	in	in	ADP
ap-2083	28	13	an	an	DET
ap-2083	28	14	external	external	ADJ
ap-2083	28	15	potential	potential	NOUN
ap-2083	28	16	is	be	AUX
ap-2083	28	17	116	116	NUM
ap-2083	28	18	http://dx.doi.org/10.14311/ap.2014.54.0116	http://dx.doi.org/10.14311/ap.2014.54.0116	NOUN
ap-2083	28	19	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	NOUN
ap-2083	28	20	vol	vol	NOUN
ap-2083	28	21	.	.	PUNCT
ap-2083	29	1	54	54	NUM
ap-2083	30	1	no	no	NOUN
ap-2083	30	2	.	.	PUNCT
ap-2083	31	1	2/2014	2/2014	NUM
ap-2083	31	2	bec	bec	PROPN
ap-2083	31	3	with	with	ADP
ap-2083	31	4	pt	pt	PROPN
ap-2083	31	5	-	-	ADJ
ap-2083	31	6	symmetric	symmetric	ADJ
ap-2083	31	7	double	double	ADJ
ap-2083	31	8	-	-	PUNCT
ap-2083	31	9	delta	delta	NOUN
ap-2083	31	10	loss	loss	NOUN
ap-2083	31	11	and	and	CCONJ
ap-2083	31	12	gain	gain	NOUN
ap-2083	31	13	:	:	PUNCT
ap-2083	31	14	test	test	NOUN
ap-2083	31	15	of	of	ADP
ap-2083	31	16	estimates	estimate	NOUN
ap-2083	31	17	that	that	SCONJ
ap-2083	31	18	by	by	ADP
ap-2083	31	19	jakubský	jakubský	PROPN
ap-2083	31	20	and	and	CCONJ
ap-2083	31	21	znojil	znojil	NOUN
ap-2083	31	22	[	[	X
ap-2083	31	23	19	19	NUM
ap-2083	31	24	]	]	X
ap-2083	31	25	,	,	PUNCT
ap-2083	31	26	who	who	PRON
ap-2083	31	27	positioned	position	VERB
ap-2083	31	28	the	the	DET
ap-2083	31	29	delta	delta	NOUN
ap-2083	31	30	functions	function	NOUN
ap-2083	31	31	in	in	ADP
ap-2083	31	32	an	an	DET
ap-2083	31	33	infinitely	infinitely	ADV
ap-2083	31	34	high	high	ADJ
ap-2083	31	35	square	square	ADJ
ap-2083	31	36	well	well	ADV
ap-2083	31	37	and	and	CCONJ
ap-2083	31	38	analysed	analyse	VERB
ap-2083	31	39	the	the	DET
ap-2083	31	40	spectrum	spectrum	NOUN
ap-2083	31	41	in	in	ADP
ap-2083	31	42	dependence	dependence	NOUN
ap-2083	31	43	on	on	ADP
ap-2083	31	44	the	the	DET
ap-2083	31	45	position	position	NOUN
ap-2083	31	46	of	of	ADP
ap-2083	31	47	the	the	DET
ap-2083	31	48	delta	delta	NOUN
ap-2083	31	49	functions	function	NOUN
ap-2083	31	50	within	within	ADP
ap-2083	31	51	the	the	DET
ap-2083	31	52	well	well	NOUN
ap-2083	31	53	.	.	PUNCT
ap-2083	32	1	their	their	PRON
ap-2083	32	2	work	work	NOUN
ap-2083	32	3	was	be	AUX
ap-2083	32	4	extended	extend	VERB
ap-2083	32	5	by	by	ADP
ap-2083	32	6	krejčiřík	krejčiřík	NOUN
ap-2083	32	7	and	and	CCONJ
ap-2083	32	8	siegl	siegl	VERB
ap-2083	33	1	[	[	X
ap-2083	33	2	20	20	NUM
ap-2083	33	3	,	,	PUNCT
ap-2083	33	4	21	21	NUM
ap-2083	33	5	]	]	PUNCT
ap-2083	33	6	who	who	PRON
ap-2083	33	7	replaced	replace	VERB
ap-2083	33	8	the	the	DET
ap-2083	33	9	delta	delta	NOUN
ap-2083	33	10	functions	function	NOUN
ap-2083	33	11	by	by	ADP
ap-2083	33	12	pt	pt	X
ap-2083	33	13	-symmetric	-symmetric	ADJ
ap-2083	33	14	robin	robin	PROPN
ap-2083	33	15	boundary	boundary	ADJ
ap-2083	33	16	conditions	condition	NOUN
ap-2083	33	17	at	at	ADP
ap-2083	33	18	the	the	DET
ap-2083	33	19	edges	edge	NOUN
ap-2083	33	20	of	of	ADP
ap-2083	33	21	the	the	DET
ap-2083	33	22	square	square	ADJ
ap-2083	33	23	well	well	ADV
ap-2083	33	24	.	.	PUNCT
ap-2083	34	1	we	we	PRON
ap-2083	34	2	note	note	VERB
ap-2083	34	3	that	that	SCONJ
ap-2083	34	4	the	the	DET
ap-2083	34	5	spectrum	spectrum	NOUN
ap-2083	34	6	of	of	ADP
ap-2083	34	7	a	a	DET
ap-2083	34	8	harmonic	harmonic	ADJ
ap-2083	34	9	oscillator	oscillator	NOUN
ap-2083	34	10	perturbed	perturb	VERB
ap-2083	34	11	by	by	ADP
ap-2083	34	12	two	two	NUM
ap-2083	34	13	identical	identical	ADJ
ap-2083	34	14	real	real	ADV
ap-2083	34	15	-	-	PUNCT
ap-2083	34	16	valued	value	VERB
ap-2083	34	17	point	point	NOUN
ap-2083	34	18	interactions	interaction	NOUN
ap-2083	34	19	has	have	AUX
ap-2083	34	20	been	be	AUX
ap-2083	34	21	analysed	analyse	VERB
ap-2083	34	22	by	by	ADP
ap-2083	34	23	fassari	fassari	PROPN
ap-2083	34	24	and	and	CCONJ
ap-2083	34	25	rinaldi	rinaldi	PROPN
ap-2083	34	26	[	[	X
ap-2083	34	27	22	22	NUM
ap-2083	34	28	]	]	PUNCT
ap-2083	34	29	.	.	PUNCT
ap-2083	35	1	however	however	ADV
ap-2083	35	2	,	,	PUNCT
ap-2083	35	3	to	to	ADP
ap-2083	35	4	our	our	PRON
ap-2083	35	5	knowledge	knowledge	NOUN
ap-2083	35	6	the	the	DET
ap-2083	35	7	situation	situation	NOUN
ap-2083	35	8	of	of	ADP
ap-2083	35	9	two	two	NUM
ap-2083	35	10	pt	pt	NOUN
ap-2083	35	11	-symmetric	-symmetric	ADJ
ap-2083	35	12	delta	delta	NOUN
ap-2083	35	13	functions	function	NOUN
ap-2083	35	14	in	in	ADP
ap-2083	35	15	an	an	DET
ap-2083	35	16	external	external	ADJ
ap-2083	35	17	harmonic	harmonic	ADJ
ap-2083	35	18	potential	potential	NOUN
ap-2083	35	19	has	have	AUX
ap-2083	35	20	not	not	PART
ap-2083	35	21	yet	yet	ADV
ap-2083	35	22	been	be	AUX
ap-2083	35	23	investigated	investigate	VERB
ap-2083	35	24	.	.	PUNCT
ap-2083	36	1	while	while	SCONJ
ap-2083	36	2	in	in	ADP
ap-2083	36	3	the	the	DET
ap-2083	36	4	square	square	ADJ
ap-2083	36	5	well	well	INTJ
ap-2083	36	6	the	the	DET
ap-2083	36	7	delta	delta	NOUN
ap-2083	36	8	functions	function	NOUN
ap-2083	36	9	can	can	AUX
ap-2083	36	10	be	be	AUX
ap-2083	36	11	placed	place	VERB
ap-2083	36	12	only	only	ADV
ap-2083	36	13	within	within	ADP
ap-2083	36	14	the	the	DET
ap-2083	36	15	well	well	NOUN
ap-2083	36	16	,	,	PUNCT
ap-2083	36	17	the	the	DET
ap-2083	36	18	harmonic	harmonic	ADJ
ap-2083	36	19	oscillator	oscillator	NOUN
ap-2083	36	20	potential	potential	NOUN
ap-2083	36	21	has	have	VERB
ap-2083	36	22	the	the	DET
ap-2083	36	23	advantage	advantage	NOUN
ap-2083	36	24	that	that	PRON
ap-2083	36	25	the	the	DET
ap-2083	36	26	delta	delta	NOUN
ap-2083	36	27	functions	function	NOUN
ap-2083	36	28	can	can	AUX
ap-2083	36	29	in	in	ADP
ap-2083	36	30	principle	principle	NOUN
ap-2083	36	31	be	be	AUX
ap-2083	36	32	shifted	shift	VERB
ap-2083	36	33	to	to	ADP
ap-2083	36	34	any	any	DET
ap-2083	36	35	position	position	NOUN
ap-2083	36	36	on	on	ADP
ap-2083	36	37	the	the	DET
ap-2083	36	38	real	real	ADJ
ap-2083	36	39	axis	axis	NOUN
ap-2083	36	40	.	.	PUNCT
ap-2083	37	1	2	2	X
ap-2083	37	2	.	.	X
ap-2083	37	3	bose	bose	NOUN
ap-2083	37	4	-	-	PUNCT
ap-2083	37	5	einstein	einstein	PROPN
ap-2083	37	6	condensate	condensate	NOUN
ap-2083	37	7	in	in	ADP
ap-2083	37	8	a	a	DET
ap-2083	37	9	pt	pt	NOUN
ap-2083	37	10	-symmetric	-symmetric	ADJ
ap-2083	37	11	harmonic	harmonic	ADJ
ap-2083	37	12	trap	trap	NOUN
ap-2083	37	13	at	at	ADP
ap-2083	37	14	low	low	ADJ
ap-2083	37	15	temperatures	temperature	NOUN
ap-2083	37	16	and	and	CCONJ
ap-2083	37	17	densities	density	NOUN
ap-2083	37	18	bose	bose	NOUN
ap-2083	37	19	-	-	PUNCT
ap-2083	37	20	einstein	einstein	NOUN
ap-2083	37	21	condensates	condensate	NOUN
ap-2083	37	22	are	be	AUX
ap-2083	37	23	well	well	ADV
ap-2083	37	24	described	describe	VERB
ap-2083	37	25	by	by	ADP
ap-2083	37	26	the	the	DET
ap-2083	37	27	gross	gross	ADJ
ap-2083	37	28	-	-	PUNCT
ap-2083	37	29	pitaevskii	pitaevskii	ADJ
ap-2083	37	30	equation	equation	NOUN
ap-2083	37	31	[	[	X
ap-2083	37	32	23	23	NUM
ap-2083	37	33	,	,	PUNCT
ap-2083	37	34	24	24	NUM
ap-2083	37	35	]	]	PUNCT
ap-2083	37	36	(	(	PUNCT
ap-2083	37	37	−	−	PROPN
ap-2083	37	38	d2	d2	PROPN
ap-2083	37	39	dx2	dx2	PROPN
ap-2083	37	40	+	+	CCONJ
ap-2083	37	41	v	v	PROPN
ap-2083	37	42	(	(	PUNCT
ap-2083	37	43	x	x	NOUN
ap-2083	37	44	)	)	PUNCT
ap-2083	37	45	+	+	CCONJ
ap-2083	38	1	g|ψ|2	g|ψ|2	NOUN
ap-2083	38	2	)	)	PUNCT
ap-2083	38	3	ψ	ψ	PROPN
ap-2083	39	1	=	=	SYM
ap-2083	39	2	µψ	µψ	PROPN
ap-2083	39	3	.	.	PUNCT
ap-2083	40	1	(	(	PUNCT
ap-2083	40	2	2	2	X
ap-2083	40	3	)	)	PUNCT
ap-2083	40	4	here	here	ADV
ap-2083	40	5	ψ	ψ	ADP
ap-2083	40	6	denotes	denote	NOUN
ap-2083	40	7	the	the	DET
ap-2083	40	8	condensate	condensate	NOUN
ap-2083	40	9	wave	wave	NOUN
ap-2083	40	10	function	function	NOUN
ap-2083	40	11	,	,	PUNCT
ap-2083	40	12	the	the	DET
ap-2083	40	13	eigenvalue	eigenvalue	PROPN
ap-2083	40	14	µ	µ	PROPN
ap-2083	40	15	is	be	AUX
ap-2083	40	16	the	the	DET
ap-2083	40	17	chemical	chemical	NOUN
ap-2083	40	18	potential	potential	NOUN
ap-2083	40	19	,	,	PUNCT
ap-2083	40	20	and	and	CCONJ
ap-2083	40	21	v	v	NOUN
ap-2083	40	22	(	(	PUNCT
ap-2083	40	23	x	x	X
ap-2083	40	24	)	)	PUNCT
ap-2083	40	25	is	be	AUX
ap-2083	40	26	the	the	DET
ap-2083	40	27	trapping	trap	VERB
ap-2083	40	28	potential	potential	NOUN
ap-2083	40	29	to	to	PART
ap-2083	40	30	confine	confine	VERB
ap-2083	40	31	the	the	DET
ap-2083	40	32	condensate	condensate	NOUN
ap-2083	40	33	.	.	PUNCT
ap-2083	41	1	the	the	DET
ap-2083	41	2	nonlinear	nonlinear	ADJ
ap-2083	41	3	term	term	NOUN
ap-2083	41	4	in	in	ADP
ap-2083	41	5	(	(	PUNCT
ap-2083	41	6	2	2	NUM
ap-2083	41	7	)	)	PUNCT
ap-2083	41	8	arises	arise	VERB
ap-2083	41	9	from	from	ADP
ap-2083	41	10	the	the	DET
ap-2083	41	11	s	s	NOUN
ap-2083	41	12	-	-	PUNCT
ap-2083	41	13	wave	wave	NOUN
ap-2083	41	14	scattering	scatter	VERB
ap-2083	41	15	interaction	interaction	NOUN
ap-2083	41	16	of	of	ADP
ap-2083	41	17	the	the	DET
ap-2083	41	18	atoms	atom	NOUN
ap-2083	41	19	;	;	PUNCT
ap-2083	41	20	g	g	PROPN
ap-2083	41	21	is	be	AUX
ap-2083	41	22	a	a	DET
ap-2083	41	23	measure	measure	NOUN
ap-2083	41	24	for	for	ADP
ap-2083	41	25	the	the	DET
ap-2083	41	26	strength	strength	NOUN
ap-2083	41	27	of	of	ADP
ap-2083	41	28	this	this	DET
ap-2083	41	29	interaction	interaction	NOUN
ap-2083	41	30	.	.	PUNCT
ap-2083	42	1	we	we	PRON
ap-2083	42	2	consider	consider	VERB
ap-2083	42	3	a	a	DET
ap-2083	42	4	harmonic	harmonic	ADJ
ap-2083	42	5	trapping	trap	VERB
ap-2083	42	6	potential	potential	NOUN
ap-2083	42	7	and	and	CCONJ
ap-2083	42	8	model	model	VERB
ap-2083	42	9	a	a	DET
ap-2083	42	10	pt	pt	NOUN
ap-2083	42	11	-symmetric	-symmetric	NOUN
ap-2083	42	12	double	double	ADJ
ap-2083	42	13	well	well	ADV
ap-2083	42	14	with	with	ADP
ap-2083	42	15	equilibrated	equilibrated	ADJ
ap-2083	42	16	loss	loss	NOUN
ap-2083	42	17	and	and	CCONJ
ap-2083	42	18	gain	gain	NOUN
ap-2083	42	19	by	by	ADP
ap-2083	42	20	imaginary	imaginary	ADJ
ap-2083	42	21	delta	delta	NOUN
ap-2083	42	22	functions	function	NOUN
ap-2083	42	23	.	.	PUNCT
ap-2083	43	1	thus	thus	ADV
ap-2083	43	2	the	the	DET
ap-2083	43	3	hamiltonian	hamiltonian	NOUN
ap-2083	43	4	that	that	PRON
ap-2083	43	5	we	we	PRON
ap-2083	43	6	consider	consider	VERB
ap-2083	43	7	here	here	ADV
ap-2083	43	8	is	be	AUX
ap-2083	43	9	given	give	VERB
ap-2083	43	10	by	by	ADP
ap-2083	43	11	ĥ	ĥ	NOUN
ap-2083	43	12	=	=	SYM
ap-2083	43	13	−	−	PROPN
ap-2083	43	14	d2	d2	PROPN
ap-2083	43	15	dx2	dx2	PROPN
ap-2083	44	1	+	+	PROPN
ap-2083	44	2	x2+iγ	x2+iγ	PROPN
ap-2083	44	3	(	(	PUNCT
ap-2083	44	4	δ(x−b)−δ(x+b	δ(x−b)−δ(x+b	PROPN
ap-2083	44	5	)	)	PUNCT
ap-2083	44	6	)	)	PUNCT
ap-2083	45	1	+	+	ADP
ap-2083	45	2	g	g	NOUN
ap-2083	45	3	∣∣ψ(x	∣∣ψ(x	NOUN
ap-2083	45	4	)	)	PUNCT
ap-2083	45	5	∣∣2	∣∣2	PROPN
ap-2083	45	6	.	.	PUNCT
ap-2083	46	1	(	(	PUNCT
ap-2083	46	2	3	3	X
ap-2083	46	3	)	)	PUNCT
ap-2083	46	4	here	here	ADV
ap-2083	46	5	±b	±b	PUNCT
ap-2083	46	6	denotes	denote	VERB
ap-2083	46	7	the	the	DET
ap-2083	46	8	position	position	NOUN
ap-2083	46	9	of	of	ADP
ap-2083	46	10	the	the	DET
ap-2083	46	11	imaginary	imaginary	ADJ
ap-2083	46	12	deltas	delta	NOUN
ap-2083	46	13	and	and	CCONJ
ap-2083	46	14	γ	γ	X
ap-2083	46	15	the	the	DET
ap-2083	46	16	strength	strength	NOUN
ap-2083	46	17	of	of	ADP
ap-2083	46	18	the	the	DET
ap-2083	46	19	non	non	NOUN
ap-2083	46	20	-	-	NOUN
ap-2083	46	21	hermiticity	hermiticity	NOUN
ap-2083	46	22	.	.	PUNCT
ap-2083	47	1	we	we	PRON
ap-2083	47	2	will	will	AUX
ap-2083	47	3	later	later	ADV
ap-2083	47	4	consider	consider	VERB
ap-2083	47	5	the	the	DET
ap-2083	47	6	effects	effect	NOUN
ap-2083	47	7	of	of	ADP
ap-2083	47	8	the	the	DET
ap-2083	47	9	nonlinearity	nonlinearity	NOUN
ap-2083	47	10	on	on	ADP
ap-2083	47	11	the	the	DET
ap-2083	47	12	spectrum	spectrum	NOUN
ap-2083	47	13	,	,	PUNCT
ap-2083	47	14	but	but	CCONJ
ap-2083	47	15	for	for	ADP
ap-2083	47	16	the	the	DET
ap-2083	47	17	time	time	NOUN
ap-2083	47	18	being	be	AUX
ap-2083	47	19	we	we	PRON
ap-2083	47	20	assume	assume	VERB
ap-2083	47	21	that	that	SCONJ
ap-2083	47	22	the	the	DET
ap-2083	47	23	nonlinearity	nonlinearity	NOUN
ap-2083	47	24	is	be	AUX
ap-2083	47	25	negligible	negligible	ADJ
ap-2083	47	26	in	in	ADP
ap-2083	47	27	order	order	NOUN
ap-2083	47	28	to	to	PART
ap-2083	47	29	be	be	AUX
ap-2083	47	30	in	in	ADP
ap-2083	47	31	a	a	DET
ap-2083	47	32	position	position	NOUN
ap-2083	47	33	to	to	PART
ap-2083	47	34	compare	compare	VERB
ap-2083	47	35	with	with	ADP
ap-2083	47	36	the	the	DET
ap-2083	47	37	predictions	prediction	NOUN
ap-2083	47	38	of	of	ADP
ap-2083	47	39	mityagin	mityagin	NOUN
ap-2083	47	40	and	and	CCONJ
ap-2083	47	41	siegl	siegl	VERB
ap-2083	48	1	[	[	X
ap-2083	48	2	9	9	NUM
ap-2083	48	3	]	]	PUNCT
ap-2083	48	4	.	.	PUNCT
ap-2083	49	1	the	the	DET
ap-2083	49	2	eigenvalues	eigenvalue	NOUN
ap-2083	49	3	of	of	ADP
ap-2083	49	4	the	the	DET
ap-2083	49	5	unperturbed	unperturbed	ADJ
ap-2083	49	6	spectrum	spectrum	NOUN
ap-2083	49	7	are	be	AUX
ap-2083	49	8	given	give	VERB
ap-2083	49	9	by	by	ADP
ap-2083	49	10	µn	µn	PROPN
ap-2083	49	11	=	=	SYM
ap-2083	49	12	2n+1	2n+1	PROPN
ap-2083	49	13	(	(	PUNCT
ap-2083	49	14	n	n	NOUN
ap-2083	49	15	=	=	SYM
ap-2083	49	16	0	0	NUM
ap-2083	49	17	,	,	PUNCT
ap-2083	49	18	1	1	NUM
ap-2083	49	19	,	,	PUNCT
ap-2083	49	20	2	2	NUM
ap-2083	49	21	,	,	PUNCT
ap-2083	49	22	.	.	PUNCT
ap-2083	49	23	.	.	PUNCT
ap-2083	49	24	.	.	PUNCT
ap-2083	49	25	)	)	PUNCT
ap-2083	49	26	.	.	PUNCT
ap-2083	50	1	figure	figure	NOUN
ap-2083	50	2	1	1	NUM
ap-2083	50	3	shows	show	VERB
ap-2083	50	4	the	the	DET
ap-2083	50	5	unperturbed	unperturbed	ADJ
ap-2083	50	6	spectrum	spectrum	NOUN
ap-2083	50	7	together	together	ADV
ap-2083	50	8	with	with	ADP
ap-2083	50	9	the	the	DET
ap-2083	50	10	wave	wave	NOUN
ap-2083	50	11	functions	function	NOUN
ap-2083	50	12	of	of	ADP
ap-2083	50	13	the	the	DET
ap-2083	50	14	lowest	low	ADJ
ap-2083	50	15	five	five	NUM
ap-2083	50	16	states	state	NOUN
ap-2083	50	17	.	.	PUNCT
ap-2083	51	1	the	the	DET
ap-2083	51	2	dashed	dash	VERB
ap-2083	51	3	vertical	vertical	ADJ
ap-2083	51	4	lines	line	NOUN
ap-2083	51	5	designate	designate	VERB
ap-2083	51	6	different	different	ADJ
ap-2083	51	7	positions	position	NOUN
ap-2083	51	8	at	at	ADP
ap-2083	51	9	which	which	PRON
ap-2083	51	10	the	the	DET
ap-2083	51	11	delta	delta	NOUN
ap-2083	51	12	functions	function	NOUN
ap-2083	51	13	are	be	AUX
ap-2083	51	14	placed	place	VERB
ap-2083	51	15	.	.	PUNCT
ap-2083	52	1	from	from	ADP
ap-2083	52	2	the	the	DET
ap-2083	52	3	figure	figure	NOUN
ap-2083	52	4	it	it	PRON
ap-2083	52	5	is	be	AUX
ap-2083	52	6	already	already	ADV
ap-2083	52	7	obvious	obvious	ADJ
ap-2083	52	8	that	that	SCONJ
ap-2083	52	9	only	only	ADV
ap-2083	52	10	such	such	ADJ
ap-2083	52	11	states	state	NOUN
ap-2083	52	12	will	will	AUX
ap-2083	52	13	be	be	AUX
ap-2083	52	14	significantly	significantly	ADV
ap-2083	52	15	affected	affect	VERB
ap-2083	52	16	by	by	ADP
ap-2083	52	17	the	the	DET
ap-2083	52	18	perturbation	perturbation	NOUN
ap-2083	52	19	which	which	PRON
ap-2083	52	20	are	be	AUX
ap-2083	52	21	within	within	ADP
ap-2083	52	22	the	the	DET
ap-2083	52	23	classically	classically	ADV
ap-2083	52	24	allowed	allow	VERB
ap-2083	52	25	region	region	NOUN
ap-2083	52	26	at	at	ADP
ap-2083	52	27	the	the	DET
ap-2083	52	28	positions	position	NOUN
ap-2083	52	29	of	of	ADP
ap-2083	52	30	the	the	DET
ap-2083	52	31	delta	delta	NOUN
ap-2083	52	32	functions	function	NOUN
ap-2083	52	33	.	.	PUNCT
ap-2083	53	1	by	by	ADP
ap-2083	53	2	contrast	contrast	NOUN
ap-2083	53	3	,	,	PUNCT
ap-2083	53	4	states	state	NOUN
ap-2083	53	5	for	for	ADP
ap-2083	53	6	which	which	PRON
ap-2083	53	7	the	the	DET
ap-2083	53	8	delta	delta	NOUN
ap-2083	53	9	functions	function	NOUN
ap-2083	53	10	lie	lie	VERB
ap-2083	53	11	in	in	ADP
ap-2083	53	12	the	the	DET
ap-2083	53	13	classically	classically	ADV
ap-2083	53	14	forbidden	forbidden	ADJ
ap-2083	53	15	(	(	PUNCT
ap-2083	53	16	exponentially	exponentially	ADV
ap-2083	53	17	decaying	decay	VERB
ap-2083	53	18	)	)	PUNCT
ap-2083	53	19	regime	regime	NOUN
ap-2083	53	20	will	will	AUX
ap-2083	53	21	not	not	PART
ap-2083	53	22	be	be	AUX
ap-2083	53	23	affected	affect	VERB
ap-2083	53	24	.	.	PUNCT
ap-2083	54	1	this	this	PRON
ap-2083	54	2	means	mean	VERB
ap-2083	54	3	that	that	SCONJ
ap-2083	54	4	0	0	NUM
ap-2083	54	5	2	2	NUM
ap-2083	54	6	4	4	NUM
ap-2083	54	7	6	6	NUM
ap-2083	54	8	8	8	NUM
ap-2083	54	9	10	10	NUM
ap-2083	54	10	−3	−3	ADJ
ap-2083	54	11	−2	−2	NOUN
ap-2083	54	12	−1	−1	NOUN
ap-2083	54	13	0	0	NUM
ap-2083	54	14	1	1	NUM
ap-2083	54	15	2	2	NUM
ap-2083	54	16	3	3	NUM
ap-2083	54	17	-0.5	-0.5	X
ap-2083	54	18	0	0	NUM
ap-2083	54	19	0.5	0.5	NUM
ap-2083	54	20	-0.5	-0.5	NUM
ap-2083	54	21	0	0	NUM
ap-2083	54	22	0.5	0.5	NUM
ap-2083	54	23	-0.5	-0.5	NUM
ap-2083	54	24	0	0	NUM
ap-2083	54	25	0.5	0.5	NUM
ap-2083	54	26	-0.5	-0.5	NUM
ap-2083	54	27	0	0	NUM
ap-2083	54	28	0.5	0.5	NUM
ap-2083	54	29	-0.5	-0.5	NOUN
ap-2083	54	30	0	0	NUM
ap-2083	54	31	0.5	0.5	NUM
ap-2083	54	32	v	v	NOUN
ap-2083	54	33	ψ	ψ	NOUN
ap-2083	54	34	x	x	PRON
ap-2083	54	35	figure	figure	NOUN
ap-2083	54	36	1	1	NUM
ap-2083	54	37	.	.	PUNCT
ap-2083	54	38	unperturbed	unperturbed	ADJ
ap-2083	54	39	spectrum	spectrum	NOUN
ap-2083	54	40	of	of	ADP
ap-2083	54	41	the	the	DET
ap-2083	54	42	harmonic	harmonic	ADJ
ap-2083	54	43	oscillator	oscillator	NOUN
ap-2083	54	44	and	and	CCONJ
ap-2083	54	45	the	the	DET
ap-2083	54	46	lowest	low	ADJ
ap-2083	54	47	five	five	NUM
ap-2083	54	48	wave	wave	NOUN
ap-2083	54	49	functions	function	NOUN
ap-2083	54	50	.	.	PUNCT
ap-2083	55	1	vertical	vertical	PROPN
ap-2083	55	2	dashed	dash	VERB
ap-2083	55	3	lines	line	NOUN
ap-2083	55	4	designate	designate	VERB
ap-2083	55	5	different	different	ADJ
ap-2083	55	6	positions	position	NOUN
ap-2083	55	7	of	of	ADP
ap-2083	55	8	the	the	DET
ap-2083	55	9	pt	pt	PROPN
ap-2083	55	10	symmetric	symmetric	PROPN
ap-2083	55	11	delta	delta	NOUN
ap-2083	55	12	-	-	PUNCT
ap-2083	55	13	function	function	NOUN
ap-2083	55	14	perturbations	perturbation	NOUN
ap-2083	55	15	.	.	PUNCT
ap-2083	56	1	as	as	SCONJ
ap-2083	56	2	the	the	DET
ap-2083	56	3	delta	delta	NOUN
ap-2083	56	4	functions	function	NOUN
ap-2083	56	5	are	be	AUX
ap-2083	56	6	shifted	shift	VERB
ap-2083	56	7	further	far	ADV
ap-2083	56	8	and	and	CCONJ
ap-2083	56	9	further	far	ADV
ap-2083	56	10	out	out	ADP
ap-2083	56	11	an	an	DET
ap-2083	56	12	increasing	increase	VERB
ap-2083	56	13	number	number	NOUN
ap-2083	56	14	of	of	ADP
ap-2083	56	15	low	low	ADJ
ap-2083	56	16	-	-	PUNCT
ap-2083	56	17	lying	lie	VERB
ap-2083	56	18	eigenvalues	eigenvalue	NOUN
ap-2083	56	19	will	will	AUX
ap-2083	56	20	not	not	PART
ap-2083	56	21	be	be	AUX
ap-2083	56	22	changed	change	VERB
ap-2083	56	23	by	by	ADP
ap-2083	56	24	the	the	DET
ap-2083	56	25	perturbation	perturbation	NOUN
ap-2083	56	26	.	.	PUNCT
ap-2083	57	1	it	it	PRON
ap-2083	57	2	is	be	AUX
ap-2083	57	3	easy	easy	ADJ
ap-2083	57	4	to	to	PART
ap-2083	57	5	show	show	VERB
ap-2083	57	6	that	that	SCONJ
ap-2083	57	7	the	the	DET
ap-2083	57	8	mityagin	mityagin	NOUN
ap-2083	57	9	-	-	PUNCT
ap-2083	57	10	siegl	siegl	NOUN
ap-2083	57	11	criterion	criterion	NOUN
ap-2083	57	12	(	(	PUNCT
ap-2083	57	13	1	1	X
ap-2083	57	14	)	)	PUNCT
ap-2083	57	15	is	be	AUX
ap-2083	57	16	fulfilled	fulfil	VERB
ap-2083	57	17	for	for	ADP
ap-2083	57	18	the	the	DET
ap-2083	57	19	imaginary	imaginary	ADJ
ap-2083	57	20	delta	delta	NOUN
ap-2083	57	21	function	function	NOUN
ap-2083	57	22	perturbation	perturbation	NOUN
ap-2083	57	23	in	in	ADP
ap-2083	57	24	(	(	PUNCT
ap-2083	57	25	3	3	X
ap-2083	57	26	)	)	PUNCT
ap-2083	57	27	since∣∣〈ψm|b̂|ψn〉∣∣	since∣∣〈ψm|b̂|ψn〉∣∣	PROPN
ap-2083	58	1	=	=	SYM
ap-2083	58	2	|γ|	|γ|	PROPN
ap-2083	58	3	∣∣ψm(b)ψn(b)−	∣∣ψm(b)ψn(b)−	NOUN
ap-2083	58	4	ψm(−b)ψn(−b	ψm(−b)ψn(−b	NOUN
ap-2083	58	5	)	)	PUNCT
ap-2083	58	6	∣∣.	∣∣.	NOUN
ap-2083	58	7	(	(	PUNCT
ap-2083	58	8	4	4	NUM
ap-2083	58	9	)	)	PUNCT
ap-2083	58	10	the	the	DET
ap-2083	58	11	oscillator	oscillator	NOUN
ap-2083	58	12	eigenfunctions	eigenfunction	NOUN
ap-2083	58	13	have	have	AUX
ap-2083	58	14	either	either	CCONJ
ap-2083	58	15	even	even	ADV
ap-2083	58	16	or	or	CCONJ
ap-2083	58	17	odd	odd	ADJ
ap-2083	58	18	parity	parity	NOUN
ap-2083	58	19	,	,	PUNCT
ap-2083	58	20	therefore	therefore	ADV
ap-2083	58	21	|〈ψm|b̂|ψn〉|	|〈ψm|b̂|ψn〉|	X
ap-2083	58	22	=	=	SYM
ap-2083	58	23	0	0	PUNCT
ap-2083	58	24	if	if	SCONJ
ap-2083	58	25	m	m	VERB
ap-2083	58	26	and	and	CCONJ
ap-2083	58	27	n	n	PRON
ap-2083	58	28	are	be	AUX
ap-2083	58	29	both	both	PRON
ap-2083	58	30	even	even	ADV
ap-2083	58	31	or	or	CCONJ
ap-2083	58	32	odd	odd	ADJ
ap-2083	58	33	,	,	PUNCT
ap-2083	58	34	while	while	SCONJ
ap-2083	58	35	for	for	SCONJ
ap-2083	58	36	m	m	PRON
ap-2083	58	37	even	even	ADV
ap-2083	58	38	and	and	CCONJ
ap-2083	58	39	n	n	PRON
ap-2083	58	40	odd	odd	ADJ
ap-2083	58	41	,	,	PUNCT
ap-2083	58	42	and	and	CCONJ
ap-2083	58	43	vice	vice	ADV
ap-2083	58	44	versa	versa	ADV
ap-2083	58	45	,	,	PUNCT
ap-2083	58	46	we	we	PRON
ap-2083	58	47	have∣∣〈ψm|b̂|ψn〉∣∣	have∣∣〈ψm|b̂|ψn〉∣∣	PROPN
ap-2083	58	48	=	=	PUNCT
ap-2083	58	49	2|γ|	2|γ|	NUM
ap-2083	58	50	∣∣ψm(b	∣∣ψm(b	PROPN
ap-2083	58	51	)	)	PUNCT
ap-2083	58	52	∣∣∣∣ψn(b	∣∣∣∣ψn(b	NOUN
ap-2083	58	53	)	)	PUNCT
ap-2083	58	54	∣∣	∣∣	NUM
ap-2083	58	55	≤	≤	NUM
ap-2083	58	56	2|γ|c̃m−1/4n−1/4	2|γ|c̃m−1/4n−1/4	NUM
ap-2083	58	57	.	.	PUNCT
ap-2083	59	1	(	(	PUNCT
ap-2083	59	2	5	5	NUM
ap-2083	59	3	)	)	PUNCT
ap-2083	59	4	in	in	ADP
ap-2083	59	5	the	the	DET
ap-2083	59	6	last	last	ADJ
ap-2083	59	7	line	line	NOUN
ap-2083	59	8	we	we	PRON
ap-2083	59	9	have	have	AUX
ap-2083	59	10	exploited	exploit	VERB
ap-2083	59	11	an	an	DET
ap-2083	59	12	inequality	inequality	NOUN
ap-2083	59	13	given	give	VERB
ap-2083	59	14	by	by	ADP
ap-2083	59	15	mityagin	mityagin	NOUN
ap-2083	59	16	and	and	CCONJ
ap-2083	59	17	siegl	siegl	VERB
ap-2083	60	1	[	[	X
ap-2083	60	2	9	9	NUM
ap-2083	60	3	]	]	PUNCT
ap-2083	60	4	which	which	PRON
ap-2083	60	5	is	be	AUX
ap-2083	60	6	valid	valid	ADJ
ap-2083	60	7	for	for	ADP
ap-2083	60	8	2(2n+1	2(2n+1	NUM
ap-2083	60	9	)	)	PUNCT
ap-2083	60	10	≥	≥	NOUN
ap-2083	60	11	b2	b2	NOUN
ap-2083	60	12	.	.	PUNCT
ap-2083	61	1	the	the	DET
ap-2083	61	2	prediction	prediction	NOUN
ap-2083	61	3	then	then	ADV
ap-2083	61	4	is	be	AUX
ap-2083	61	5	that	that	SCONJ
ap-2083	61	6	eigenvalues	eigenvalue	NOUN
ap-2083	61	7	can	can	AUX
ap-2083	61	8	only	only	ADV
ap-2083	61	9	move	move	VERB
ap-2083	61	10	to	to	ADP
ap-2083	61	11	a	a	DET
ap-2083	61	12	distance	distance	NOUN
ap-2083	61	13	m	m	VERB
ap-2083	61	14	,	,	PUNCT
ap-2083	61	15	where	where	SCONJ
ap-2083	61	16	m	m	NOUN
ap-2083	61	17	is	be	AUX
ap-2083	61	18	a	a	DET
ap-2083	61	19	constant	constant	ADJ
ap-2083	61	20	,	,	PUNCT
ap-2083	61	21	uniform	uniform	NOUN
ap-2083	61	22	for	for	ADP
ap-2083	61	23	all	all	DET
ap-2083	61	24	eigenvalues	eigenvalue	NOUN
ap-2083	61	25	,	,	PUNCT
ap-2083	61	26	and	and	CCONJ
ap-2083	61	27	in	in	ADP
ap-2083	61	28	particular	particular	ADJ
ap-2083	61	29	,	,	PUNCT
ap-2083	61	30	that	that	SCONJ
ap-2083	61	31	there	there	PRON
ap-2083	61	32	exists	exist	VERB
ap-2083	61	33	an	an	DET
ap-2083	61	34	n0	n0	NOUN
ap-2083	61	35	such	such	ADJ
ap-2083	61	36	that	that	PRON
ap-2083	61	37	for	for	ADP
ap-2083	61	38	n	n	PRON
ap-2083	61	39	≥	≥	NOUN
ap-2083	61	40	n0	n0	NOUN
ap-2083	61	41	all	all	PRON
ap-2083	61	42	eigenvalues	eigenvalue	VERB
ap-2083	61	43	stay	stay	VERB
ap-2083	61	44	in	in	ADP
ap-2083	61	45	disjoint	disjoint	NOUN
ap-2083	61	46	disks	disk	NOUN
ap-2083	61	47	with	with	ADP
ap-2083	61	48	shrinking	shrink	VERB
ap-2083	61	49	radii	radius	NOUN
ap-2083	61	50	,	,	PUNCT
ap-2083	61	51	with	with	ADP
ap-2083	61	52	the	the	DET
ap-2083	61	53	shrink	shrink	NOUN
ap-2083	61	54	rate	rate	NOUN
ap-2083	61	55	being	be	AUX
ap-2083	61	56	bounded	bound	VERB
ap-2083	61	57	from	from	ADP
ap-2083	61	58	above	above	ADV
ap-2083	61	59	by	by	ADP
ap-2083	61	60	cn−1/2	cn−1/2	PROPN
ap-2083	61	61	.	.	PUNCT
ap-2083	62	1	in	in	ADP
ap-2083	62	2	fact	fact	NOUN
ap-2083	62	3	,	,	PUNCT
ap-2083	62	4	one	one	NUM
ap-2083	62	5	of	of	ADP
ap-2083	62	6	the	the	DET
ap-2083	62	7	authors	author	NOUN
ap-2083	62	8	of	of	ADP
ap-2083	62	9	ref	ref	NOUN
ap-2083	62	10	.	.	PUNCT
ap-2083	63	1	[	[	X
ap-2083	63	2	9	9	NUM
ap-2083	63	3	]	]	PUNCT
ap-2083	63	4	has	have	AUX
ap-2083	63	5	pointed	point	VERB
ap-2083	63	6	out	out	ADP
ap-2083	63	7	[	[	X
ap-2083	63	8	10	10	NUM
ap-2083	63	9	]	]	PUNCT
ap-2083	63	10	that	that	SCONJ
ap-2083	63	11	for	for	ADP
ap-2083	63	12	the	the	DET
ap-2083	63	13	case	case	NOUN
ap-2083	63	14	of	of	ADP
ap-2083	63	15	two	two	NUM
ap-2083	63	16	delta	delta	NOUN
ap-2083	63	17	potentials	potential	VERB
ap-2083	63	18	the	the	DET
ap-2083	63	19	shrink	shrink	NOUN
ap-2083	63	20	rate	rate	NOUN
ap-2083	63	21	can	can	AUX
ap-2083	63	22	be	be	AUX
ap-2083	63	23	estimated	estimate	VERB
ap-2083	63	24	even	even	ADV
ap-2083	63	25	more	more	ADV
ap-2083	63	26	precisely	precisely	ADV
ap-2083	63	27	to	to	PART
ap-2083	63	28	behave	behave	VERB
ap-2083	63	29	as	as	ADP
ap-2083	63	30	log(n)/n3/2	log(n)/n3/2	PROPN
ap-2083	63	31	.	.	PUNCT
ap-2083	64	1	note	note	VERB
ap-2083	64	2	that	that	SCONJ
ap-2083	64	3	no	no	DET
ap-2083	64	4	such	such	ADJ
ap-2083	64	5	statements	statement	NOUN
ap-2083	64	6	can	can	AUX
ap-2083	64	7	be	be	AUX
ap-2083	64	8	made	make	VERB
ap-2083	64	9	from	from	ADP
ap-2083	64	10	their	their	PRON
ap-2083	64	11	theorems	theorem	NOUN
ap-2083	64	12	for	for	ADP
ap-2083	64	13	the	the	DET
ap-2083	64	14	case	case	NOUN
ap-2083	64	15	that	that	SCONJ
ap-2083	64	16	the	the	DET
ap-2083	64	17	nonlinearity	nonlinearity	NOUN
ap-2083	64	18	is	be	AUX
ap-2083	64	19	also	also	ADV
ap-2083	64	20	included	include	VERB
ap-2083	64	21	as	as	ADP
ap-2083	64	22	a	a	DET
ap-2083	64	23	perturbation	perturbation	NOUN
ap-2083	64	24	.	.	PUNCT
ap-2083	65	1	3	3	X
ap-2083	65	2	.	.	X
ap-2083	65	3	eigenvalue	eigenvalue	PROPN
ap-2083	65	4	spectra	spectra	ADJ
ap-2083	65	5	the	the	PRON
ap-2083	65	6	(	(	PUNCT
ap-2083	65	7	real	real	ADJ
ap-2083	65	8	and	and	CCONJ
ap-2083	65	9	complex	complex	ADJ
ap-2083	65	10	)	)	PUNCT
ap-2083	65	11	eigenvalues	eigenvalue	VERB
ap-2083	65	12	µ	µ	NOUN
ap-2083	65	13	of	of	ADP
ap-2083	65	14	the	the	DET
ap-2083	65	15	hamiltonian	hamiltonian	NOUN
ap-2083	65	16	(	(	PUNCT
ap-2083	65	17	3	3	NUM
ap-2083	65	18	)	)	PUNCT
ap-2083	65	19	and	and	CCONJ
ap-2083	65	20	its	its	PRON
ap-2083	65	21	eigenstates	eigenstate	NOUN
ap-2083	65	22	ψ	ψ	NOUN
ap-2083	65	23	are	be	AUX
ap-2083	65	24	obtained	obtain	VERB
ap-2083	65	25	,	,	PUNCT
ap-2083	65	26	in	in	ADP
ap-2083	65	27	both	both	CCONJ
ap-2083	65	28	the	the	DET
ap-2083	65	29	linear	linear	NOUN
ap-2083	65	30	and	and	CCONJ
ap-2083	65	31	the	the	DET
ap-2083	65	32	nonlinear	nonlinear	ADJ
ap-2083	65	33	case	case	NOUN
ap-2083	65	34	,	,	PUNCT
ap-2083	65	35	by	by	ADP
ap-2083	65	36	integrating	integrate	VERB
ap-2083	65	37	the	the	DET
ap-2083	65	38	wave	wave	NOUN
ap-2083	65	39	functions	function	NOUN
ap-2083	65	40	outward	outward	ADV
ap-2083	65	41	from	from	ADP
ap-2083	65	42	x	x	X
ap-2083	65	43	=	=	SYM
ap-2083	65	44	0	0	NUM
ap-2083	65	45	,	,	PUNCT
ap-2083	65	46	and	and	CCONJ
ap-2083	65	47	varying	vary	VERB
ap-2083	65	48	the	the	DET
ap-2083	65	49	initial	initial	ADJ
ap-2083	65	50	values	value	NOUN
ap-2083	65	51	of	of	ADP
ap-2083	65	52	reψ(0	reψ(0	NOUN
ap-2083	65	53	)	)	PUNCT
ap-2083	65	54	,	,	PUNCT
ap-2083	65	55	ψ′(0	ψ′(0	PRON
ap-2083	65	56	)	)	PUNCT
ap-2083	65	57	∈	∈	PROPN
ap-2083	65	58	c	c	NOUN
ap-2083	65	59	,	,	PUNCT
ap-2083	65	60	and	and	CCONJ
ap-2083	65	61	µ	µ	X
ap-2083	65	62	∈	∈	NOUN
ap-2083	65	63	c	c	NOUN
ap-2083	65	64	to	to	PART
ap-2083	65	65	find	find	VERB
ap-2083	65	66	square	square	ADJ
ap-2083	65	67	-	-	PUNCT
ap-2083	65	68	integrable	integrable	ADJ
ap-2083	65	69	normalised	normalise	VERB
ap-2083	65	70	solutions	solution	NOUN
ap-2083	65	71	(	(	PUNCT
ap-2083	65	72	the	the	DET
ap-2083	65	73	arbitrary	arbitrary	ADJ
ap-2083	65	74	global	global	ADJ
ap-2083	65	75	phase	phase	NOUN
ap-2083	65	76	is	be	AUX
ap-2083	65	77	exploited	exploit	VERB
ap-2083	65	78	by	by	ADP
ap-2083	65	79	choosing	choose	VERB
ap-2083	65	80	imψ(0	imψ(0	NOUN
ap-2083	65	81	)	)	PUNCT
ap-2083	66	1	=	=	PUNCT
ap-2083	66	2	0	0	NUM
ap-2083	66	3	)	)	PUNCT
ap-2083	66	4	.	.	PUNCT
ap-2083	67	1	figure	figure	NOUN
ap-2083	67	2	2	2	NUM
ap-2083	67	3	shows	show	NOUN
ap-2083	67	4	for	for	ADP
ap-2083	67	5	the	the	DET
ap-2083	67	6	lowest	low	ADJ
ap-2083	67	7	30	30	NUM
ap-2083	67	8	levels	level	NOUN
ap-2083	67	9	the	the	DET
ap-2083	67	10	real	real	ADJ
ap-2083	67	11	and	and	CCONJ
ap-2083	67	12	imaginary	imaginary	ADJ
ap-2083	67	13	parts	part	NOUN
ap-2083	67	14	of	of	ADP
ap-2083	67	15	the	the	DET
ap-2083	67	16	eigenvalues	eigenvalue	NOUN
ap-2083	67	17	of	of	ADP
ap-2083	67	18	(	(	PUNCT
ap-2083	67	19	3	3	NUM
ap-2083	67	20	)	)	PUNCT
ap-2083	67	21	(	(	PUNCT
ap-2083	67	22	for	for	ADP
ap-2083	67	23	g	g	NOUN
ap-2083	67	24	=	=	SYM
ap-2083	67	25	0	0	NUM
ap-2083	67	26	)	)	PUNCT
ap-2083	67	27	as	as	ADP
ap-2083	67	28	117	117	NUM
ap-2083	67	29	d.	d.	PROPN
ap-2083	67	30	haag	haag	PROPN
ap-2083	67	31	,	,	PUNCT
ap-2083	67	32	h.	h.	PROPN
ap-2083	67	33	cartarius	cartarius	PROPN
ap-2083	67	34	,	,	PUNCT
ap-2083	67	35	g.	g.	PROPN
ap-2083	67	36	wunner	wunner	PROPN
ap-2083	67	37	acta	acta	PROPN
ap-2083	67	38	polytechnica	polytechnica	PROPN
ap-2083	67	39	0	0	NUM
ap-2083	67	40	10	10	NUM
ap-2083	67	41	20	20	NUM
ap-2083	67	42	30	30	NUM
ap-2083	67	43	40	40	NUM
ap-2083	67	44	50	50	NUM
ap-2083	67	45	60	60	NUM
ap-2083	67	46	70	70	NUM
ap-2083	67	47	0	0	NUM
ap-2083	67	48	5	5	NUM
ap-2083	67	49	10	10	NUM
ap-2083	67	50	15	15	NUM
ap-2083	67	51	20	20	NUM
ap-2083	67	52	25	25	NUM
ap-2083	67	53	30	30	NUM
ap-2083	67	54	µ	µ	NOUN
ap-2083	67	55	r	r	NOUN
ap-2083	67	56	γ	γ	X
ap-2083	67	57	−10	−10	X
ap-2083	67	58	−5	−5	ADV
ap-2083	67	59	0	0	NUM
ap-2083	67	60	5	5	NUM
ap-2083	67	61	10	10	NUM
ap-2083	67	62	0	0	NUM
ap-2083	67	63	5	5	NUM
ap-2083	67	64	10	10	NUM
ap-2083	67	65	15	15	NUM
ap-2083	67	66	20	20	NUM
ap-2083	67	67	25	25	NUM
ap-2083	67	68	30	30	NUM
ap-2083	67	69	µ	µ	NOUN
ap-2083	67	70	i	i	PRON
ap-2083	67	71	γ	γ	NOUN
ap-2083	67	72	figure	figure	NOUN
ap-2083	67	73	2	2	NUM
ap-2083	67	74	.	.	PUNCT
ap-2083	67	75	real	real	ADJ
ap-2083	67	76	parts	part	NOUN
ap-2083	67	77	(	(	PUNCT
ap-2083	67	78	top	top	ADJ
ap-2083	67	79	)	)	PUNCT
ap-2083	67	80	and	and	CCONJ
ap-2083	67	81	imaginary	imaginary	ADJ
ap-2083	67	82	parts	part	NOUN
ap-2083	67	83	(	(	PUNCT
ap-2083	67	84	bottom	bottom	NOUN
ap-2083	67	85	)	)	PUNCT
ap-2083	67	86	of	of	ADP
ap-2083	67	87	the	the	DET
ap-2083	67	88	eigenvalues	eigenvalue	NOUN
ap-2083	67	89	of	of	ADP
ap-2083	67	90	(	(	PUNCT
ap-2083	67	91	3	3	NUM
ap-2083	67	92	)	)	PUNCT
ap-2083	67	93	(	(	PUNCT
ap-2083	67	94	with	with	ADP
ap-2083	67	95	g	g	PROPN
ap-2083	67	96	=	=	SYM
ap-2083	67	97	0	0	NUM
ap-2083	67	98	)	)	PUNCT
ap-2083	67	99	for	for	ADP
ap-2083	67	100	b	b	NOUN
ap-2083	67	101	=	=	SYM
ap-2083	67	102	0.2	0.2	NUM
ap-2083	67	103	,	,	PUNCT
ap-2083	67	104	evolving	evolve	VERB
ap-2083	67	105	from	from	ADP
ap-2083	67	106	the	the	DET
ap-2083	67	107	unperturbed	unperturbed	ADJ
ap-2083	67	108	levels	level	NOUN
ap-2083	67	109	with	with	ADP
ap-2083	67	110	n	n	NOUN
ap-2083	67	111	=	=	SYM
ap-2083	67	112	0	0	NUM
ap-2083	67	113	,	,	PUNCT
ap-2083	67	114	.	.	PUNCT
ap-2083	67	115	.	.	PUNCT
ap-2083	68	1	.	.	PUNCT
ap-2083	69	1	,	,	PUNCT
ap-2083	69	2	29	29	NUM
ap-2083	69	3	,	,	PUNCT
ap-2083	69	4	in	in	ADP
ap-2083	69	5	dependence	dependence	NOUN
ap-2083	69	6	on	on	ADP
ap-2083	69	7	the	the	DET
ap-2083	69	8	strength	strength	NOUN
ap-2083	69	9	γ	γ	NOUN
ap-2083	69	10	of	of	ADP
ap-2083	69	11	the	the	DET
ap-2083	69	12	non	non	ADJ
ap-2083	69	13	-	-	NOUN
ap-2083	69	14	hermiticity	hermiticity	ADJ
ap-2083	69	15	.	.	PUNCT
ap-2083	70	1	functions	function	NOUN
ap-2083	70	2	of	of	ADP
ap-2083	70	3	the	the	DET
ap-2083	70	4	strength	strength	NOUN
ap-2083	70	5	γ	γ	PROPN
ap-2083	70	6	of	of	ADP
ap-2083	70	7	the	the	DET
ap-2083	70	8	non	non	NOUN
ap-2083	70	9	-	-	NOUN
ap-2083	70	10	hermiticity	hermiticity	NOUN
ap-2083	70	11	,	,	PUNCT
ap-2083	70	12	for	for	ADP
ap-2083	70	13	a	a	DET
ap-2083	70	14	position	position	NOUN
ap-2083	70	15	of	of	ADP
ap-2083	70	16	the	the	DET
ap-2083	70	17	delta	delta	NOUN
ap-2083	70	18	functions	function	NOUN
ap-2083	70	19	at	at	ADP
ap-2083	70	20	b	b	NOUN
ap-2083	70	21	=	=	SYM
ap-2083	70	22	0.2	0.2	NUM
ap-2083	70	23	,	,	PUNCT
ap-2083	70	24	close	close	ADJ
ap-2083	70	25	to	to	ADP
ap-2083	70	26	the	the	DET
ap-2083	70	27	centre	centre	NOUN
ap-2083	70	28	of	of	ADP
ap-2083	70	29	the	the	DET
ap-2083	70	30	oscillator	oscillator	NOUN
ap-2083	70	31	.	.	PUNCT
ap-2083	71	1	one	one	NUM
ap-2083	71	2	recognises	recognise	VERB
ap-2083	71	3	that	that	PRON
ap-2083	71	4	successive	successive	ADJ
ap-2083	71	5	pairs	pair	NOUN
ap-2083	71	6	of	of	ADP
ap-2083	71	7	eigenvalues	eigenvalue	NOUN
ap-2083	71	8	coalesce	coalesce	NOUN
ap-2083	71	9	at	at	ADP
ap-2083	71	10	branch	branch	NOUN
ap-2083	71	11	points	point	NOUN
ap-2083	71	12	,	,	PUNCT
ap-2083	71	13	from	from	ADP
ap-2083	71	14	where	where	SCONJ
ap-2083	71	15	onwards	onwards	ADV
ap-2083	71	16	they	they	PRON
ap-2083	71	17	turn	turn	VERB
ap-2083	71	18	into	into	ADP
ap-2083	71	19	complex	complex	ADJ
ap-2083	71	20	conjugate	conjugate	ADJ
ap-2083	71	21	pairs	pair	NOUN
ap-2083	71	22	.	.	PUNCT
ap-2083	72	1	the	the	DET
ap-2083	72	2	branch	branch	NOUN
ap-2083	72	3	points	point	NOUN
ap-2083	72	4	are	be	AUX
ap-2083	72	5	shifted	shift	VERB
ap-2083	72	6	to	to	ADP
ap-2083	72	7	larger	large	ADJ
ap-2083	72	8	values	value	NOUN
ap-2083	72	9	of	of	ADP
ap-2083	72	10	γ	γ	NOUN
ap-2083	72	11	as	as	SCONJ
ap-2083	72	12	one	one	NUM
ap-2083	72	13	goes	go	VERB
ap-2083	72	14	up	up	ADP
ap-2083	72	15	in	in	ADP
ap-2083	72	16	the	the	DET
ap-2083	72	17	spectrum	spectrum	NOUN
ap-2083	72	18	.	.	PUNCT
ap-2083	73	1	what	what	PRON
ap-2083	73	2	is	be	AUX
ap-2083	73	3	surprising	surprising	ADJ
ap-2083	73	4	is	be	AUX
ap-2083	73	5	that	that	SCONJ
ap-2083	73	6	both	both	CCONJ
ap-2083	73	7	the	the	DET
ap-2083	73	8	real	real	ADJ
ap-2083	73	9	and	and	CCONJ
ap-2083	73	10	the	the	DET
ap-2083	73	11	imaginary	imaginary	ADJ
ap-2083	73	12	part	part	NOUN
ap-2083	73	13	of	of	ADP
ap-2083	73	14	the	the	DET
ap-2083	73	15	complex	complex	ADJ
ap-2083	73	16	eigenvalues	eigenvalue	NOUN
ap-2083	73	17	emerging	emerge	VERB
ap-2083	73	18	from	from	ADP
ap-2083	73	19	the	the	DET
ap-2083	73	20	branch	branch	NOUN
ap-2083	73	21	point	point	NOUN
ap-2083	73	22	of	of	ADP
ap-2083	73	23	the	the	DET
ap-2083	73	24	eighth	eighth	ADJ
ap-2083	73	25	and	and	CCONJ
ap-2083	73	26	ninth	ninth	ADJ
ap-2083	73	27	excited	excited	ADJ
ap-2083	73	28	state	state	NOUN
ap-2083	73	29	experience	experience	NOUN
ap-2083	73	30	huge	huge	ADJ
ap-2083	73	31	shifts	shift	NOUN
ap-2083	73	32	,	,	PUNCT
ap-2083	73	33	but	but	CCONJ
ap-2083	73	34	eventually	eventually	ADV
ap-2083	73	35	saturate	saturate	VERB
ap-2083	73	36	,	,	PUNCT
ap-2083	73	37	like	like	ADP
ap-2083	73	38	the	the	DET
ap-2083	73	39	other	other	ADJ
ap-2083	73	40	levels	level	NOUN
ap-2083	73	41	.	.	PUNCT
ap-2083	74	1	for	for	ADP
ap-2083	74	2	the	the	DET
ap-2083	74	3	ninth	ninth	ADJ
ap-2083	74	4	excited	excited	ADJ
ap-2083	74	5	state	state	NOUN
ap-2083	74	6	,	,	PUNCT
ap-2083	74	7	the	the	DET
ap-2083	74	8	real	real	ADJ
ap-2083	74	9	parts	part	NOUN
ap-2083	74	10	remain	remain	VERB
ap-2083	74	11	approximately	approximately	ADV
ap-2083	74	12	constant	constant	ADJ
ap-2083	74	13	beyond	beyond	ADP
ap-2083	74	14	the	the	DET
ap-2083	74	15	branch	branch	NOUN
ap-2083	74	16	points	point	NOUN
ap-2083	74	17	,	,	PUNCT
ap-2083	74	18	and	and	CCONJ
ap-2083	74	19	the	the	DET
ap-2083	74	20	imaginary	imaginary	ADJ
ap-2083	74	21	parts	part	NOUN
ap-2083	74	22	quickly	quickly	ADV
ap-2083	74	23	tend	tend	VERB
ap-2083	74	24	to	to	ADP
ap-2083	74	25	zero	zero	NUM
ap-2083	74	26	.	.	PUNCT
ap-2083	75	1	in	in	ADP
ap-2083	75	2	figure	figure	NOUN
ap-2083	75	3	3	3	NUM
ap-2083	75	4	we	we	PRON
ap-2083	75	5	move	move	VERB
ap-2083	75	6	the	the	DET
ap-2083	75	7	delta	delta	NOUN
ap-2083	75	8	functions	function	NOUN
ap-2083	75	9	further	far	ADV
ap-2083	75	10	away	away	ADV
ap-2083	75	11	from	from	ADP
ap-2083	75	12	the	the	DET
ap-2083	75	13	centre	centre	NOUN
ap-2083	75	14	of	of	ADP
ap-2083	75	15	the	the	DET
ap-2083	75	16	harmonic	harmonic	ADJ
ap-2083	75	17	oscillator	oscillator	NOUN
ap-2083	75	18	to	to	ADP
ap-2083	75	19	the	the	DET
ap-2083	75	20	classical	classical	ADJ
ap-2083	75	21	turning	turning	NOUN
ap-2083	75	22	points	point	NOUN
ap-2083	75	23	b	b	NOUN
ap-2083	76	1	=	=	SYM
ap-2083	76	2	1	1	NUM
ap-2083	76	3	and	and	CCONJ
ap-2083	76	4	√	√	NUM
ap-2083	76	5	7	7	NUM
ap-2083	76	6	of	of	ADP
ap-2083	76	7	the	the	DET
ap-2083	76	8	unperturbed	unperturbed	ADJ
ap-2083	76	9	levels	level	NOUN
ap-2083	76	10	with	with	ADP
ap-2083	76	11	n	n	NOUN
ap-2083	76	12	=	=	SYM
ap-2083	76	13	0	0	NUM
ap-2083	76	14	and	and	CCONJ
ap-2083	76	15	n	n	CCONJ
ap-2083	76	16	=	=	SYM
ap-2083	76	17	3	3	NUM
ap-2083	76	18	,	,	PUNCT
ap-2083	76	19	respectively	respectively	ADV
ap-2083	76	20	.	.	PUNCT
ap-2083	77	1	at	at	ADP
ap-2083	77	2	the	the	DET
ap-2083	77	3	turning	turning	NOUN
ap-2083	77	4	points	point	NOUN
ap-2083	77	5	the	the	DET
ap-2083	77	6	unperturbed	unperturbed	ADJ
ap-2083	77	7	wave	wave	NOUN
ap-2083	77	8	functions	function	NOUN
ap-2083	77	9	enter	enter	VERB
ap-2083	77	10	into	into	ADP
ap-2083	77	11	the	the	DET
ap-2083	77	12	classically	classically	ADV
ap-2083	77	13	forbidden	forbid	VERB
ap-2083	77	14	,	,	PUNCT
ap-2083	77	15	i.e.	i.e.	ADV
ap-2083	77	16	exponentially	exponentially	ADV
ap-2083	77	17	decreasing	decrease	VERB
ap-2083	77	18	region	region	NOUN
ap-2083	77	19	.	.	PUNCT
ap-2083	78	1	it	it	PRON
ap-2083	78	2	is	be	AUX
ap-2083	78	3	therefore	therefore	ADV
ap-2083	78	4	no	no	DET
ap-2083	78	5	surprise	surprise	NOUN
ap-2083	78	6	that	that	PRON
ap-2083	78	7	for	for	SCONJ
ap-2083	78	8	b	b	NOUN
ap-2083	78	9	=	=	SYM
ap-2083	78	10	1	1	NUM
ap-2083	78	11	the	the	DET
ap-2083	78	12	ground	ground	NOUN
ap-2083	78	13	state	state	NOUN
ap-2083	78	14	no	no	ADV
ap-2083	78	15	longer	long	ADV
ap-2083	78	16	“	"	PUNCT
ap-2083	78	17	feels	feel	VERB
ap-2083	78	18	”	"	PUNCT
ap-2083	78	19	the	the	DET
ap-2083	78	20	delta	delta	NOUN
ap-2083	78	21	functions	function	NOUN
ap-2083	78	22	,	,	PUNCT
ap-2083	78	23	and	and	CCONJ
ap-2083	78	24	no	no	ADV
ap-2083	78	25	longer	long	ADV
ap-2083	78	26	unites	unite	VERB
ap-2083	78	27	with	with	ADP
ap-2083	78	28	the	the	DET
ap-2083	78	29	first	first	ADJ
ap-2083	78	30	excited	excited	ADJ
ap-2083	78	31	state	state	NOUN
ap-2083	78	32	at	at	ADP
ap-2083	78	33	a	a	DET
ap-2083	78	34	branch	branch	NOUN
ap-2083	78	35	point	point	NOUN
ap-2083	78	36	.	.	PUNCT
ap-2083	79	1	rather	rather	ADV
ap-2083	79	2	its	its	PRON
ap-2083	79	3	eigenvalue	eigenvalue	NOUN
ap-2083	79	4	remains	remain	VERB
ap-2083	79	5	real	real	ADJ
ap-2083	79	6	for	for	ADP
ap-2083	79	7	any	any	DET
ap-2083	79	8	strength	strength	NOUN
ap-2083	79	9	of	of	ADP
ap-2083	79	10	the	the	DET
ap-2083	79	11	non	non	NOUN
ap-2083	79	12	-	-	NOUN
ap-2083	79	13	hermiticity	hermiticity	NOUN
ap-2083	79	14	.	.	PUNCT
ap-2083	80	1	for	for	ADP
ap-2083	80	2	b	b	NOUN
ap-2083	80	3	=	=	NOUN
ap-2083	80	4	√	√	PROPN
ap-2083	80	5	7	7	NUM
ap-2083	80	6	it	it	PRON
ap-2083	80	7	is	be	AUX
ap-2083	80	8	the	the	DET
ap-2083	80	9	states	state	NOUN
ap-2083	80	10	with	with	ADP
ap-2083	80	11	n	n	PROPN
ap-2083	80	12	=	=	SYM
ap-2083	80	13	0	0	NUM
ap-2083	80	14	,	,	PUNCT
ap-2083	80	15	1	1	NUM
ap-2083	80	16	,	,	PUNCT
ap-2083	80	17	2	2	NUM
ap-2083	80	18	,	,	PUNCT
ap-2083	80	19	3	3	NUM
ap-2083	80	20	which	which	PRON
ap-2083	80	21	exhibit	exhibit	VERB
ap-2083	80	22	this	this	DET
ap-2083	80	23	property	property	NOUN
ap-2083	80	24	.	.	PUNCT
ap-2083	81	1	we	we	PRON
ap-2083	81	2	note	note	VERB
ap-2083	81	3	that	that	SCONJ
ap-2083	81	4	similar	similar	ADJ
ap-2083	81	5	behaviour	behaviour	NOUN
ap-2083	81	6	was	be	AUX
ap-2083	81	7	found	find	VERB
ap-2083	81	8	by	by	ADP
ap-2083	81	9	jakubský	jakubský	PROPN
ap-2083	81	10	and	and	CCONJ
ap-2083	81	11	znojil	znojil	NOUN
ap-2083	82	1	[	[	X
ap-2083	82	2	19	19	NUM
ap-2083	82	3	]	]	PUNCT
ap-2083	82	4	in	in	ADP
ap-2083	82	5	their	their	PRON
ap-2083	82	6	pt	pt	NOUN
ap-2083	82	7	-symmetric	-symmetric	ADJ
ap-2083	82	8	square	square	ADJ
ap-2083	83	1	well	well	NOUN
ap-2083	83	2	0	0	NUM
ap-2083	83	3	10	10	NUM
ap-2083	83	4	20	20	NUM
ap-2083	83	5	30	30	NUM
ap-2083	83	6	40	40	NUM
ap-2083	83	7	50	50	NUM
ap-2083	83	8	60	60	NUM
ap-2083	83	9	70	70	NUM
ap-2083	83	10	0	0	NUM
ap-2083	83	11	5	5	NUM
ap-2083	83	12	10	10	NUM
ap-2083	83	13	15	15	NUM
ap-2083	83	14	20	20	NUM
ap-2083	83	15	25	25	NUM
ap-2083	83	16	30	30	NUM
ap-2083	83	17	µ	µ	NOUN
ap-2083	83	18	r	r	NOUN
ap-2083	83	19	γ	γ	X
ap-2083	83	20	0	0	NUM
ap-2083	83	21	10	10	NUM
ap-2083	83	22	20	20	NUM
ap-2083	83	23	30	30	NUM
ap-2083	83	24	40	40	NUM
ap-2083	83	25	50	50	NUM
ap-2083	83	26	60	60	NUM
ap-2083	83	27	70	70	NUM
ap-2083	83	28	0	0	NUM
ap-2083	83	29	5	5	NUM
ap-2083	83	30	10	10	NUM
ap-2083	83	31	15	15	NUM
ap-2083	83	32	20	20	NUM
ap-2083	83	33	25	25	NUM
ap-2083	83	34	30	30	NUM
ap-2083	83	35	µ	µ	NOUN
ap-2083	83	36	r	r	NOUN
ap-2083	83	37	γ	γ	X
ap-2083	83	38	figure	figure	NOUN
ap-2083	83	39	3	3	NUM
ap-2083	83	40	.	.	PUNCT
ap-2083	84	1	real	real	ADJ
ap-2083	84	2	parts	part	NOUN
ap-2083	84	3	of	of	ADP
ap-2083	84	4	the	the	DET
ap-2083	84	5	eigenvalues	eigenvalue	NOUN
ap-2083	84	6	of	of	ADP
ap-2083	84	7	(	(	PUNCT
ap-2083	84	8	3	3	NUM
ap-2083	84	9	)	)	PUNCT
ap-2083	84	10	(	(	PUNCT
ap-2083	84	11	with	with	ADP
ap-2083	84	12	g	g	PROPN
ap-2083	84	13	=	=	SYM
ap-2083	84	14	0	0	NUM
ap-2083	84	15	)	)	PUNCT
ap-2083	84	16	,	,	PUNCT
ap-2083	84	17	evolving	evolve	VERB
ap-2083	84	18	from	from	ADP
ap-2083	84	19	the	the	DET
ap-2083	84	20	unperturbed	unperturbed	ADJ
ap-2083	84	21	levels	level	NOUN
ap-2083	84	22	with	with	ADP
ap-2083	84	23	n	n	NOUN
ap-2083	84	24	=	=	SYM
ap-2083	84	25	0	0	NUM
ap-2083	84	26	,	,	PUNCT
ap-2083	84	27	.	.	PUNCT
ap-2083	84	28	.	.	PUNCT
ap-2083	85	1	.	.	PUNCT
ap-2083	86	1	,	,	PUNCT
ap-2083	86	2	29	29	NUM
ap-2083	86	3	,	,	PUNCT
ap-2083	86	4	with	with	ADP
ap-2083	86	5	the	the	DET
ap-2083	86	6	delta	delta	NOUN
ap-2083	86	7	functions	function	NOUN
ap-2083	86	8	placed	place	VERB
ap-2083	86	9	into	into	ADP
ap-2083	86	10	the	the	DET
ap-2083	86	11	classical	classical	ADJ
ap-2083	86	12	turning	turning	NOUN
ap-2083	86	13	point	point	NOUN
ap-2083	86	14	of	of	ADP
ap-2083	86	15	the	the	DET
ap-2083	86	16	unperturbed	unperturbed	ADJ
ap-2083	86	17	ground	ground	NOUN
ap-2083	86	18	state	state	NOUN
ap-2083	86	19	(	(	PUNCT
ap-2083	86	20	b	b	NOUN
ap-2083	86	21	=	=	SYM
ap-2083	86	22	1	1	NUM
ap-2083	86	23	,	,	PUNCT
ap-2083	86	24	top	top	ADJ
ap-2083	86	25	)	)	PUNCT
ap-2083	86	26	and	and	CCONJ
ap-2083	86	27	the	the	DET
ap-2083	86	28	third	third	ADJ
ap-2083	86	29	excited	excited	ADJ
ap-2083	86	30	state	state	NOUN
ap-2083	86	31	(	(	PUNCT
ap-2083	86	32	b	b	X
ap-2083	86	33	=	=	NOUN
ap-2083	86	34	√	√	PROPN
ap-2083	86	35	7	7	NUM
ap-2083	86	36	,	,	PUNCT
ap-2083	86	37	bottom	bottom	NOUN
ap-2083	86	38	)	)	PUNCT
ap-2083	86	39	.	.	PUNCT
ap-2083	87	1	model	model	NOUN
ap-2083	87	2	.	.	PUNCT
ap-2083	88	1	in	in	ADP
ap-2083	88	2	their	their	PRON
ap-2083	88	3	terminology	terminology	NOUN
ap-2083	88	4	,	,	PUNCT
ap-2083	88	5	energy	energy	NOUN
ap-2083	88	6	levels	level	NOUN
ap-2083	88	7	which	which	PRON
ap-2083	88	8	coalesce	coalesce	VERB
ap-2083	88	9	at	at	ADP
ap-2083	88	10	a	a	DET
ap-2083	88	11	branch	branch	NOUN
ap-2083	88	12	point	point	NOUN
ap-2083	88	13	and	and	CCONJ
ap-2083	88	14	turn	turn	VERB
ap-2083	88	15	complex	complex	ADJ
ap-2083	88	16	are	be	AUX
ap-2083	88	17	called	call	VERB
ap-2083	88	18	“	"	PUNCT
ap-2083	88	19	fragile	fragile	ADJ
ap-2083	88	20	”	"	PUNCT
ap-2083	88	21	,	,	PUNCT
ap-2083	88	22	while	while	SCONJ
ap-2083	88	23	energy	energy	NOUN
ap-2083	88	24	levels	level	NOUN
ap-2083	88	25	whose	whose	DET
ap-2083	88	26	eigenvalues	eigenvalue	NOUN
ap-2083	88	27	remain	remain	VERB
ap-2083	88	28	real	real	ADJ
ap-2083	88	29	for	for	ADP
ap-2083	88	30	any	any	DET
ap-2083	88	31	strength	strength	NOUN
ap-2083	88	32	of	of	ADP
ap-2083	88	33	the	the	DET
ap-2083	88	34	perturbation	perturbation	NOUN
ap-2083	88	35	are	be	AUX
ap-2083	88	36	called	call	VERB
ap-2083	88	37	“	"	PUNCT
ap-2083	88	38	robust	robust	ADJ
ap-2083	88	39	”	"	PUNCT
ap-2083	88	40	.	.	PUNCT
ap-2083	89	1	the	the	DET
ap-2083	89	2	latter	latter	ADJ
ap-2083	89	3	also	also	ADV
ap-2083	89	4	include	include	VERB
ap-2083	89	5	states	state	NOUN
ap-2083	89	6	where	where	SCONJ
ap-2083	89	7	the	the	DET
ap-2083	89	8	delta	delta	NOUN
ap-2083	89	9	functions	function	NOUN
ap-2083	89	10	happen	happen	VERB
ap-2083	89	11	to	to	PART
ap-2083	89	12	be	be	AUX
ap-2083	89	13	at	at	ADP
ap-2083	89	14	or	or	CCONJ
ap-2083	89	15	close	close	ADJ
ap-2083	89	16	to	to	ADP
ap-2083	89	17	a	a	DET
ap-2083	89	18	node	node	NOUN
ap-2083	89	19	of	of	ADP
ap-2083	89	20	the	the	DET
ap-2083	89	21	wave	wave	NOUN
ap-2083	89	22	function	function	NOUN
ap-2083	89	23	,	,	PUNCT
ap-2083	89	24	and	and	CCONJ
ap-2083	89	25	therefore	therefore	ADV
ap-2083	89	26	remain	remain	VERB
ap-2083	89	27	unaffected	unaffected	ADJ
ap-2083	89	28	by	by	ADP
ap-2083	89	29	the	the	DET
ap-2083	89	30	perturbation	perturbation	NOUN
ap-2083	89	31	.	.	PUNCT
ap-2083	90	1	examples	example	NOUN
ap-2083	90	2	of	of	ADP
ap-2083	90	3	this	this	PRON
ap-2083	90	4	can	can	AUX
ap-2083	90	5	be	be	AUX
ap-2083	90	6	seen	see	VERB
ap-2083	90	7	in	in	ADP
ap-2083	90	8	figure	figure	NOUN
ap-2083	90	9	3	3	NUM
ap-2083	90	10	.	.	PUNCT
ap-2083	91	1	in	in	ADP
ap-2083	91	2	figure	figure	NOUN
ap-2083	91	3	2	2	NUM
ap-2083	91	4	the	the	DET
ap-2083	91	5	ground	ground	NOUN
ap-2083	91	6	state	state	NOUN
ap-2083	91	7	coalesces	coalesce	VERB
ap-2083	91	8	with	with	ADP
ap-2083	91	9	the	the	DET
ap-2083	91	10	first	first	ADJ
ap-2083	91	11	excited	excited	ADJ
ap-2083	91	12	state	state	NOUN
ap-2083	91	13	,	,	PUNCT
ap-2083	91	14	while	while	SCONJ
ap-2083	91	15	in	in	ADP
ap-2083	91	16	figure	figure	NOUN
ap-2083	91	17	3	3	NUM
ap-2083	91	18	,	,	PUNCT
ap-2083	91	19	at	at	ADP
ap-2083	91	20	b	b	NOUN
ap-2083	91	21	=	=	SYM
ap-2083	91	22	1	1	NUM
ap-2083	91	23	(	(	PUNCT
ap-2083	91	24	top	top	ADJ
ap-2083	91	25	panel	panel	NOUN
ap-2083	91	26	)	)	PUNCT
ap-2083	91	27	,	,	PUNCT
ap-2083	91	28	it	it	PRON
ap-2083	91	29	has	have	AUX
ap-2083	91	30	become	become	VERB
ap-2083	91	31	a	a	DET
ap-2083	91	32	single	single	ADJ
ap-2083	91	33	real	real	ADJ
ap-2083	91	34	level	level	NOUN
ap-2083	91	35	for	for	ADP
ap-2083	91	36	any	any	DET
ap-2083	91	37	value	value	NOUN
ap-2083	91	38	of	of	ADP
ap-2083	91	39	γ	γ	NOUN
ap-2083	91	40	,	,	PUNCT
ap-2083	91	41	and	and	CCONJ
ap-2083	91	42	the	the	DET
ap-2083	91	43	first	first	ADJ
ap-2083	91	44	excited	excited	ADJ
ap-2083	91	45	state	state	NOUN
ap-2083	91	46	coalesces	coalesce	VERB
ap-2083	91	47	with	with	ADP
ap-2083	91	48	the	the	DET
ap-2083	91	49	second	second	ADJ
ap-2083	91	50	excited	excited	ADJ
ap-2083	91	51	one	one	NUM
ap-2083	91	52	.	.	PUNCT
ap-2083	92	1	the	the	DET
ap-2083	92	2	question	question	NOUN
ap-2083	92	3	arises	arise	VERB
ap-2083	92	4	how	how	SCONJ
ap-2083	92	5	the	the	DET
ap-2083	92	6	transition	transition	NOUN
ap-2083	92	7	between	between	ADP
ap-2083	92	8	the	the	DET
ap-2083	92	9	different	different	ADJ
ap-2083	92	10	coalescence	coalescence	NOUN
ap-2083	92	11	behaviour	behaviour	NOUN
ap-2083	92	12	occurs	occur	VERB
ap-2083	92	13	.	.	PUNCT
ap-2083	93	1	this	this	PRON
ap-2083	93	2	is	be	AUX
ap-2083	93	3	illustrated	illustrate	VERB
ap-2083	93	4	in	in	ADP
ap-2083	93	5	figure	figure	NOUN
ap-2083	93	6	4	4	NUM
ap-2083	93	7	,	,	PUNCT
ap-2083	93	8	where	where	SCONJ
ap-2083	93	9	the	the	DET
ap-2083	93	10	real	real	ADJ
ap-2083	93	11	and	and	CCONJ
ap-2083	93	12	imaginary	imaginary	ADJ
ap-2083	93	13	parts	part	NOUN
ap-2083	93	14	of	of	ADP
ap-2083	93	15	the	the	DET
ap-2083	93	16	eigenvalues	eigenvalue	NOUN
ap-2083	93	17	emerging	emerge	VERB
ap-2083	93	18	from	from	ADP
ap-2083	93	19	the	the	DET
ap-2083	93	20	ground	ground	NOUN
ap-2083	93	21	state	state	NOUN
ap-2083	93	22	and	and	CCONJ
ap-2083	93	23	the	the	DET
ap-2083	93	24	first	first	ADJ
ap-2083	93	25	two	two	NUM
ap-2083	93	26	excited	excited	ADJ
ap-2083	93	27	levels	level	NOUN
ap-2083	93	28	are	be	AUX
ap-2083	93	29	shown	show	VERB
ap-2083	93	30	as	as	ADP
ap-2083	93	31	functions	function	NOUN
ap-2083	93	32	of	of	ADP
ap-2083	93	33	γ	γ	NOUN
ap-2083	93	34	,	,	PUNCT
ap-2083	93	35	for	for	ADP
ap-2083	93	36	three	three	NUM
ap-2083	93	37	positions	position	NOUN
ap-2083	93	38	of	of	ADP
ap-2083	93	39	the	the	DET
ap-2083	93	40	delta	delta	NOUN
ap-2083	93	41	functions	function	NOUN
ap-2083	93	42	around	around	ADP
ap-2083	93	43	b	b	PROPN
ap-2083	93	44	≈	≈	PROPN
ap-2083	93	45	0.9	0.9	NUM
ap-2083	93	46	.	.	PUNCT
ap-2083	94	1	it	it	PRON
ap-2083	94	2	is	be	AUX
ap-2083	94	3	evident	evident	ADJ
ap-2083	94	4	that	that	SCONJ
ap-2083	94	5	at	at	ADP
ap-2083	94	6	b	b	PROPN
ap-2083	94	7	=	=	SYM
ap-2083	94	8	0.897	0.897	NUM
ap-2083	94	9	the	the	DET
ap-2083	94	10	ground	ground	NOUN
ap-2083	94	11	and	and	CCONJ
ap-2083	94	12	first	first	ADJ
ap-2083	94	13	excited	excited	ADJ
ap-2083	94	14	state	state	NOUN
ap-2083	94	15	still	still	ADV
ap-2083	94	16	coalesce	coalesce	VERB
ap-2083	94	17	,	,	PUNCT
ap-2083	94	18	giving	give	VERB
ap-2083	94	19	rise	rise	NOUN
ap-2083	94	20	to	to	ADP
ap-2083	94	21	a	a	DET
ap-2083	94	22	pair	pair	NOUN
ap-2083	94	23	of	of	ADP
ap-2083	94	24	complex	complex	ADJ
ap-2083	94	25	conjugate	conjugate	NOUN
ap-2083	94	26	eigenvalues	eigenvalue	NOUN
ap-2083	94	27	which	which	PRON
ap-2083	94	28	“	"	PUNCT
ap-2083	94	29	collides	collide	VERB
ap-2083	94	30	”	"	PUNCT
ap-2083	94	31	with	with	ADP
ap-2083	94	32	the	the	DET
ap-2083	94	33	real	real	ADJ
ap-2083	94	34	eigenvalue	eigenvalue	NOUN
ap-2083	94	35	of	of	ADP
ap-2083	94	36	the	the	DET
ap-2083	94	37	second	second	ADJ
ap-2083	94	38	excited	excited	ADJ
ap-2083	94	39	level	level	NOUN
ap-2083	94	40	.	.	PUNCT
ap-2083	95	1	the	the	DET
ap-2083	95	2	latter	latter	ADJ
ap-2083	95	3	then	then	ADV
ap-2083	95	4	turns	turn	VERB
ap-2083	95	5	into	into	ADP
ap-2083	95	6	another	another	DET
ap-2083	95	7	pair	pair	NOUN
ap-2083	95	8	of	of	ADP
ap-2083	95	9	complex	complex	ADJ
ap-2083	95	10	conjugate	conjugate	ADJ
ap-2083	95	11	eigenvalues	eigenvalue	NOUN
ap-2083	95	12	.	.	PUNCT
ap-2083	96	1	the	the	DET
ap-2083	96	2	behaviour	behaviour	NOUN
ap-2083	96	3	is	be	AUX
ap-2083	96	4	similar	similar	ADJ
ap-2083	96	5	for	for	ADP
ap-2083	96	6	b	b	NOUN
ap-2083	96	7	=	=	SYM
ap-2083	96	8	0.915	0.915	NUM
ap-2083	96	9	but	but	CCONJ
ap-2083	96	10	here	here	ADV
ap-2083	96	11	the	the	DET
ap-2083	96	12	pair	pair	NOUN
ap-2083	96	13	of	of	ADP
ap-2083	96	14	complex	complex	ADJ
ap-2083	96	15	eigenvalues	eigenvalue	NOUN
ap-2083	96	16	resulting	result	VERB
ap-2083	96	17	from	from	ADP
ap-2083	96	18	the	the	DET
ap-2083	96	19	merger	merger	NOUN
ap-2083	96	20	of	of	ADP
ap-2083	96	21	the	the	DET
ap-2083	96	22	ground	ground	NOUN
ap-2083	96	23	and	and	CCONJ
ap-2083	96	24	first	first	ADJ
ap-2083	96	25	excited	excited	ADJ
ap-2083	96	26	state	state	NOUN
ap-2083	96	27	disappears	disappear	VERB
ap-2083	96	28	by	by	ADP
ap-2083	96	29	splitting	splitting	NOUN
ap-2083	96	30	into	into	ADP
ap-2083	96	31	118	118	NUM
ap-2083	96	32	vol	vol	NOUN
ap-2083	96	33	.	.	PUNCT
ap-2083	97	1	54	54	NUM
ap-2083	97	2	no	no	NOUN
ap-2083	97	3	.	.	PUNCT
ap-2083	98	1	2/2014	2/2014	NUM
ap-2083	98	2	bec	bec	PROPN
ap-2083	98	3	with	with	ADP
ap-2083	98	4	pt	pt	PROPN
ap-2083	98	5	-	-	ADJ
ap-2083	98	6	symmetric	symmetric	ADJ
ap-2083	98	7	double	double	ADJ
ap-2083	98	8	-	-	PUNCT
ap-2083	98	9	delta	delta	NOUN
ap-2083	98	10	loss	loss	NOUN
ap-2083	98	11	and	and	CCONJ
ap-2083	98	12	gain	gain	NOUN
ap-2083	98	13	:	:	PUNCT
ap-2083	98	14	test	test	NOUN
ap-2083	98	15	of	of	ADP
ap-2083	98	16	estimates	estimate	NOUN
ap-2083	98	17	1	1	NUM
ap-2083	98	18	2	2	NUM
ap-2083	98	19	3	3	NUM
ap-2083	98	20	4	4	NUM
ap-2083	98	21	5	5	NUM
ap-2083	98	22	0	0	NUM
ap-2083	98	23	1	1	NUM
ap-2083	98	24	2	2	NUM
ap-2083	98	25	3	3	NUM
ap-2083	98	26	4	4	NUM
ap-2083	98	27	5	5	NUM
ap-2083	98	28	µ	µ	NOUN
ap-2083	98	29	r	r	NOUN
ap-2083	98	30	γ	γ	X
ap-2083	98	31	b=0.897	b=0.897	X
ap-2083	98	32	b=0.915	b=0.915	X
ap-2083	98	33	b=0.925	b=0.925	X
ap-2083	98	34	−2	−2	NOUN
ap-2083	98	35	−1.5	−1.5	NOUN
ap-2083	98	36	−1	−1	NOUN
ap-2083	99	1	−0.5	−0.5	NOUN
ap-2083	99	2	0	0	NUM
ap-2083	99	3	0.5	0.5	NUM
ap-2083	99	4	1	1	NUM
ap-2083	99	5	1.5	1.5	NUM
ap-2083	99	6	2	2	NUM
ap-2083	99	7	0	0	NUM
ap-2083	99	8	1	1	NUM
ap-2083	99	9	2	2	NUM
ap-2083	99	10	3	3	NUM
ap-2083	99	11	4	4	NUM
ap-2083	99	12	5	5	NUM
ap-2083	99	13	µ	µ	NOUN
ap-2083	99	14	i	i	PROPN
ap-2083	99	15	γ	γ	PROPN
ap-2083	99	16	b=0.897	b=0.897	X
ap-2083	99	17	b=0.915	b=0.915	X
ap-2083	99	18	b=0.925	b=0.925	NOUN
ap-2083	99	19	figure	figure	NOUN
ap-2083	99	20	4	4	NUM
ap-2083	99	21	.	.	PUNCT
ap-2083	100	1	change	change	NOUN
ap-2083	100	2	in	in	ADP
ap-2083	100	3	the	the	DET
ap-2083	100	4	coalescence	coalescence	NOUN
ap-2083	100	5	and	and	CCONJ
ap-2083	100	6	bifurcation	bifurcation	NOUN
ap-2083	100	7	behaviour	behaviour	NOUN
ap-2083	100	8	of	of	ADP
ap-2083	100	9	the	the	DET
ap-2083	100	10	three	three	NUM
ap-2083	100	11	lowest	low	ADJ
ap-2083	100	12	eigenstates	eigenstate	NOUN
ap-2083	100	13	as	as	ADP
ap-2083	100	14	a	a	DET
ap-2083	100	15	function	function	NOUN
ap-2083	100	16	of	of	ADP
ap-2083	100	17	γ	γ	NOUN
ap-2083	100	18	at	at	ADP
ap-2083	100	19	three	three	NUM
ap-2083	100	20	different	different	ADJ
ap-2083	100	21	positions	position	NOUN
ap-2083	100	22	of	of	ADP
ap-2083	100	23	the	the	DET
ap-2083	100	24	delta	delta	NOUN
ap-2083	100	25	functions	function	NOUN
ap-2083	100	26	in	in	ADP
ap-2083	100	27	the	the	DET
ap-2083	100	28	vicinity	vicinity	NOUN
ap-2083	100	29	of	of	ADP
ap-2083	100	30	b	b	PROPN
ap-2083	100	31	=	=	SYM
ap-2083	100	32	0.9	0.9	NUM
ap-2083	100	33	.	.	PUNCT
ap-2083	101	1	(	(	PUNCT
ap-2083	101	2	top	top	ADJ
ap-2083	101	3	:	:	PUNCT
ap-2083	101	4	real	real	ADJ
ap-2083	101	5	parts	part	NOUN
ap-2083	101	6	,	,	PUNCT
ap-2083	101	7	bottom	bottom	ADJ
ap-2083	101	8	:	:	PUNCT
ap-2083	101	9	imaginary	imaginary	ADJ
ap-2083	101	10	parts	part	NOUN
ap-2083	101	11	of	of	ADP
ap-2083	101	12	the	the	DET
ap-2083	101	13	eigenvalues	eigenvalue	NOUN
ap-2083	101	14	.	.	PUNCT
ap-2083	101	15	)	)	PUNCT
ap-2083	102	1	two	two	NUM
ap-2083	102	2	real	real	ADJ
ap-2083	102	3	eigenvalues	eigenvalue	VERB
ap-2083	102	4	the	the	DET
ap-2083	102	5	lower	low	ADJ
ap-2083	102	6	of	of	ADP
ap-2083	102	7	which	which	PRON
ap-2083	102	8	remains	remain	VERB
ap-2083	102	9	real	real	ADJ
ap-2083	102	10	for	for	ADP
ap-2083	102	11	any	any	DET
ap-2083	102	12	γ	γ	NOUN
ap-2083	102	13	,	,	PUNCT
ap-2083	102	14	while	while	SCONJ
ap-2083	102	15	the	the	DET
ap-2083	102	16	higher	high	ADJ
ap-2083	102	17	after	after	ADP
ap-2083	102	18	a	a	DET
ap-2083	102	19	small	small	ADJ
ap-2083	102	20	interval	interval	NOUN
ap-2083	102	21	of	of	ADP
ap-2083	102	22	γ	γ	X
ap-2083	102	23	coalesces	coalesce	VERB
ap-2083	102	24	with	with	ADP
ap-2083	102	25	the	the	DET
ap-2083	102	26	real	real	ADJ
ap-2083	102	27	eigenvalue	eigenvalue	NOUN
ap-2083	102	28	of	of	ADP
ap-2083	102	29	the	the	DET
ap-2083	102	30	second	second	ADJ
ap-2083	102	31	excited	excited	ADJ
ap-2083	102	32	state	state	NOUN
ap-2083	102	33	and	and	CCONJ
ap-2083	102	34	a	a	DET
ap-2083	102	35	new	new	ADJ
ap-2083	102	36	pair	pair	NOUN
ap-2083	102	37	of	of	ADP
ap-2083	102	38	complex	complex	ADJ
ap-2083	102	39	eigenvalues	eigenvalue	NOUN
ap-2083	102	40	is	be	AUX
ap-2083	102	41	born	bear	VERB
ap-2083	102	42	.	.	PUNCT
ap-2083	103	1	finally	finally	ADV
ap-2083	103	2	,	,	PUNCT
ap-2083	103	3	at	at	ADP
ap-2083	103	4	b	b	NOUN
ap-2083	103	5	=	=	SYM
ap-2083	103	6	0.925	0.925	NUM
ap-2083	103	7	the	the	DET
ap-2083	103	8	transition	transition	NOUN
ap-2083	103	9	has	have	AUX
ap-2083	103	10	occured	occur	VERB
ap-2083	103	11	,	,	PUNCT
ap-2083	103	12	the	the	DET
ap-2083	103	13	ground	ground	NOUN
ap-2083	103	14	state	state	NOUN
ap-2083	103	15	has	have	AUX
ap-2083	103	16	become	become	VERB
ap-2083	103	17	a	a	DET
ap-2083	103	18	single	single	ADJ
ap-2083	103	19	real	real	ADJ
ap-2083	103	20	level	level	NOUN
ap-2083	103	21	,	,	PUNCT
ap-2083	103	22	and	and	CCONJ
ap-2083	103	23	the	the	DET
ap-2083	103	24	first	first	ADJ
ap-2083	103	25	two	two	NUM
ap-2083	103	26	excited	excited	ADJ
ap-2083	103	27	states	state	NOUN
ap-2083	103	28	come	come	VERB
ap-2083	103	29	together	together	ADV
ap-2083	103	30	.	.	PUNCT
ap-2083	104	1	we	we	PRON
ap-2083	104	2	note	note	VERB
ap-2083	104	3	again	again	ADV
ap-2083	104	4	that	that	SCONJ
ap-2083	104	5	similar	similar	ADJ
ap-2083	104	6	behaviour	behaviour	NOUN
ap-2083	104	7	was	be	AUX
ap-2083	104	8	found	find	VERB
ap-2083	104	9	by	by	ADP
ap-2083	104	10	krejčiřík	krejčiřík	NOUN
ap-2083	104	11	and	and	CCONJ
ap-2083	104	12	siegl	siegl	VERB
ap-2083	105	1	[	[	X
ap-2083	105	2	20	20	NUM
ap-2083	105	3	]	]	PUNCT
ap-2083	105	4	in	in	ADP
ap-2083	105	5	their	their	PRON
ap-2083	105	6	studies	study	NOUN
ap-2083	105	7	of	of	ADP
ap-2083	105	8	eigenvalues	eigenvalue	NOUN
ap-2083	105	9	in	in	ADP
ap-2083	105	10	a	a	DET
ap-2083	105	11	square	square	ADJ
ap-2083	105	12	well	well	NOUN
ap-2083	105	13	with	with	ADP
ap-2083	105	14	robin	robin	PROPN
ap-2083	105	15	boundary	boundary	ADJ
ap-2083	105	16	conditions	condition	NOUN
ap-2083	105	17	(	(	PUNCT
ap-2083	105	18	cf	cf	NOUN
ap-2083	105	19	.	.	PUNCT
ap-2083	105	20	figure	figure	NOUN
ap-2083	105	21	6	6	NUM
ap-2083	105	22	in	in	ADP
ap-2083	105	23	[	[	X
ap-2083	105	24	20	20	NUM
ap-2083	105	25	]	]	NUM
ap-2083	105	26	)	)	PUNCT
ap-2083	105	27	.	.	PUNCT
ap-2083	106	1	we	we	PRON
ap-2083	106	2	now	now	ADV
ap-2083	106	3	proceed	proceed	VERB
ap-2083	106	4	to	to	PART
ap-2083	106	5	results	result	NOUN
ap-2083	106	6	for	for	ADP
ap-2083	106	7	nonvanishing	nonvanishe	VERB
ap-2083	106	8	nonlinearity	nonlinearity	NOUN
ap-2083	106	9	.	.	PUNCT
ap-2083	107	1	figure	figure	NOUN
ap-2083	107	2	5	5	NUM
ap-2083	107	3	shows	show	VERB
ap-2083	107	4	the	the	DET
ap-2083	107	5	spectrum	spectrum	NOUN
ap-2083	107	6	for	for	ADP
ap-2083	107	7	a	a	DET
ap-2083	107	8	value	value	NOUN
ap-2083	107	9	of	of	ADP
ap-2083	107	10	g	g	NOUN
ap-2083	107	11	=	=	NOUN
ap-2083	107	12	5	5	NUM
ap-2083	107	13	with	with	ADP
ap-2083	107	14	the	the	DET
ap-2083	107	15	delta	delta	NOUN
ap-2083	107	16	functions	function	NOUN
ap-2083	107	17	placed	place	VERB
ap-2083	107	18	at	at	ADP
ap-2083	107	19	b	b	NOUN
ap-2083	107	20	=	=	SYM
ap-2083	107	21	1	1	NUM
ap-2083	107	22	.	.	PUNCT
ap-2083	108	1	the	the	DET
ap-2083	108	2	overall	overall	ADJ
ap-2083	108	3	behaviour	behaviour	NOUN
ap-2083	108	4	is	be	AUX
ap-2083	108	5	similar	similar	ADJ
ap-2083	108	6	(	(	PUNCT
ap-2083	108	7	many	many	ADJ
ap-2083	108	8	states	state	NOUN
ap-2083	108	9	coalesce	coalesce	VERB
ap-2083	108	10	at	at	ADP
ap-2083	108	11	branch	branch	NOUN
ap-2083	108	12	points	point	NOUN
ap-2083	108	13	)	)	PUNCT
ap-2083	108	14	,	,	PUNCT
ap-2083	108	15	but	but	CCONJ
ap-2083	108	16	there	there	PRON
ap-2083	108	17	are	be	VERB
ap-2083	108	18	significant	significant	ADJ
ap-2083	108	19	differences	difference	NOUN
ap-2083	108	20	.	.	PUNCT
ap-2083	109	1	like	like	INTJ
ap-2083	109	2	in	in	ADP
ap-2083	109	3	our	our	PRON
ap-2083	109	4	previous	previous	ADJ
ap-2083	109	5	studies	study	NOUN
ap-2083	109	6	of	of	ADP
ap-2083	109	7	pt	pt	NOUN
ap-2083	109	8	-symmetric	-symmetric	ADJ
ap-2083	109	9	hamiltonians	hamiltonian	NOUN
ap-2083	109	10	with	with	ADP
ap-2083	109	11	nonlinearity	nonlinearity	NOUN
ap-2083	109	12	[	[	X
ap-2083	109	13	2–6	2–6	NOUN
ap-2083	109	14	,	,	PUNCT
ap-2083	109	15	25	25	NUM
ap-2083	109	16	]	]	PUNCT
ap-2083	109	17	,	,	PUNCT
ap-2083	109	18	pairs	pair	NOUN
ap-2083	109	19	of	of	ADP
ap-2083	109	20	complex	complex	ADJ
ap-2083	109	21	conjugate	conjugate	ADJ
ap-2083	109	22	eigenvalues	eigenvalue	NOUN
ap-2083	109	23	(	(	PUNCT
ap-2083	109	24	imaginary	imaginary	ADJ
ap-2083	109	25	parts	part	NOUN
ap-2083	109	26	not	not	PART
ap-2083	109	27	shown	show	VERB
ap-2083	109	28	)	)	PUNCT
ap-2083	109	29	appear	appear	VERB
ap-2083	109	30	before	before	SCONJ
ap-2083	109	31	the	the	DET
ap-2083	109	32	branch	branch	NOUN
ap-2083	109	33	points	point	NOUN
ap-2083	109	34	are	be	AUX
ap-2083	109	35	reached	reach	VERB
ap-2083	109	36	.	.	PUNCT
ap-2083	110	1	again	again	ADV
ap-2083	110	2	there	there	PRON
ap-2083	110	3	exist	exist	VERB
ap-2083	110	4	“	"	PUNCT
ap-2083	110	5	robust	robust	ADJ
ap-2083	110	6	”	"	PUNCT
ap-2083	110	7	levels	level	NOUN
ap-2083	110	8	whose	whose	DET
ap-2083	110	9	eigenvalues	eigenvalue	NOUN
ap-2083	110	10	remain	remain	VERB
ap-2083	110	11	real	real	ADJ
ap-2083	110	12	for	for	ADP
ap-2083	110	13	any	any	DET
ap-2083	110	14	value	value	NOUN
ap-2083	110	15	of	of	ADP
ap-2083	110	16	γ	γ	PROPN
ap-2083	110	17	.	.	PROPN
ap-2083	110	18	4	4	NUM
ap-2083	110	19	.	.	PUNCT
ap-2083	110	20	eigenvalue	eigenvalue	ADJ
ap-2083	110	21	shifts	shift	NOUN
ap-2083	110	22	for	for	ADP
ap-2083	110	23	vanishing	vanish	VERB
ap-2083	110	24	nonlinearity	nonlinearity	NOUN
ap-2083	110	25	,	,	PUNCT
ap-2083	110	26	the	the	DET
ap-2083	110	27	upper	upper	ADJ
ap-2083	110	28	part	part	NOUN
ap-2083	110	29	of	of	ADP
ap-2083	110	30	figure	figure	NOUN
ap-2083	110	31	6	6	NUM
ap-2083	110	32	shows	show	NOUN
ap-2083	110	33	,	,	PUNCT
ap-2083	110	34	for	for	ADP
ap-2083	110	35	γ	γ	X
ap-2083	110	36	=	=	SYM
ap-2083	110	37	1	1	NUM
ap-2083	110	38	and	and	CCONJ
ap-2083	110	39	different	different	ADJ
ap-2083	110	40	positions	position	NOUN
ap-2083	110	41	of	of	ADP
ap-2083	110	42	the	the	DET
ap-2083	110	43	delta	delta	NOUN
ap-2083	110	44	functions	function	NOUN
ap-2083	110	45	,	,	PUNCT
ap-2083	110	46	the	the	DET
ap-2083	110	47	shifts	shift	NOUN
ap-2083	110	48	of	of	ADP
ap-2083	110	49	the	the	DET
ap-2083	110	50	eigenvalues	eigenvalue	NOUN
ap-2083	110	51	as	as	ADP
ap-2083	110	52	a	a	DET
ap-2083	110	53	function	function	NOUN
ap-2083	110	54	of	of	ADP
ap-2083	110	55	the	the	DET
ap-2083	110	56	quantum	quantum	ADJ
ap-2083	110	57	number	number	NOUN
ap-2083	110	58	n	n	NUM
ap-2083	110	59	in	in	ADP
ap-2083	110	60	comparison	comparison	NOUN
ap-2083	110	61	with	with	ADP
ap-2083	110	62	the	the	DET
ap-2083	110	63	predicted	predict	VERB
ap-2083	110	64	shrink	shrink	NOUN
ap-2083	110	65	rates	rate	NOUN
ap-2083	110	66	of	of	ADP
ap-2083	110	67	n−1/2	n−1/2	PROPN
ap-2083	110	68	of	of	ADP
ap-2083	110	69	[	[	X
ap-2083	110	70	9	9	NUM
ap-2083	110	71	]	]	PUNCT
ap-2083	110	72	and	and	CCONJ
ap-2083	110	73	the	the	DET
ap-2083	110	74	improved	improved	ADJ
ap-2083	110	75	0	0	NUM
ap-2083	110	76	10	10	NUM
ap-2083	110	77	20	20	NUM
ap-2083	110	78	30	30	NUM
ap-2083	110	79	40	40	NUM
ap-2083	110	80	50	50	NUM
ap-2083	110	81	60	60	NUM
ap-2083	110	82	0	0	NUM
ap-2083	110	83	1	1	NUM
ap-2083	110	84	2	2	NUM
ap-2083	110	85	3	3	NUM
ap-2083	110	86	4	4	NUM
ap-2083	110	87	5	5	NUM
ap-2083	110	88	6	6	NUM
ap-2083	110	89	7	7	NUM
ap-2083	110	90	8	8	NUM
ap-2083	110	91	9	9	NUM
ap-2083	110	92	µ	µ	NOUN
ap-2083	110	93	r	r	NOUN
ap-2083	110	94	γ	γ	X
ap-2083	110	95	figure	figure	NOUN
ap-2083	110	96	5	5	NUM
ap-2083	110	97	.	.	PUNCT
ap-2083	111	1	real	real	ADJ
ap-2083	111	2	parts	part	NOUN
ap-2083	111	3	of	of	ADP
ap-2083	111	4	the	the	DET
ap-2083	111	5	eigenvalues	eigenvalue	NOUN
ap-2083	111	6	of	of	ADP
ap-2083	111	7	(	(	PUNCT
ap-2083	111	8	3	3	NUM
ap-2083	111	9	)	)	PUNCT
ap-2083	111	10	with	with	ADP
ap-2083	111	11	finite	finite	ADJ
ap-2083	111	12	nonlinearity	nonlinearity	NOUN
ap-2083	111	13	g	g	NOUN
ap-2083	111	14	=	=	SYM
ap-2083	111	15	5	5	NUM
ap-2083	111	16	,	,	PUNCT
ap-2083	111	17	evolving	evolve	VERB
ap-2083	111	18	from	from	ADP
ap-2083	111	19	the	the	DET
ap-2083	111	20	unperturbed	unperturbed	ADJ
ap-2083	111	21	levels	level	NOUN
ap-2083	111	22	with	with	ADP
ap-2083	111	23	n	n	NOUN
ap-2083	111	24	=	=	SYM
ap-2083	111	25	0	0	NUM
ap-2083	111	26	,	,	PUNCT
ap-2083	111	27	.	.	PUNCT
ap-2083	111	28	.	.	PUNCT
ap-2083	112	1	.	.	PUNCT
ap-2083	113	1	,	,	PUNCT
ap-2083	113	2	29	29	NUM
ap-2083	113	3	,	,	PUNCT
ap-2083	113	4	for	for	ADP
ap-2083	113	5	b	b	NOUN
ap-2083	113	6	=	=	SYM
ap-2083	113	7	1	1	NUM
ap-2083	113	8	in	in	ADP
ap-2083	113	9	dependence	dependence	NOUN
ap-2083	113	10	on	on	ADP
ap-2083	113	11	the	the	DET
ap-2083	113	12	strength	strength	NOUN
ap-2083	113	13	of	of	ADP
ap-2083	113	14	the	the	DET
ap-2083	113	15	non	non	NOUN
ap-2083	113	16	-	-	NOUN
ap-2083	113	17	hermiticity	hermiticity	NOUN
ap-2083	113	18	.	.	PUNCT
ap-2083	114	1	blue	blue	ADJ
ap-2083	114	2	lines	line	NOUN
ap-2083	114	3	denote	denote	VERB
ap-2083	114	4	purely	purely	ADV
ap-2083	114	5	real	real	ADJ
ap-2083	114	6	eigenvalues	eigenvalue	NOUN
ap-2083	114	7	,	,	PUNCT
ap-2083	114	8	whereas	whereas	SCONJ
ap-2083	114	9	real	real	ADJ
ap-2083	114	10	parts	part	NOUN
ap-2083	114	11	of	of	ADP
ap-2083	114	12	complex	complex	ADJ
ap-2083	114	13	eigenvalues	eigenvalue	NOUN
ap-2083	114	14	(	(	PUNCT
ap-2083	114	15	single	single	ADJ
ap-2083	114	16	lines	line	NOUN
ap-2083	114	17	)	)	PUNCT
ap-2083	114	18	are	be	AUX
ap-2083	114	19	shown	show	VERB
ap-2083	114	20	in	in	ADP
ap-2083	114	21	red	red	PROPN
ap-2083	114	22	.	.	PUNCT
ap-2083	115	1	10−4	10−4	NUM
ap-2083	115	2	10−3	10−3	NUM
ap-2083	115	3	10−2	10−2	NUM
ap-2083	115	4	10−1	10−1	NUM
ap-2083	115	5	100	100	NUM
ap-2083	115	6	1	1	NUM
ap-2083	115	7	10	10	NUM
ap-2083	115	8	100	100	NUM
ap-2083	115	9	∆	∆	NOUN
ap-2083	115	10	µ	µ	VERB
ap-2083	115	11	n	n	PRON
ap-2083	115	12	∝	∝	PROPN
ap-2083	115	13	n−0.5	n−0.5	NUM
ap-2083	115	14	∝	∝	PROPN
ap-2083	115	15	log(n)/n3/2	log(n)/n3/2	PUNCT
ap-2083	115	16	b	b	NOUN
ap-2083	115	17	=	=	SYM
ap-2083	115	18	1	1	NUM
ap-2083	115	19	b	b	NOUN
ap-2083	115	20	=	=	SYM
ap-2083	115	21	2	2	NUM
ap-2083	115	22	b	b	NOUN
ap-2083	115	23	=	=	SYM
ap-2083	115	24	3	3	NUM
ap-2083	115	25	b	b	NOUN
ap-2083	115	26	=	=	SYM
ap-2083	115	27	5	5	NUM
ap-2083	115	28	0.1	0.1	NUM
ap-2083	115	29	1	1	NUM
ap-2083	115	30	1	1	NUM
ap-2083	115	31	10	10	NUM
ap-2083	115	32	100	100	NUM
ap-2083	115	33	∆	∆	NOUN
ap-2083	115	34	µ	µ	VERB
ap-2083	115	35	n	n	PRON
ap-2083	115	36	∝	∝	PROPN
ap-2083	115	37	n−0.5	n−0.5	NUM
ap-2083	115	38	∝	∝	PROPN
ap-2083	115	39	log(n)/n3/2	log(n)/n3/2	PUNCT
ap-2083	115	40	b	b	NOUN
ap-2083	115	41	=	=	SYM
ap-2083	115	42	1	1	NUM
ap-2083	115	43	b	b	NOUN
ap-2083	115	44	=	=	SYM
ap-2083	115	45	2	2	NUM
ap-2083	115	46	b	b	NOUN
ap-2083	115	47	=	=	SYM
ap-2083	115	48	3	3	NUM
ap-2083	115	49	b	b	NOUN
ap-2083	115	50	=	=	SYM
ap-2083	115	51	5	5	NUM
ap-2083	115	52	figure	figure	NOUN
ap-2083	115	53	6	6	NUM
ap-2083	115	54	.	.	PUNCT
ap-2083	115	55	shift	shift	NOUN
ap-2083	115	56	of	of	ADP
ap-2083	115	57	the	the	DET
ap-2083	115	58	eigenvalues	eigenvalue	NOUN
ap-2083	115	59	for	for	ADP
ap-2083	115	60	γ	γ	X
ap-2083	115	61	=	=	SYM
ap-2083	115	62	1	1	NUM
ap-2083	115	63	and	and	CCONJ
ap-2083	115	64	different	different	ADJ
ap-2083	115	65	positions	position	NOUN
ap-2083	115	66	of	of	ADP
ap-2083	115	67	the	the	DET
ap-2083	115	68	delta	delta	NOUN
ap-2083	115	69	functions	function	NOUN
ap-2083	115	70	in	in	ADP
ap-2083	115	71	comparison	comparison	NOUN
ap-2083	115	72	with	with	ADP
ap-2083	115	73	the	the	DET
ap-2083	115	74	mathematically	mathematically	ADV
ap-2083	115	75	estimated	estimate	VERB
ap-2083	115	76	n−1/2	n−1/2	PROPN
ap-2083	115	77	and	and	CCONJ
ap-2083	115	78	log(n)/n3/2	log(n)/n3/2	NOUN
ap-2083	115	79	dependence	dependence	NOUN
ap-2083	115	80	.	.	PUNCT
ap-2083	116	1	top	top	ADJ
ap-2083	116	2	:	:	PUNCT
ap-2083	116	3	vanishing	vanish	VERB
ap-2083	116	4	nonlinearity	nonlinearity	NOUN
ap-2083	116	5	,	,	PUNCT
ap-2083	116	6	g	g	NOUN
ap-2083	116	7	=	=	SYM
ap-2083	116	8	0	0	NUM
ap-2083	116	9	,	,	PUNCT
ap-2083	116	10	bottom	bottom	NOUN
ap-2083	116	11	:	:	PUNCT
ap-2083	116	12	g	g	NOUN
ap-2083	116	13	=	=	SYM
ap-2083	116	14	2	2	X
ap-2083	116	15	.	.	NUM
ap-2083	116	16	estimate	estimate	NOUN
ap-2083	116	17	of	of	ADP
ap-2083	116	18	log(n)/n3/2	log(n)/n3/2	PROPN
ap-2083	116	19	[	[	X
ap-2083	116	20	10	10	NUM
ap-2083	116	21	]	]	PUNCT
ap-2083	116	22	.	.	PUNCT
ap-2083	117	1	it	it	PRON
ap-2083	117	2	can	can	AUX
ap-2083	117	3	be	be	AUX
ap-2083	117	4	recognized	recognize	VERB
ap-2083	117	5	that	that	SCONJ
ap-2083	117	6	the	the	DET
ap-2083	117	7	n−1/2	n−1/2	PROPN
ap-2083	117	8	dependence	dependence	NOUN
ap-2083	117	9	is	be	AUX
ap-2083	117	10	indeed	indeed	ADV
ap-2083	117	11	an	an	DET
ap-2083	117	12	upper	upper	ADJ
ap-2083	117	13	bound	bind	VERB
ap-2083	117	14	on	on	ADP
ap-2083	117	15	the	the	DET
ap-2083	117	16	shrink	shrink	NOUN
ap-2083	117	17	rate	rate	NOUN
ap-2083	117	18	,	,	PUNCT
ap-2083	117	19	and	and	CCONJ
ap-2083	117	20	,	,	PUNCT
ap-2083	117	21	moreover	moreover	ADV
ap-2083	117	22	,	,	PUNCT
ap-2083	117	23	that	that	SCONJ
ap-2083	117	24	the	the	DET
ap-2083	117	25	improved	improved	ADJ
ap-2083	117	26	estimate	estimate	NOUN
ap-2083	117	27	is	be	AUX
ap-2083	117	28	in	in	ADP
ap-2083	117	29	excellent	excellent	ADJ
ap-2083	117	30	agreement	agreement	NOUN
ap-2083	117	31	with	with	ADP
ap-2083	117	32	the	the	DET
ap-2083	117	33	numerical	numerical	PROPN
ap-2083	117	34	data	data	PROPN
ap-2083	117	35	,	,	PUNCT
ap-2083	117	36	irrespective	irrespective	ADV
ap-2083	117	37	of	of	ADP
ap-2083	117	38	the	the	DET
ap-2083	117	39	position	position	NOUN
ap-2083	117	40	of	of	ADP
ap-2083	117	41	the	the	DET
ap-2083	117	42	deltas	delta	NOUN
ap-2083	117	43	!	!	PUNCT
ap-2083	118	1	the	the	DET
ap-2083	118	2	picture	picture	NOUN
ap-2083	118	3	changes	change	VERB
ap-2083	118	4	when	when	SCONJ
ap-2083	118	5	the	the	DET
ap-2083	118	6	nonlinearity	nonlinearity	NOUN
ap-2083	118	7	is	be	AUX
ap-2083	118	8	switched	switch	VERB
ap-2083	118	9	on	on	ADP
ap-2083	118	10	.	.	PUNCT
ap-2083	119	1	the	the	DET
ap-2083	119	2	bottom	bottom	ADJ
ap-2083	119	3	part	part	NOUN
ap-2083	119	4	of	of	ADP
ap-2083	119	5	figure	figure	NOUN
ap-2083	119	6	6	6	NUM
ap-2083	119	7	shows	show	VERB
ap-2083	119	8	eigenvalue	eigenvalue	ADJ
ap-2083	119	9	shifts	shift	NOUN
ap-2083	119	10	for	for	ADP
ap-2083	119	11	g	g	NOUN
ap-2083	119	12	=	=	SYM
ap-2083	119	13	2	2	NUM
ap-2083	119	14	,	,	PUNCT
ap-2083	119	15	and	and	CCONJ
ap-2083	119	16	different	different	ADJ
ap-2083	119	17	positions	position	NOUN
ap-2083	119	18	of	of	ADP
ap-2083	119	19	the	the	DET
ap-2083	119	20	imaginary	imaginary	ADJ
ap-2083	119	21	delta	delta	NOUN
ap-2083	119	22	potentials	potential	VERB
ap-2083	119	23	.	.	PUNCT
ap-2083	120	1	from	from	ADP
ap-2083	120	2	the	the	DET
ap-2083	120	3	comparison	comparison	NOUN
ap-2083	120	4	of	of	ADP
ap-2083	120	5	the	the	DET
ap-2083	120	6	scales	scale	NOUN
ap-2083	120	7	of	of	ADP
ap-2083	120	8	the	the	DET
ap-2083	120	9	vertical	vertical	ADJ
ap-2083	120	10	axes	axis	NOUN
ap-2083	120	11	in	in	ADP
ap-2083	120	12	figure	figure	NOUN
ap-2083	120	13	6	6	NUM
ap-2083	120	14	it	it	PRON
ap-2083	120	15	can	can	AUX
ap-2083	120	16	119	119	NUM
ap-2083	120	17	d.	d.	PROPN
ap-2083	120	18	haag	haag	PROPN
ap-2083	120	19	,	,	PUNCT
ap-2083	120	20	h.	h.	PROPN
ap-2083	120	21	cartarius	cartarius	PROPN
ap-2083	120	22	,	,	PUNCT
ap-2083	120	23	g.	g.	PROPN
ap-2083	120	24	wunner	wunner	PROPN
ap-2083	120	25	acta	acta	PROPN
ap-2083	120	26	polytechnica	polytechnica	PROPN
ap-2083	120	27	10−2	10−2	NUM
ap-2083	120	28	100	100	NUM
ap-2083	120	29	102	102	NUM
ap-2083	120	30	1	1	NUM
ap-2083	120	31	10	10	NUM
ap-2083	120	32	∆	∆	PROPN
ap-2083	120	33	µ	µ	X
ap-2083	120	34	n	n	PRON
ap-2083	120	35	γ	γ	X
ap-2083	120	36	=	=	SYM
ap-2083	120	37	5	5	NUM
ap-2083	120	38	γ	γ	X
ap-2083	120	39	=	=	SYM
ap-2083	120	40	10	10	NUM
ap-2083	120	41	γ	γ	X
ap-2083	120	42	=	=	SYM
ap-2083	120	43	15	15	NUM
ap-2083	120	44	γ	γ	X
ap-2083	120	45	=	=	SYM
ap-2083	120	46	20	20	NUM
ap-2083	120	47	figure	figure	NOUN
ap-2083	120	48	7	7	NUM
ap-2083	120	49	.	.	PUNCT
ap-2083	120	50	shift	shift	NOUN
ap-2083	120	51	of	of	ADP
ap-2083	120	52	the	the	DET
ap-2083	120	53	real	real	ADJ
ap-2083	120	54	and	and	CCONJ
ap-2083	120	55	complex	complex	ADJ
ap-2083	120	56	eigenvalues	eigenvalue	NOUN
ap-2083	120	57	for	for	ADP
ap-2083	120	58	growing	grow	VERB
ap-2083	120	59	values	value	NOUN
ap-2083	120	60	of	of	ADP
ap-2083	120	61	γ	γ	PROPN
ap-2083	120	62	for	for	ADP
ap-2083	120	63	b	b	NOUN
ap-2083	120	64	=	=	SYM
ap-2083	120	65	0.2	0.2	NUM
ap-2083	120	66	,	,	PUNCT
ap-2083	120	67	and	and	CCONJ
ap-2083	120	68	g	g	PROPN
ap-2083	120	69	=	=	SYM
ap-2083	120	70	0	0	X
ap-2083	120	71	.	.	PUNCT
ap-2083	120	72	be	be	AUX
ap-2083	120	73	seen	see	VERB
ap-2083	120	74	that	that	SCONJ
ap-2083	120	75	with	with	ADP
ap-2083	120	76	nonlinearity	nonlinearity	NOUN
ap-2083	120	77	the	the	DET
ap-2083	120	78	shifts	shift	NOUN
ap-2083	120	79	even	even	ADV
ap-2083	120	80	for	for	ADP
ap-2083	120	81	the	the	DET
ap-2083	120	82	highest	high	ADJ
ap-2083	120	83	states	state	NOUN
ap-2083	120	84	are	be	AUX
ap-2083	120	85	still	still	ADV
ap-2083	120	86	bigger	big	ADJ
ap-2083	120	87	than	than	ADP
ap-2083	120	88	0.1	0.1	NUM
ap-2083	120	89	,	,	PUNCT
ap-2083	120	90	while	while	SCONJ
ap-2083	120	91	they	they	PRON
ap-2083	120	92	have	have	AUX
ap-2083	120	93	already	already	ADV
ap-2083	120	94	dropped	drop	VERB
ap-2083	120	95	well	well	ADV
ap-2083	120	96	below	below	ADP
ap-2083	120	97	10−2	10−2	NUM
ap-2083	120	98	in	in	ADP
ap-2083	120	99	the	the	DET
ap-2083	120	100	linear	linear	ADJ
ap-2083	120	101	case	case	NOUN
ap-2083	120	102	.	.	PUNCT
ap-2083	121	1	furthermore	furthermore	ADV
ap-2083	121	2	,	,	PUNCT
ap-2083	121	3	the	the	DET
ap-2083	121	4	shrink	shrink	NOUN
ap-2083	121	5	rate	rate	NOUN
ap-2083	121	6	is	be	AUX
ap-2083	121	7	found	find	VERB
ap-2083	121	8	to	to	PART
ap-2083	121	9	be	be	AUX
ap-2083	121	10	slower	slow	ADJ
ap-2083	121	11	(	(	PUNCT
ap-2083	121	12	approximately	approximately	ADV
ap-2083	121	13	proportional	proportional	ADJ
ap-2083	121	14	to	to	ADP
ap-2083	121	15	n−0.37	n−0.37	PROPN
ap-2083	121	16	)	)	PUNCT
ap-2083	121	17	than	than	SCONJ
ap-2083	121	18	predicted	predict	VERB
ap-2083	121	19	by	by	ADP
ap-2083	121	20	both	both	DET
ap-2083	121	21	rigorous	rigorous	ADJ
ap-2083	121	22	mathematical	mathematical	ADJ
ap-2083	121	23	estimates	estimate	NOUN
ap-2083	121	24	for	for	ADP
ap-2083	121	25	the	the	DET
ap-2083	121	26	linear	linear	ADJ
ap-2083	121	27	case	case	NOUN
ap-2083	121	28	.	.	PUNCT
ap-2083	122	1	we	we	PRON
ap-2083	122	2	therefore	therefore	ADV
ap-2083	122	3	find	find	VERB
ap-2083	122	4	significant	significant	ADJ
ap-2083	122	5	differences	difference	NOUN
ap-2083	122	6	in	in	ADP
ap-2083	122	7	the	the	DET
ap-2083	122	8	shrink	shrink	NOUN
ap-2083	122	9	rates	rate	NOUN
ap-2083	122	10	with	with	ADP
ap-2083	122	11	and	and	CCONJ
ap-2083	122	12	without	without	ADP
ap-2083	122	13	nonlinearity	nonlinearity	NOUN
ap-2083	122	14	.	.	PUNCT
ap-2083	123	1	for	for	ADP
ap-2083	123	2	small	small	ADJ
ap-2083	123	3	γ	γ	NOUN
ap-2083	123	4	,	,	PUNCT
ap-2083	123	5	all	all	DET
ap-2083	123	6	eigenvalues	eigenvalue	NOUN
ap-2083	123	7	are	be	AUX
ap-2083	123	8	still	still	ADV
ap-2083	123	9	real	real	ADJ
ap-2083	123	10	.	.	PUNCT
ap-2083	124	1	the	the	DET
ap-2083	124	2	question	question	NOUN
ap-2083	124	3	therefore	therefore	ADV
ap-2083	124	4	suggests	suggest	VERB
ap-2083	124	5	itself	itself	PRON
ap-2083	124	6	how	how	SCONJ
ap-2083	124	7	the	the	DET
ap-2083	124	8	situation	situation	NOUN
ap-2083	124	9	changes	change	VERB
ap-2083	124	10	when	when	SCONJ
ap-2083	124	11	eigenvalues	eigenvalue	NOUN
ap-2083	124	12	are	be	AUX
ap-2083	124	13	involved	involve	VERB
ap-2083	124	14	that	that	PRON
ap-2083	124	15	are	be	AUX
ap-2083	124	16	shifted	shift	VERB
ap-2083	124	17	into	into	ADP
ap-2083	124	18	the	the	DET
ap-2083	124	19	complex	complex	ADJ
ap-2083	124	20	plane	plane	NOUN
ap-2083	124	21	,	,	PUNCT
ap-2083	124	22	which	which	PRON
ap-2083	124	23	happens	happen	VERB
ap-2083	124	24	for	for	ADP
ap-2083	124	25	increasing	increase	VERB
ap-2083	124	26	γ	γ	PROPN
ap-2083	124	27	.	.	PROPN
ap-2083	124	28	figure	figure	NOUN
ap-2083	124	29	7	7	NUM
ap-2083	124	30	shows	show	NOUN
ap-2083	124	31	for	for	ADP
ap-2083	124	32	the	the	DET
ap-2083	124	33	eigenvalue	eigenvalue	ADJ
ap-2083	124	34	spectra	spectra	NOUN
ap-2083	124	35	with	with	ADP
ap-2083	124	36	b	b	PROPN
ap-2083	124	37	=	=	SYM
ap-2083	124	38	0.2	0.2	NUM
ap-2083	124	39	,	,	PUNCT
ap-2083	124	40	vanishing	vanish	VERB
ap-2083	124	41	nonlinearity	nonlinearity	NOUN
ap-2083	124	42	and	and	CCONJ
ap-2083	124	43	different	different	ADJ
ap-2083	124	44	values	value	NOUN
ap-2083	124	45	of	of	ADP
ap-2083	124	46	γ	γ	PROPN
ap-2083	124	47	the	the	DET
ap-2083	124	48	distances	distance	NOUN
ap-2083	124	49	|∆µ|	|∆µ|	PROPN
ap-2083	124	50	of	of	ADP
ap-2083	124	51	the	the	DET
ap-2083	124	52	real	real	ADJ
ap-2083	124	53	or	or	CCONJ
ap-2083	124	54	complex	complex	ADJ
ap-2083	124	55	eigenvalues	eigenvalue	NOUN
ap-2083	124	56	from	from	ADP
ap-2083	124	57	their	their	PRON
ap-2083	124	58	original	original	ADJ
ap-2083	124	59	values	value	NOUN
ap-2083	124	60	(	(	PUNCT
ap-2083	124	61	cf	cf	NOUN
ap-2083	124	62	.	.	PUNCT
ap-2083	125	1	also	also	ADV
ap-2083	125	2	figure	figure	VERB
ap-2083	125	3	2	2	NUM
ap-2083	125	4	)	)	PUNCT
ap-2083	125	5	.	.	PUNCT
ap-2083	126	1	the	the	DET
ap-2083	126	2	outlier	outlier	NOUN
ap-2083	126	3	at	at	ADP
ap-2083	126	4	n	n	PROPN
ap-2083	126	5	=	=	SYM
ap-2083	126	6	8	8	NUM
ap-2083	126	7	and	and	CCONJ
ap-2083	126	8	9	9	NUM
ap-2083	126	9	is	be	AUX
ap-2083	126	10	caused	cause	VERB
ap-2083	126	11	by	by	ADP
ap-2083	126	12	the	the	DET
ap-2083	126	13	giant	giant	ADJ
ap-2083	126	14	change	change	NOUN
ap-2083	126	15	of	of	ADP
ap-2083	126	16	the	the	DET
ap-2083	126	17	real	real	ADJ
ap-2083	126	18	and	and	CCONJ
ap-2083	126	19	imaginary	imaginary	ADJ
ap-2083	126	20	parts	part	NOUN
ap-2083	126	21	of	of	ADP
ap-2083	126	22	the	the	DET
ap-2083	126	23	complex	complex	ADJ
ap-2083	126	24	eigenvalues	eigenvalue	NOUN
ap-2083	126	25	beyond	beyond	ADP
ap-2083	126	26	the	the	DET
ap-2083	126	27	branch	branch	NOUN
ap-2083	126	28	point	point	NOUN
ap-2083	126	29	of	of	ADP
ap-2083	126	30	the	the	DET
ap-2083	126	31	corresponding	correspond	VERB
ap-2083	126	32	states	state	NOUN
ap-2083	126	33	observed	observe	VERB
ap-2083	126	34	already	already	ADV
ap-2083	126	35	in	in	ADP
ap-2083	126	36	figure	figure	NOUN
ap-2083	126	37	2	2	NUM
ap-2083	126	38	.	.	PUNCT
ap-2083	127	1	a	a	DET
ap-2083	127	2	similar	similar	ADJ
ap-2083	127	3	outlier	outlier	NOUN
ap-2083	127	4	occurs	occur	VERB
ap-2083	127	5	around	around	ADP
ap-2083	127	6	n	n	NOUN
ap-2083	127	7	=	=	SYM
ap-2083	127	8	75	75	NUM
ap-2083	127	9	,	,	PUNCT
ap-2083	127	10	and	and	CCONJ
ap-2083	127	11	a	a	DET
ap-2083	127	12	monotonous	monotonous	ADJ
ap-2083	127	13	decrease	decrease	NOUN
ap-2083	127	14	of	of	ADP
ap-2083	127	15	the	the	DET
ap-2083	127	16	eigenvalue	eigenvalue	ADJ
ap-2083	127	17	shifts	shift	NOUN
ap-2083	127	18	in	in	ADP
ap-2083	127	19	our	our	PRON
ap-2083	127	20	calculations	calculation	NOUN
ap-2083	127	21	only	only	ADV
ap-2083	127	22	sets	set	VERB
ap-2083	127	23	in	in	ADP
ap-2083	127	24	for	for	ADP
ap-2083	127	25	n	n	DET
ap-2083	127	26	≈	≈	PROPN
ap-2083	127	27	80	80	NUM
ap-2083	127	28	.	.	PUNCT
ap-2083	128	1	finally	finally	ADV
ap-2083	128	2	,	,	PUNCT
ap-2083	128	3	in	in	ADP
ap-2083	128	4	figure	figure	NOUN
ap-2083	128	5	8	8	NUM
ap-2083	128	6	we	we	PRON
ap-2083	128	7	investigate	investigate	VERB
ap-2083	128	8	the	the	DET
ap-2083	128	9	effect	effect	NOUN
ap-2083	128	10	of	of	ADP
ap-2083	128	11	the	the	DET
ap-2083	128	12	nonlinearity	nonlinearity	NOUN
ap-2083	128	13	on	on	ADP
ap-2083	128	14	the	the	DET
ap-2083	128	15	eigenvalue	eigenvalue	ADJ
ap-2083	128	16	shifts	shift	NOUN
ap-2083	128	17	for	for	ADP
ap-2083	128	18	γ	γ	X
ap-2083	128	19	=	=	SYM
ap-2083	128	20	1.5	1.5	NUM
ap-2083	128	21	and	and	CCONJ
ap-2083	128	22	b	b	NOUN
ap-2083	128	23	=	=	SYM
ap-2083	128	24	0.5	0.5	NUM
ap-2083	128	25	and	and	CCONJ
ap-2083	128	26	b	b	NOUN
ap-2083	128	27	=	=	SYM
ap-2083	128	28	1	1	X
ap-2083	128	29	.	.	PUNCT
ap-2083	129	1	we	we	PRON
ap-2083	129	2	find	find	VERB
ap-2083	129	3	that	that	SCONJ
ap-2083	129	4	the	the	DET
ap-2083	129	5	eigenvalue	eigenvalue	ADJ
ap-2083	129	6	shifts	shift	NOUN
ap-2083	129	7	oscillate	oscillate	VERB
ap-2083	129	8	around	around	ADP
ap-2083	129	9	straight	straight	ADJ
ap-2083	129	10	lines	line	NOUN
ap-2083	129	11	with	with	ADP
ap-2083	129	12	slopes	slope	NOUN
ap-2083	129	13	-0.37	-0.37	ADJ
ap-2083	129	14	,	,	PUNCT
ap-2083	129	15	irrespective	irrespective	ADV
ap-2083	129	16	of	of	ADP
ap-2083	129	17	the	the	DET
ap-2083	129	18	strength	strength	NOUN
ap-2083	129	19	of	of	ADP
ap-2083	129	20	the	the	DET
ap-2083	129	21	nonlinearity	nonlinearity	NOUN
ap-2083	129	22	.	.	PUNCT
ap-2083	130	1	the	the	DET
ap-2083	130	2	amplitude	amplitude	NOUN
ap-2083	130	3	of	of	ADP
ap-2083	130	4	the	the	DET
ap-2083	130	5	oscillations	oscillation	NOUN
ap-2083	130	6	,	,	PUNCT
ap-2083	130	7	however	however	ADV
ap-2083	130	8	,	,	PUNCT
ap-2083	130	9	and	and	CCONJ
ap-2083	130	10	their	their	PRON
ap-2083	130	11	numbers	number	NOUN
ap-2083	130	12	depend	depend	VERB
ap-2083	130	13	on	on	ADP
ap-2083	130	14	the	the	DET
ap-2083	130	15	position	position	NOUN
ap-2083	130	16	of	of	ADP
ap-2083	130	17	the	the	DET
ap-2083	130	18	delta	delta	NOUN
ap-2083	130	19	functions	function	NOUN
ap-2083	130	20	.	.	PUNCT
ap-2083	131	1	again	again	ADV
ap-2083	131	2	the	the	DET
ap-2083	131	3	slope	slope	NOUN
ap-2083	131	4	of	of	ADP
ap-2083	131	5	the	the	DET
ap-2083	131	6	estimate	estimate	NOUN
ap-2083	131	7	proportional	proportional	ADJ
ap-2083	131	8	to	to	ADP
ap-2083	131	9	n−1/2	n−1/2	PROPN
ap-2083	131	10	,	,	PUNCT
ap-2083	131	11	also	also	ADV
ap-2083	131	12	shown	show	VERB
ap-2083	131	13	in	in	ADP
ap-2083	131	14	the	the	DET
ap-2083	131	15	figure	figure	NOUN
ap-2083	131	16	,	,	PUNCT
ap-2083	131	17	is	be	AUX
ap-2083	131	18	steeper	steep	ADJ
ap-2083	131	19	than	than	ADP
ap-2083	131	20	the	the	DET
ap-2083	131	21	actual	actual	ADJ
ap-2083	131	22	slopes	slope	NOUN
ap-2083	131	23	found	find	VERB
ap-2083	131	24	in	in	ADP
ap-2083	131	25	the	the	DET
ap-2083	131	26	numerical	numerical	ADJ
ap-2083	131	27	results	result	NOUN
ap-2083	131	28	.	.	PUNCT
ap-2083	132	1	5	5	X
ap-2083	132	2	.	.	X
ap-2083	132	3	conclusions	conclusion	NOUN
ap-2083	132	4	we	we	PRON
ap-2083	132	5	have	have	AUX
ap-2083	132	6	carried	carry	VERB
ap-2083	132	7	out	out	ADP
ap-2083	132	8	a	a	DET
ap-2083	132	9	numerical	numerical	ADJ
ap-2083	132	10	analysis	analysis	NOUN
ap-2083	132	11	of	of	ADP
ap-2083	132	12	a	a	DET
ap-2083	132	13	pt	pt	NOUN
ap-2083	132	14	symmetric	symmetric	ADJ
ap-2083	132	15	double	double	PROPN
ap-2083	132	16	delta	delta	NOUN
ap-2083	132	17	perturbation	perturbation	NOUN
ap-2083	132	18	of	of	ADP
ap-2083	132	19	the	the	DET
ap-2083	132	20	harmonic	harmonic	ADJ
ap-2083	132	21	oscillator	oscillator	NOUN
ap-2083	132	22	.	.	PUNCT
ap-2083	133	1	we	we	PRON
ap-2083	133	2	have	have	AUX
ap-2083	133	3	also	also	ADV
ap-2083	133	4	considered	consider	VERB
ap-2083	133	5	the	the	DET
ap-2083	133	6	case	case	NOUN
ap-2083	133	7	were	be	AUX
ap-2083	133	8	in	in	ADP
ap-2083	133	9	addition	addition	NOUN
ap-2083	133	10	a	a	DET
ap-2083	133	11	gross	gross	ADJ
ap-2083	133	12	-	-	PUNCT
ap-2083	133	13	pitaevskii	pitaevskii	ADJ
ap-2083	133	14	nonlinearity	nonlinearity	NOUN
ap-2083	133	15	proportional	proportional	NOUN
ap-2083	133	16	to	to	ADP
ap-2083	133	17	|ψ|2	|ψ|2	PROPN
ap-2083	133	18	is	be	AUX
ap-2083	133	19	present	present	ADJ
ap-2083	133	20	.	.	PUNCT
ap-2083	134	1	with	with	ADP
ap-2083	134	2	the	the	DET
ap-2083	134	3	latter	latter	ADJ
ap-2083	134	4	,	,	PUNCT
ap-2083	134	5	the	the	DET
ap-2083	134	6	system	system	NOUN
ap-2083	134	7	can	can	AUX
ap-2083	134	8	be	be	AUX
ap-2083	134	9	considered	consider	VERB
ap-2083	134	10	as	as	ADP
ap-2083	134	11	a	a	DET
ap-2083	134	12	model	model	NOUN
ap-2083	134	13	of	of	ADP
ap-2083	134	14	a	a	DET
ap-2083	134	15	bose	bose	NOUN
ap-2083	134	16	-	-	PUNCT
ap-2083	134	17	einstein	einstein	NOUN
ap-2083	134	18	condensate	condensate	NOUN
ap-2083	134	19	in	in	ADP
ap-2083	134	20	a	a	DET
ap-2083	134	21	double	double	ADJ
ap-2083	134	22	well	well	NOUN
ap-2083	134	23	with	with	ADP
ap-2083	134	24	loss	loss	NOUN
ap-2083	134	25	and	and	CCONJ
ap-2083	134	26	gain	gain	NOUN
ap-2083	134	27	of	of	ADP
ap-2083	134	28	atoms	atom	NOUN
ap-2083	134	29	.	.	PUNCT
ap-2083	135	1	10−1	10−1	NUM
ap-2083	135	2	100	100	NUM
ap-2083	135	3	1	1	NUM
ap-2083	135	4	10	10	NUM
ap-2083	135	5	∆	∆	PROPN
ap-2083	135	6	µ	µ	X
ap-2083	135	7	n	n	PRON
ap-2083	135	8	g	g	NOUN
ap-2083	135	9	=	=	SYM
ap-2083	135	10	1	1	NUM
ap-2083	135	11	g	g	NOUN
ap-2083	135	12	=	=	SYM
ap-2083	135	13	2	2	NUM
ap-2083	135	14	g	g	NOUN
ap-2083	135	15	=	=	SYM
ap-2083	135	16	3	3	NUM
ap-2083	135	17	g	g	NOUN
ap-2083	135	18	=	=	SYM
ap-2083	135	19	4	4	NUM
ap-2083	135	20	10−1	10−1	NUM
ap-2083	135	21	100	100	NUM
ap-2083	135	22	1	1	NUM
ap-2083	135	23	10	10	NUM
ap-2083	135	24	∆	∆	PROPN
ap-2083	135	25	µ	µ	X
ap-2083	135	26	n	n	DET
ap-2083	135	27	∝	∝	PROPN
ap-2083	135	28	n−0.37	n−0.37	PROPN
ap-2083	135	29	∝	∝	PROPN
ap-2083	135	30	n−0.5	n−0.5	NUM
ap-2083	135	31	figure	figure	NOUN
ap-2083	135	32	8	8	NUM
ap-2083	135	33	.	.	PUNCT
ap-2083	136	1	shift	shift	NOUN
ap-2083	136	2	of	of	ADP
ap-2083	136	3	the	the	DET
ap-2083	136	4	eigenvalues	eigenvalues	PROPN
ap-2083	136	5	n	n	X
ap-2083	136	6	=	=	SYM
ap-2083	136	7	2n	2n	NUM
ap-2083	137	1	+	+	CCONJ
ap-2083	137	2	1	1	NUM
ap-2083	137	3	for	for	ADP
ap-2083	137	4	four	four	NUM
ap-2083	137	5	different	different	ADJ
ap-2083	137	6	values	value	NOUN
ap-2083	137	7	of	of	ADP
ap-2083	137	8	the	the	DET
ap-2083	137	9	nonlinearity	nonlinearity	NOUN
ap-2083	137	10	at	at	ADP
ap-2083	137	11	γ	γ	X
ap-2083	137	12	=	=	SYM
ap-2083	137	13	1.5	1.5	NUM
ap-2083	137	14	for	for	ADP
ap-2083	137	15	b	b	NOUN
ap-2083	137	16	=	=	SYM
ap-2083	137	17	0.5	0.5	NUM
ap-2083	137	18	(	(	PUNCT
ap-2083	137	19	top	top	NOUN
ap-2083	137	20	)	)	PUNCT
ap-2083	137	21	and	and	CCONJ
ap-2083	137	22	b	b	X
ap-2083	137	23	=	=	SYM
ap-2083	137	24	1	1	NUM
ap-2083	137	25	(	(	PUNCT
ap-2083	137	26	bottom	bottom	NOUN
ap-2083	137	27	)	)	PUNCT
ap-2083	137	28	.	.	PUNCT
ap-2083	138	1	we	we	PRON
ap-2083	138	2	have	have	AUX
ap-2083	138	3	checked	check	VERB
ap-2083	138	4	that	that	SCONJ
ap-2083	138	5	the	the	DET
ap-2083	138	6	mityagin	mityagin	NOUN
ap-2083	138	7	-	-	PUNCT
ap-2083	138	8	siegl	siegl	NOUN
ap-2083	138	9	criterion	criterion	NOUN
ap-2083	138	10	for	for	ADP
ap-2083	138	11	the	the	DET
ap-2083	138	12	perturbed	perturb	VERB
ap-2083	138	13	eigenfunctions	eigenfunction	NOUN
ap-2083	138	14	to	to	PART
ap-2083	138	15	form	form	VERB
ap-2083	138	16	a	a	DET
ap-2083	138	17	riesz	riesz	NOUN
ap-2083	138	18	basis	basis	NOUN
ap-2083	138	19	is	be	AUX
ap-2083	138	20	fulfilled	fulfil	VERB
ap-2083	138	21	,	,	PUNCT
ap-2083	138	22	and	and	CCONJ
ap-2083	138	23	compared	compare	VERB
ap-2083	138	24	rigorous	rigorous	ADJ
ap-2083	138	25	mathematical	mathematical	ADJ
ap-2083	138	26	estimates	estimate	NOUN
ap-2083	138	27	for	for	ADP
ap-2083	138	28	the	the	DET
ap-2083	138	29	shrink	shrink	ADJ
ap-2083	138	30	rate	rate	NOUN
ap-2083	138	31	of	of	ADP
ap-2083	138	32	the	the	DET
ap-2083	138	33	eigenvalue	eigenvalue	ADJ
ap-2083	138	34	shifts	shift	NOUN
ap-2083	138	35	in	in	ADP
ap-2083	138	36	dependence	dependence	NOUN
ap-2083	138	37	on	on	ADP
ap-2083	138	38	the	the	DET
ap-2083	138	39	harmonic	harmonic	ADJ
ap-2083	138	40	oscillator	oscillator	NOUN
ap-2083	138	41	quantum	quantum	ADJ
ap-2083	138	42	number	number	NOUN
ap-2083	138	43	n	n	NOUN
ap-2083	138	44	for	for	ADP
ap-2083	138	45	various	various	ADJ
ap-2083	138	46	strengths	strength	NOUN
ap-2083	138	47	of	of	ADP
ap-2083	138	48	the	the	DET
ap-2083	138	49	non	non	ADJ
ap-2083	138	50	-	-	NOUN
ap-2083	138	51	hermiticity	hermiticity	NOUN
ap-2083	138	52	and	and	CCONJ
ap-2083	138	53	the	the	DET
ap-2083	138	54	nonlinearity	nonlinearity	NOUN
ap-2083	138	55	.	.	PUNCT
ap-2083	139	1	we	we	PRON
ap-2083	139	2	have	have	AUX
ap-2083	139	3	verified	verify	VERB
ap-2083	139	4	that	that	SCONJ
ap-2083	139	5	in	in	ADP
ap-2083	139	6	the	the	DET
ap-2083	139	7	linear	linear	ADJ
ap-2083	139	8	case	case	NOUN
ap-2083	139	9	the	the	DET
ap-2083	139	10	mathematical	mathematical	ADJ
ap-2083	139	11	prediction	prediction	NOUN
ap-2083	139	12	for	for	ADP
ap-2083	139	13	the	the	DET
ap-2083	139	14	shrink	shrink	NOUN
ap-2083	139	15	rates	rate	NOUN
ap-2083	139	16	proportional	proportional	ADJ
ap-2083	139	17	to	to	ADP
ap-2083	139	18	1	1	NUM
ap-2083	139	19	/	/	SYM
ap-2083	139	20	n1/2	n1/2	NOUN
ap-2083	139	21	is	be	AUX
ap-2083	139	22	a	a	DET
ap-2083	139	23	valid	valid	ADJ
ap-2083	139	24	estimate	estimate	NOUN
ap-2083	139	25	,	,	PUNCT
ap-2083	139	26	and	and	CCONJ
ap-2083	139	27	that	that	SCONJ
ap-2083	139	28	the	the	DET
ap-2083	139	29	improved	improved	ADJ
ap-2083	139	30	estimate	estimate	NOUN
ap-2083	139	31	proportional	proportional	ADJ
ap-2083	139	32	to	to	ADP
ap-2083	139	33	log(n)/n3/2	log(n)/n3/2	PROPN
ap-2083	139	34	is	be	AUX
ap-2083	139	35	in	in	ADP
ap-2083	139	36	excellent	excellent	ADJ
ap-2083	139	37	agreement	agreement	NOUN
ap-2083	139	38	with	with	ADP
ap-2083	139	39	the	the	DET
ap-2083	139	40	behaviour	behaviour	NOUN
ap-2083	139	41	of	of	ADP
ap-2083	139	42	the	the	DET
ap-2083	139	43	shrink	shrink	NOUN
ap-2083	139	44	rates	rate	NOUN
ap-2083	139	45	found	find	VERB
ap-2083	139	46	in	in	ADP
ap-2083	139	47	the	the	DET
ap-2083	139	48	numerical	numerical	ADJ
ap-2083	139	49	results	result	NOUN
ap-2083	139	50	.	.	PUNCT
ap-2083	140	1	by	by	ADP
ap-2083	140	2	contrast	contrast	NOUN
ap-2083	140	3	,	,	PUNCT
ap-2083	140	4	with	with	ADP
ap-2083	140	5	nonlinearity	nonlinearity	NOUN
ap-2083	140	6	we	we	PRON
ap-2083	140	7	find	find	VERB
ap-2083	140	8	slopes	slope	NOUN
ap-2083	140	9	of	of	ADP
ap-2083	140	10	approximately	approximately	ADV
ap-2083	140	11	−0.37	−0.37	NOUN
ap-2083	140	12	,	,	PUNCT
ap-2083	140	13	less	less	ADV
ap-2083	140	14	steep	steep	ADJ
ap-2083	140	15	than	than	ADP
ap-2083	140	16	both	both	DET
ap-2083	140	17	mathematical	mathematical	ADJ
ap-2083	140	18	estimates	estimate	NOUN
ap-2083	140	19	.	.	PUNCT
ap-2083	141	1	evidently	evidently	ADV
ap-2083	141	2	,	,	PUNCT
ap-2083	141	3	to	to	PART
ap-2083	141	4	derive	derive	VERB
ap-2083	141	5	estimates	estimate	NOUN
ap-2083	141	6	also	also	ADV
ap-2083	141	7	for	for	SCONJ
ap-2083	141	8	the	the	DET
ap-2083	141	9	nonlinear	nonlinear	ADJ
ap-2083	141	10	case	case	NOUN
ap-2083	141	11	remains	remain	VERB
ap-2083	141	12	a	a	DET
ap-2083	141	13	mathematical	mathematical	ADJ
ap-2083	141	14	challenge	challenge	NOUN
ap-2083	141	15	.	.	PUNCT
ap-2083	142	1	a	a	DET
ap-2083	142	2	peculiarity	peculiarity	NOUN
ap-2083	142	3	that	that	PRON
ap-2083	142	4	is	be	AUX
ap-2083	142	5	found	find	VERB
ap-2083	142	6	is	be	AUX
ap-2083	142	7	the	the	DET
ap-2083	142	8	occurrence	occurrence	NOUN
ap-2083	142	9	of	of	ADP
ap-2083	142	10	outliers	outlier	NOUN
ap-2083	142	11	in	in	ADP
ap-2083	142	12	the	the	DET
ap-2083	142	13	eigenvalue	eigenvalue	PROPN
ap-2083	142	14	spectra	spectra	NOUN
ap-2083	142	15	which	which	PRON
ap-2083	142	16	appear	appear	VERB
ap-2083	142	17	beyond	beyond	ADP
ap-2083	142	18	branch	branch	NOUN
ap-2083	142	19	points	point	NOUN
ap-2083	142	20	with	with	ADP
ap-2083	142	21	unusually	unusually	ADV
ap-2083	142	22	large	large	ADJ
ap-2083	142	23	real	real	ADJ
ap-2083	142	24	and	and	CCONJ
ap-2083	142	25	imaginary	imaginary	ADJ
ap-2083	142	26	parts	part	NOUN
ap-2083	142	27	of	of	ADP
ap-2083	142	28	their	their	PRON
ap-2083	142	29	complex	complex	ADJ
ap-2083	142	30	conjugate	conjugate	ADJ
ap-2083	142	31	eigenvalues	eigenvalue	NOUN
ap-2083	142	32	.	.	PUNCT
ap-2083	143	1	they	they	PRON
ap-2083	143	2	are	be	AUX
ap-2083	143	3	the	the	DET
ap-2083	143	4	reason	reason	NOUN
ap-2083	143	5	why	why	SCONJ
ap-2083	143	6	for	for	ADP
ap-2083	143	7	growing	grow	VERB
ap-2083	143	8	strength	strength	NOUN
ap-2083	143	9	of	of	ADP
ap-2083	143	10	the	the	DET
ap-2083	143	11	nonhermiticity	nonhermiticity	NOUN
ap-2083	143	12	the	the	DET
ap-2083	143	13	asymptotic	asymptotic	ADJ
ap-2083	143	14	shrink	shrink	NOUN
ap-2083	143	15	rate	rate	NOUN
ap-2083	143	16	behaviour	behaviour	NOUN
ap-2083	143	17	is	be	AUX
ap-2083	143	18	attained	attain	VERB
ap-2083	143	19	only	only	ADV
ap-2083	143	20	for	for	ADP
ap-2083	143	21	high	high	ADJ
ap-2083	143	22	values	value	NOUN
ap-2083	143	23	of	of	ADP
ap-2083	143	24	n.	n.	NOUN
ap-2083	143	25	the	the	DET
ap-2083	143	26	nature	nature	NOUN
ap-2083	143	27	of	of	ADP
ap-2083	143	28	these	these	DET
ap-2083	143	29	outliers	outlier	NOUN
ap-2083	143	30	and	and	CCONJ
ap-2083	143	31	their	their	PRON
ap-2083	143	32	mathematical	mathematical	ADJ
ap-2083	143	33	importance	importance	NOUN
ap-2083	143	34	should	should	AUX
ap-2083	143	35	certainly	certainly	ADV
ap-2083	143	36	be	be	AUX
ap-2083	143	37	clarified	clarify	VERB
ap-2083	143	38	in	in	ADP
ap-2083	143	39	future	future	ADJ
ap-2083	143	40	studies	study	NOUN
ap-2083	143	41	.	.	PUNCT
ap-2083	144	1	acknowledgements	acknowledgement	NOUN
ap-2083	144	2	we	we	PRON
ap-2083	144	3	are	be	AUX
ap-2083	144	4	grateful	grateful	ADJ
ap-2083	144	5	to	to	ADP
ap-2083	144	6	petr	petr	PROPN
ap-2083	144	7	siegl	siegl	VERB
ap-2083	144	8	for	for	ADP
ap-2083	144	9	helpful	helpful	ADJ
ap-2083	144	10	explanations	explanation	NOUN
ap-2083	144	11	and	and	CCONJ
ap-2083	144	12	discussions	discussion	NOUN
ap-2083	144	13	.	.	PUNCT
ap-2083	145	1	we	we	PRON
ap-2083	145	2	are	be	AUX
ap-2083	145	3	also	also	ADV
ap-2083	145	4	grateful	grateful	ADJ
ap-2083	145	5	to	to	ADP
ap-2083	145	6	boris	boris	PROPN
ap-2083	145	7	mityagin	mityagin	PROPN
ap-2083	145	8	for	for	ADP
ap-2083	145	9	very	very	ADV
ap-2083	145	10	helpful	helpful	ADJ
ap-2083	145	11	remarks	remark	NOUN
ap-2083	145	12	,	,	PUNCT
ap-2083	145	13	and	and	CCONJ
ap-2083	145	14	for	for	ADP
ap-2083	145	15	communicating	communicate	VERB
ap-2083	145	16	his	his	PRON
ap-2083	145	17	improved	improved	ADJ
ap-2083	145	18	estimate	estimate	NOUN
ap-2083	145	19	for	for	ADP
ap-2083	145	20	the	the	DET
ap-2083	145	21	two	two	NUM
ap-2083	145	22	-	-	PUNCT
ap-2083	145	23	delta	delta	NOUN
ap-2083	145	24	potentials	potential	NOUN
ap-2083	145	25	.	.	PUNCT
ap-2083	146	1	furthermore	furthermore	ADV
ap-2083	146	2	we	we	PRON
ap-2083	146	3	120	120	NUM
ap-2083	146	4	vol	vol	NOUN
ap-2083	146	5	.	.	PUNCT
ap-2083	147	1	54	54	NUM
ap-2083	147	2	no	no	NOUN
ap-2083	147	3	.	.	PUNCT
ap-2083	148	1	2/2014	2/2014	NUM
ap-2083	148	2	bec	bec	PROPN
ap-2083	148	3	with	with	ADP
ap-2083	148	4	pt	pt	PROPN
ap-2083	148	5	-	-	ADJ
ap-2083	148	6	symmetric	symmetric	ADJ
ap-2083	148	7	double	double	ADJ
ap-2083	148	8	-	-	PUNCT
ap-2083	148	9	delta	delta	NOUN
ap-2083	148	10	loss	loss	NOUN
ap-2083	148	11	and	and	CCONJ
ap-2083	148	12	gain	gain	NOUN
ap-2083	148	13	:	:	PUNCT
ap-2083	148	14	test	test	NOUN
ap-2083	148	15	of	of	ADP
ap-2083	148	16	estimates	estimate	NOUN
ap-2083	148	17	thank	thank	VERB
ap-2083	148	18	two	two	NUM
ap-2083	148	19	anonymous	anonymous	ADJ
ap-2083	148	20	referees	referee	NOUN
ap-2083	148	21	for	for	ADP
ap-2083	148	22	valuable	valuable	ADJ
ap-2083	148	23	comments	comment	NOUN
ap-2083	148	24	.	.	PUNCT
ap-2083	149	1	in	in	ADP
ap-2083	149	2	particular	particular	ADJ
ap-2083	149	3	,	,	PUNCT
ap-2083	149	4	one	one	NUM
ap-2083	149	5	referee	referee	NOUN
ap-2083	149	6	points	point	VERB
ap-2083	149	7	out	out	ADP
ap-2083	149	8	that	that	SCONJ
ap-2083	149	9	a	a	DET
ap-2083	149	10	deeper	deep	ADJ
ap-2083	149	11	analytic	analytic	ADJ
ap-2083	149	12	insight	insight	NOUN
ap-2083	149	13	in	in	ADP
ap-2083	149	14	the	the	DET
ap-2083	149	15	bottom	bottom	NOUN
ap-2083	149	16	of	of	ADP
ap-2083	149	17	the	the	DET
ap-2083	149	18	spectra	spectra	NOUN
ap-2083	149	19	could	could	AUX
ap-2083	149	20	probably	probably	ADV
ap-2083	149	21	be	be	AUX
ap-2083	149	22	obtained	obtain	VERB
ap-2083	149	23	using	use	VERB
ap-2083	149	24	the	the	DET
ap-2083	149	25	strategies	strategy	NOUN
ap-2083	149	26	described	describe	VERB
ap-2083	149	27	in	in	ADP
ap-2083	149	28	ref	ref	NOUN
ap-2083	149	29	.	.	PUNCT
ap-2083	150	1	[	[	X
ap-2083	150	2	22	22	NUM
ap-2083	150	3	]	]	PUNCT
ap-2083	150	4	for	for	ADP
ap-2083	150	5	the	the	DET
ap-2083	150	6	self	self	NOUN
ap-2083	150	7	-	-	PUNCT
ap-2083	150	8	adjoint	adjoint	NOUN
ap-2083	150	9	case	case	NOUN
ap-2083	150	10	,	,	PUNCT
ap-2083	150	11	if	if	SCONJ
ap-2083	150	12	adapted	adapt	VERB
ap-2083	150	13	to	to	ADP
ap-2083	150	14	the	the	DET
ap-2083	150	15	pt	pt	NOUN
ap-2083	150	16	-symmetric	-symmetric	ADJ
ap-2083	150	17	perturbation	perturbation	NOUN
ap-2083	150	18	.	.	PUNCT
ap-2083	151	1	this	this	PRON
ap-2083	151	2	is	be	AUX
ap-2083	151	3	certainly	certainly	ADV
ap-2083	151	4	also	also	ADV
ap-2083	151	5	a	a	DET
ap-2083	151	6	useful	useful	ADJ
ap-2083	151	7	suggestion	suggestion	NOUN
ap-2083	151	8	for	for	ADP
ap-2083	151	9	future	future	ADJ
ap-2083	151	10	work	work	NOUN
ap-2083	151	11	.	.	PUNCT
ap-2083	152	1	references	reference	NOUN
ap-2083	152	2	[	[	X
ap-2083	152	3	1	1	X
ap-2083	152	4	]	]	PUNCT
ap-2083	152	5	s.	s.	PROPN
ap-2083	152	6	klaiman	klaiman	PROPN
ap-2083	152	7	,	,	PUNCT
ap-2083	152	8	et	et	PROPN
ap-2083	152	9	al	al	PROPN
ap-2083	152	10	.	.	PUNCT
ap-2083	153	1	visualization	visualization	NOUN
ap-2083	153	2	of	of	ADP
ap-2083	153	3	branch	branch	NOUN
ap-2083	153	4	points	point	NOUN
ap-2083	153	5	in	in	ADP
ap-2083	153	6	pt	pt	NOUN
ap-2083	153	7	-symmetric	-symmetric	ADJ
ap-2083	153	8	waveguides	waveguide	NOUN
ap-2083	153	9	.	.	PUNCT
ap-2083	154	1	phys	phy	NOUN
ap-2083	154	2	rev	rev	VERB
ap-2083	154	3	lett	lett	PROPN
ap-2083	154	4	101:080402	101:080402	PROPN
ap-2083	154	5	,	,	PUNCT
ap-2083	154	6	2008	2008	NUM
ap-2083	154	7	.	.	PUNCT
ap-2083	155	1	doi	doi	NOUN
ap-2083	155	2	:	:	PUNCT
ap-2083	155	3	10.1103	10.1103	NUM
ap-2083	155	4	/	/	SYM
ap-2083	155	5	physrevlett.101.080402	physrevlett.101.080402	X
ap-2083	155	6	[	[	X
ap-2083	155	7	2	2	NUM
ap-2083	155	8	]	]	PUNCT
ap-2083	155	9	h.	h.	NOUN
ap-2083	155	10	cartarius	cartarius	PROPN
ap-2083	155	11	,	,	PUNCT
ap-2083	155	12	et	et	PROPN
ap-2083	155	13	al	al	PROPN
ap-2083	155	14	.	.	PROPN
ap-2083	155	15	model	model	NOUN
ap-2083	155	16	of	of	ADP
ap-2083	155	17	a	a	DET
ap-2083	155	18	pt	pt	NOUN
ap-2083	155	19	-symmetric	-symmetric	NOUN
ap-2083	155	20	bose	bose	NOUN
ap-2083	155	21	-	-	PUNCT
ap-2083	155	22	einstein	einstein	NOUN
ap-2083	155	23	condensate	condensate	NOUN
ap-2083	155	24	in	in	ADP
ap-2083	155	25	a	a	DET
ap-2083	155	26	δ	δ	NOUN
ap-2083	155	27	-	-	PUNCT
ap-2083	155	28	function	function	NOUN
ap-2083	155	29	double	double	ADJ
ap-2083	155	30	-	-	PUNCT
ap-2083	155	31	well	well	NOUN
ap-2083	155	32	potential	potential	NOUN
ap-2083	155	33	.	.	PUNCT
ap-2083	156	1	phys	phy	NOUN
ap-2083	156	2	rev	rev	VERB
ap-2083	156	3	a	a	DET
ap-2083	156	4	86:013612	86:013612	NUM
ap-2083	156	5	,	,	PUNCT
ap-2083	156	6	2012	2012	NUM
ap-2083	156	7	.	.	PUNCT
ap-2083	157	1	doi	doi	NOUN
ap-2083	157	2	:	:	PUNCT
ap-2083	157	3	10.1103	10.1103	NUM
ap-2083	157	4	/	/	SYM
ap-2083	157	5	physreva.86.013612	physreva.86.013612	VERB
ap-2083	158	1	[	[	X
ap-2083	158	2	3	3	NUM
ap-2083	158	3	]	]	X
ap-2083	158	4	h.	h.	NOUN
ap-2083	158	5	cartarius	cartarius	PROPN
ap-2083	158	6	,	,	PUNCT
ap-2083	158	7	et	et	PROPN
ap-2083	158	8	al	al	PROPN
ap-2083	158	9	.	.	PROPN
ap-2083	158	10	nonlinear	nonlinear	ADJ
ap-2083	158	11	schrödinger	schrödinger	ADJ
ap-2083	158	12	equation	equation	NOUN
ap-2083	158	13	for	for	ADP
ap-2083	158	14	a	a	DET
ap-2083	158	15	pt	pt	NOUN
ap-2083	158	16	-symmetric	-symmetric	ADJ
ap-2083	158	17	delta	delta	NOUN
ap-2083	158	18	-	-	PUNCT
ap-2083	158	19	function	function	NOUN
ap-2083	158	20	double	double	ADJ
ap-2083	158	21	well	well	ADV
ap-2083	158	22	.	.	PUNCT
ap-2083	159	1	j	j	PROPN
ap-2083	159	2	phys	phy	NOUN
ap-2083	159	3	a	a	DET
ap-2083	159	4	45:444008	45:444008	NOUN
ap-2083	159	5	,	,	PUNCT
ap-2083	159	6	2012	2012	NUM
ap-2083	159	7	.	.	PUNCT
ap-2083	160	1	doi	doi	NOUN
ap-2083	160	2	:	:	PUNCT
ap-2083	160	3	10.1088/1751	10.1088/1751	NUM
ap-2083	160	4	-	-	PUNCT
ap-2083	160	5	8113/45/44/444008	8113/45/44/444008	PROPN
ap-2083	161	1	[	[	X
ap-2083	161	2	4	4	X
ap-2083	161	3	]	]	X
ap-2083	161	4	h.	h.	NOUN
ap-2083	161	5	cartarius	cartarius	PROPN
ap-2083	161	6	,	,	PUNCT
ap-2083	161	7	et	et	PROPN
ap-2083	161	8	al	al	PROPN
ap-2083	161	9	.	.	PROPN
ap-2083	161	10	stationary	stationary	ADJ
ap-2083	161	11	and	and	CCONJ
ap-2083	161	12	dynamical	dynamical	ADJ
ap-2083	161	13	solutions	solution	NOUN
ap-2083	161	14	of	of	ADP
ap-2083	161	15	the	the	DET
ap-2083	161	16	gross	gross	ADJ
ap-2083	161	17	-	-	PUNCT
ap-2083	161	18	pitaevskii	pitaevskii	ADJ
ap-2083	161	19	equation	equation	NOUN
ap-2083	161	20	for	for	ADP
ap-2083	161	21	a	a	DET
ap-2083	161	22	bose	bose	NOUN
ap-2083	161	23	-	-	PUNCT
ap-2083	161	24	einstein	einstein	NOUN
ap-2083	161	25	condensate	condensate	NOUN
ap-2083	161	26	in	in	ADP
ap-2083	161	27	a	a	DET
ap-2083	161	28	pt	pt	NOUN
ap-2083	161	29	symmetric	symmetric	ADJ
ap-2083	161	30	double	double	ADJ
ap-2083	161	31	well	well	ADV
ap-2083	161	32	.	.	PUNCT
ap-2083	162	1	acta	acta	PROPN
ap-2083	162	2	polytechnica	polytechnica	PROPN
ap-2083	162	3	53(3):259–267	53(3):259–267	PROPN
ap-2083	162	4	,	,	PUNCT
ap-2083	162	5	2013	2013	NUM
ap-2083	162	6	.	.	PUNCT
ap-2083	163	1	[	[	X
ap-2083	163	2	5	5	X
ap-2083	163	3	]	]	PUNCT
ap-2083	163	4	d.	d.	PROPN
ap-2083	163	5	dast	dast	PROPN
ap-2083	163	6	,	,	PUNCT
ap-2083	163	7	et	et	PROPN
ap-2083	163	8	al	al	PROPN
ap-2083	163	9	.	.	PUNCT
ap-2083	164	1	a	a	DET
ap-2083	164	2	bose	bose	NOUN
ap-2083	164	3	-	-	PUNCT
ap-2083	164	4	einstein	einstein	NOUN
ap-2083	164	5	condensate	condensate	NOUN
ap-2083	164	6	in	in	ADP
ap-2083	164	7	a	a	DET
ap-2083	164	8	pt	pt	NOUN
ap-2083	164	9	symmetric	symmetric	ADJ
ap-2083	164	10	double	double	ADJ
ap-2083	164	11	well	well	ADV
ap-2083	164	12	.	.	PUNCT
ap-2083	165	1	fortschr	fortschr	PROPN
ap-2083	165	2	physik	physik	PROPN
ap-2083	165	3	61:124–139	61:124–139	PROPN
ap-2083	165	4	,	,	PUNCT
ap-2083	165	5	2013	2013	NUM
ap-2083	165	6	.	.	PUNCT
ap-2083	166	1	doi	doi	NOUN
ap-2083	166	2	:	:	PUNCT
ap-2083	167	1	10.1002	10.1002	NUM
ap-2083	167	2	/	/	SYM
ap-2083	167	3	prop.201200080	prop.201200080	NOUN
ap-2083	167	4	[	[	X
ap-2083	167	5	6	6	NUM
ap-2083	167	6	]	]	PUNCT
ap-2083	167	7	d.	d.	PROPN
ap-2083	167	8	dast	dast	PROPN
ap-2083	167	9	,	,	PUNCT
ap-2083	167	10	et	et	PROPN
ap-2083	167	11	al	al	PROPN
ap-2083	167	12	.	.	PUNCT
ap-2083	167	13	eigenvalue	eigenvalue	PROPN
ap-2083	167	14	structure	structure	NOUN
ap-2083	167	15	of	of	ADP
ap-2083	167	16	a	a	DET
ap-2083	167	17	bose	bose	NOUN
ap-2083	167	18	-	-	PUNCT
ap-2083	167	19	einstein	einstein	NOUN
ap-2083	167	20	condensate	condensate	NOUN
ap-2083	167	21	in	in	ADP
ap-2083	167	22	a	a	DET
ap-2083	167	23	pt	pt	NOUN
ap-2083	167	24	-symmetric	-symmetric	NOUN
ap-2083	167	25	double	double	ADJ
ap-2083	167	26	well	well	ADV
ap-2083	167	27	.	.	PUNCT
ap-2083	168	1	j	j	PROPN
ap-2083	168	2	phys	phy	NOUN
ap-2083	168	3	a	a	DET
ap-2083	168	4	46:375301	46:375301	NOUN
ap-2083	168	5	,	,	PUNCT
ap-2083	168	6	2013	2013	NUM
ap-2083	168	7	.	.	PUNCT
ap-2083	169	1	doi	doi	NOUN
ap-2083	169	2	:	:	PUNCT
ap-2083	169	3	10.1088/1751	10.1088/1751	NUM
ap-2083	169	4	-	-	NUM
ap-2083	169	5	8113/46/37/375301	8113/46/37/375301	PROPN
ap-2083	170	1	[	[	X
ap-2083	170	2	7	7	NUM
ap-2083	170	3	]	]	X
ap-2083	170	4	m.	m.	NOUN
ap-2083	170	5	kreibich	kreibich	PROPN
ap-2083	170	6	,	,	PUNCT
ap-2083	170	7	et	et	PROPN
ap-2083	170	8	al	al	PROPN
ap-2083	170	9	.	.	PROPN
ap-2083	171	1	hermitian	hermitian	PROPN
ap-2083	171	2	four	four	NUM
ap-2083	171	3	-	-	PUNCT
ap-2083	171	4	well	well	NOUN
ap-2083	171	5	potential	potential	NOUN
ap-2083	171	6	as	as	ADP
ap-2083	171	7	a	a	DET
ap-2083	171	8	realization	realization	NOUN
ap-2083	171	9	of	of	ADP
ap-2083	171	10	a	a	DET
ap-2083	171	11	pt	pt	NOUN
ap-2083	171	12	-symmetric	-symmetric	ADJ
ap-2083	171	13	system	system	NOUN
ap-2083	171	14	.	.	PUNCT
ap-2083	172	1	phys	phy	NOUN
ap-2083	172	2	rev	rev	VERB
ap-2083	172	3	a	a	DET
ap-2083	172	4	87:051601(r	87:051601(r	NOUN
ap-2083	172	5	)	)	PUNCT
ap-2083	172	6	,	,	PUNCT
ap-2083	172	7	2013	2013	NUM
ap-2083	172	8	.	.	PUNCT
ap-2083	173	1	doi	doi	NOUN
ap-2083	173	2	:	:	PUNCT
ap-2083	173	3	10.1103	10.1103	NUM
ap-2083	173	4	/	/	SYM
ap-2083	173	5	physreva.87.051601	physreva.87.051601	NOUN
ap-2083	174	1	[	[	X
ap-2083	174	2	8	8	NUM
ap-2083	174	3	]	]	X
ap-2083	174	4	j.	j.	PROPN
ap-2083	174	5	adduci	adduci	PROPN
ap-2083	174	6	,	,	PUNCT
ap-2083	174	7	et	et	PROPN
ap-2083	174	8	al	al	PROPN
ap-2083	174	9	.	.	PROPN
ap-2083	174	10	eigensystem	eigensystem	NOUN
ap-2083	174	11	of	of	ADP
ap-2083	174	12	an	an	DET
ap-2083	174	13	l2	l2	NOUN
ap-2083	174	14	-	-	PUNCT
ap-2083	174	15	perturbed	perturb	VERB
ap-2083	174	16	harmonic	harmonic	ADJ
ap-2083	174	17	oscillator	oscillator	NOUN
ap-2083	174	18	is	be	AUX
ap-2083	174	19	an	an	DET
ap-2083	174	20	unconditional	unconditional	ADJ
ap-2083	174	21	basis	basis	NOUN
ap-2083	174	22	.	.	PUNCT
ap-2083	175	1	cent	cent	NOUN
ap-2083	175	2	eur	eur	PROPN
ap-2083	175	3	j	j	PROPN
ap-2083	175	4	math	math	PROPN
ap-2083	175	5	10:569	10:569	PROPN
ap-2083	175	6	,	,	PUNCT
ap-2083	175	7	2012	2012	NUM
ap-2083	175	8	.	.	PUNCT
ap-2083	176	1	doi	doi	NOUN
ap-2083	176	2	:	:	PUNCT
ap-2083	176	3	10.2478	10.2478	NUM
ap-2083	176	4	/	/	SYM
ap-2083	176	5	s11533	s11533	NOUN
ap-2083	176	6	-	-	PUNCT
ap-2083	176	7	011	011	NUM
ap-2083	176	8	-	-	PUNCT
ap-2083	176	9	0139	0139	NUM
ap-2083	176	10	-	-	SYM
ap-2083	176	11	3	3	NUM
ap-2083	176	12	[	[	X
ap-2083	176	13	9	9	NUM
ap-2083	176	14	]	]	PUNCT
ap-2083	176	15	b.	b.	NOUN
ap-2083	176	16	mityagin	mityagin	PROPN
ap-2083	176	17	,	,	PUNCT
ap-2083	176	18	et	et	PROPN
ap-2083	176	19	al	al	PROPN
ap-2083	176	20	.	.	PROPN
ap-2083	176	21	root	root	PROPN
ap-2083	176	22	system	system	NOUN
ap-2083	176	23	of	of	ADP
ap-2083	176	24	singular	singular	ADJ
ap-2083	176	25	perturbations	perturbation	NOUN
ap-2083	176	26	of	of	ADP
ap-2083	176	27	harmonic	harmonic	ADJ
ap-2083	176	28	oscillator	oscillator	NOUN
ap-2083	176	29	type	type	NOUN
ap-2083	176	30	operators	operator	NOUN
ap-2083	176	31	,	,	PUNCT
ap-2083	176	32	2013	2013	NUM
ap-2083	176	33	.	.	PUNCT
ap-2083	177	1	arxiv:1307.6245	arxiv:1307.6245	NOUN
ap-2083	177	2	.	.	PUNCT
ap-2083	178	1	[	[	X
ap-2083	178	2	10	10	NUM
ap-2083	178	3	]	]	PUNCT
ap-2083	178	4	b.	b.	NOUN
ap-2083	178	5	mityagin	mityagin	PROPN
ap-2083	178	6	,	,	PUNCT
ap-2083	178	7	private	private	ADJ
ap-2083	178	8	communication	communication	NOUN
ap-2083	178	9	,	,	PUNCT
ap-2083	178	10	january	january	PROPN
ap-2083	178	11	2014	2014	NUM
ap-2083	178	12	.	.	PUNCT
ap-2083	179	1	[	[	X
ap-2083	179	2	11	11	NUM
ap-2083	179	3	]	]	PUNCT
ap-2083	179	4	h.	h.	PROPN
ap-2083	179	5	f.	f.	PROPN
ap-2083	179	6	jones	jones	PROPN
ap-2083	179	7	.	.	PUNCT
ap-2083	180	1	the	the	DET
ap-2083	180	2	energy	energy	NOUN
ap-2083	180	3	spectrum	spectrum	NOUN
ap-2083	180	4	of	of	ADP
ap-2083	180	5	complex	complex	ADJ
ap-2083	180	6	periodic	periodic	ADJ
ap-2083	180	7	potentials	potential	NOUN
ap-2083	180	8	of	of	ADP
ap-2083	180	9	the	the	DET
ap-2083	180	10	kronig	kronig	NOUN
ap-2083	180	11	-	-	PUNCT
ap-2083	180	12	penney	penney	PROPN
ap-2083	180	13	type	type	NOUN
ap-2083	180	14	.	.	PUNCT
ap-2083	181	1	phys	phy	NOUN
ap-2083	181	2	lett	lett	PROPN
ap-2083	181	3	a	a	DET
ap-2083	181	4	262:242	262:242	PROPN
ap-2083	181	5	,	,	PUNCT
ap-2083	181	6	1999	1999	NUM
ap-2083	181	7	.	.	PUNCT
ap-2083	182	1	doi	doi	NOUN
ap-2083	182	2	:	:	PUNCT
ap-2083	182	3	10.1016	10.1016	NUM
ap-2083	182	4	/	/	SYM
ap-2083	182	5	s0375	s0375	VERB
ap-2083	182	6	-	-	PUNCT
ap-2083	182	7	9601(99)00672	9601(99)00672	NUM
ap-2083	182	8	-	-	PUNCT
ap-2083	182	9	6	6	NUM
ap-2083	182	10	[	[	NOUN
ap-2083	182	11	12	12	NUM
ap-2083	182	12	]	]	PUNCT
ap-2083	182	13	z.	z.	PROPN
ap-2083	182	14	ahmed	ahmed	PROPN
ap-2083	182	15	.	.	PUNCT
ap-2083	183	1	energy	energy	NOUN
ap-2083	183	2	band	band	NOUN
ap-2083	183	3	structure	structure	NOUN
ap-2083	183	4	due	due	ADP
ap-2083	183	5	to	to	ADP
ap-2083	183	6	a	a	DET
ap-2083	183	7	complex	complex	ADJ
ap-2083	183	8	,	,	PUNCT
ap-2083	183	9	periodic	periodic	ADJ
ap-2083	183	10	,	,	PUNCT
ap-2083	183	11	pt	pt	NOUN
ap-2083	183	12	-invariant	-invariant	NOUN
ap-2083	183	13	potential	potential	NOUN
ap-2083	183	14	.	.	PUNCT
ap-2083	184	1	phys	phy	NOUN
ap-2083	184	2	lett	lett	VERB
ap-2083	184	3	a	a	DET
ap-2083	184	4	286:231	286:231	NOUN
ap-2083	184	5	,	,	PUNCT
ap-2083	184	6	2001	2001	NUM
ap-2083	184	7	.	.	PUNCT
ap-2083	185	1	[	[	X
ap-2083	185	2	13	13	NUM
ap-2083	185	3	]	]	X
ap-2083	185	4	e.	e.	PROPN
ap-2083	185	5	demiralp	demiralp	PROPN
ap-2083	185	6	.	.	PUNCT
ap-2083	186	1	bound	bind	VERB
ap-2083	186	2	states	state	NOUN
ap-2083	186	3	of	of	ADP
ap-2083	186	4	n	n	CCONJ
ap-2083	186	5	-	-	PUNCT
ap-2083	186	6	dimensional	dimensional	ADJ
ap-2083	186	7	harmonic	harmonic	ADJ
ap-2083	186	8	oscillator	oscillator	NOUN
ap-2083	186	9	decorated	decorate	VERB
ap-2083	186	10	with	with	ADP
ap-2083	186	11	dirac	dirac	NOUN
ap-2083	186	12	delta	delta	NOUN
ap-2083	186	13	functions	function	NOUN
ap-2083	186	14	.	.	PUNCT
ap-2083	187	1	j	j	PROPN
ap-2083	187	2	phys	phy	NOUN
ap-2083	187	3	a	a	DET
ap-2083	187	4	38:4783	38:4783	NUM
ap-2083	187	5	,	,	PUNCT
ap-2083	187	6	2005	2005	NUM
ap-2083	187	7	.	.	PUNCT
ap-2083	188	1	doi	doi	NOUN
ap-2083	188	2	:	:	PUNCT
ap-2083	188	3	10.1088/0305	10.1088/0305	NUM
ap-2083	188	4	-	-	PUNCT
ap-2083	188	5	4470/38/22/003	4470/38/22/003	PROPN
ap-2083	188	6	[	[	X
ap-2083	188	7	14	14	NUM
ap-2083	188	8	]	]	X
ap-2083	188	9	e.	e.	PROPN
ap-2083	188	10	demiralp	demiralp	PROPN
ap-2083	188	11	.	.	PUNCT
ap-2083	189	1	properties	property	NOUN
ap-2083	189	2	of	of	ADP
ap-2083	189	3	a	a	DET
ap-2083	189	4	pseudo	pseudo	NOUN
ap-2083	189	5	-	-	ADJ
ap-2083	189	6	hermitian	hermitian	ADJ
ap-2083	189	7	hamiltonian	hamiltonian	NOUN
ap-2083	189	8	for	for	ADP
ap-2083	189	9	harmonic	harmonic	ADJ
ap-2083	189	10	oscillator	oscillator	NOUN
ap-2083	189	11	decorated	decorate	VERB
ap-2083	189	12	with	with	ADP
ap-2083	189	13	dirac	dirac	NOUN
ap-2083	189	14	delta	delta	NOUN
ap-2083	189	15	interactions	interaction	NOUN
ap-2083	189	16	.	.	PUNCT
ap-2083	190	1	czech	czech	PROPN
ap-2083	190	2	j	j	PROPN
ap-2083	190	3	phys	phy	NOUN
ap-2083	190	4	55:1081	55:1081	NUM
ap-2083	190	5	,	,	PUNCT
ap-2083	190	6	2005	2005	NUM
ap-2083	190	7	doi	doi	NOUN
ap-2083	190	8	:	:	PUNCT
ap-2083	190	9	10.1007	10.1007	NUM
ap-2083	190	10	/	/	SYM
ap-2083	190	11	s10582	s10582	VERB
ap-2083	190	12	-	-	PUNCT
ap-2083	190	13	005	005	NUM
ap-2083	190	14	-	-	PUNCT
ap-2083	190	15	0110	0110	NUM
ap-2083	190	16	-	-	SYM
ap-2083	190	17	2	2	NUM
ap-2083	190	18	[	[	NOUN
ap-2083	190	19	15	15	NUM
ap-2083	190	20	]	]	PUNCT
ap-2083	190	21	a.	a.	NOUN
ap-2083	190	22	mostafazadeh	mostafazadeh	PROPN
ap-2083	190	23	.	.	PUNCT
ap-2083	191	1	delta	delta	ADJ
ap-2083	191	2	-	-	PUNCT
ap-2083	191	3	function	function	NOUN
ap-2083	191	4	potential	potential	NOUN
ap-2083	191	5	with	with	ADP
ap-2083	191	6	a	a	DET
ap-2083	191	7	complex	complex	ADJ
ap-2083	191	8	coupling	coupling	NOUN
ap-2083	191	9	.	.	PUNCT
ap-2083	192	1	j	j	PROPN
ap-2083	192	2	phys	phy	NOUN
ap-2083	192	3	a	a	DET
ap-2083	192	4	39:13495	39:13495	NUM
ap-2083	192	5	,	,	PUNCT
ap-2083	192	6	2006	2006	NUM
ap-2083	192	7	.	.	PUNCT
ap-2083	193	1	doi	doi	NOUN
ap-2083	193	2	:	:	PUNCT
ap-2083	193	3	10.1088/0305	10.1088/0305	NUM
ap-2083	193	4	-	-	SYM
ap-2083	193	5	4470/39/43/008	4470/39/43/008	PROPN
ap-2083	193	6	[	[	X
ap-2083	193	7	16	16	NUM
ap-2083	193	8	]	]	PUNCT
ap-2083	193	9	a.	a.	NOUN
ap-2083	193	10	mostafazadeh	mostafazadeh	PROPN
ap-2083	193	11	,	,	PUNCT
ap-2083	193	12	et	et	PROPN
ap-2083	193	13	al	al	PROPN
ap-2083	193	14	.	.	PUNCT
ap-2083	194	1	spectral	spectral	ADJ
ap-2083	194	2	singularities	singularity	NOUN
ap-2083	194	3	,	,	PUNCT
ap-2083	194	4	biorthonormal	biorthonormal	ADJ
ap-2083	194	5	systems	system	NOUN
ap-2083	194	6	and	and	CCONJ
ap-2083	194	7	a	a	DET
ap-2083	194	8	two	two	NUM
ap-2083	194	9	-	-	PUNCT
ap-2083	194	10	parameter	parameter	NOUN
ap-2083	194	11	family	family	NOUN
ap-2083	194	12	of	of	ADP
ap-2083	194	13	complex	complex	ADJ
ap-2083	194	14	point	point	NOUN
ap-2083	194	15	interactions	interaction	NOUN
ap-2083	194	16	.	.	PUNCT
ap-2083	195	1	j	j	PROPN
ap-2083	195	2	phys	phy	NOUN
ap-2083	195	3	a	a	DET
ap-2083	195	4	42:125303	42:125303	NUM
ap-2083	195	5	,	,	PUNCT
ap-2083	195	6	2009	2009	NUM
ap-2083	195	7	.	.	PUNCT
ap-2083	196	1	doi	doi	NOUN
ap-2083	196	2	:	:	PUNCT
ap-2083	196	3	10.1088/1751	10.1088/1751	NUM
ap-2083	196	4	-	-	PUNCT
ap-2083	196	5	8113/42/12/12503	8113/42/12/12503	PROPN
ap-2083	197	1	[	[	X
ap-2083	197	2	17	17	NUM
ap-2083	197	3	]	]	X
ap-2083	197	4	h.	h.	PROPN
ap-2083	197	5	mehri	mehri	PROPN
ap-2083	197	6	-	-	PUNCT
ap-2083	197	7	dehnavi	dehnavi	VERB
ap-2083	197	8	,	,	PUNCT
ap-2083	198	1	et	et	PROPN
ap-2083	198	2	al	al	PROPN
ap-2083	198	3	.	.	PUNCT
ap-2083	198	4	application	application	NOUN
ap-2083	198	5	of	of	ADP
ap-2083	198	6	pseudo	pseudo	NOUN
ap-2083	198	7	-	-	ADJ
ap-2083	198	8	hermitian	hermitian	ADJ
ap-2083	198	9	quantum	quantum	ADJ
ap-2083	198	10	mechanics	mechanic	NOUN
ap-2083	198	11	to	to	ADP
ap-2083	198	12	a	a	DET
ap-2083	198	13	complex	complex	ADJ
ap-2083	198	14	scattering	scattering	ADJ
ap-2083	198	15	potential	potential	NOUN
ap-2083	198	16	with	with	ADP
ap-2083	198	17	point	point	NOUN
ap-2083	198	18	interactions	interaction	NOUN
ap-2083	198	19	.	.	PUNCT
ap-2083	199	1	j	j	PROPN
ap-2083	199	2	phys	phy	NOUN
ap-2083	199	3	a	a	DET
ap-2083	199	4	43:145301	43:145301	NUM
ap-2083	199	5	,	,	PUNCT
ap-2083	199	6	2010	2010	NUM
ap-2083	199	7	.	.	PUNCT
ap-2083	200	1	doi	doi	NOUN
ap-2083	200	2	:	:	PUNCT
ap-2083	200	3	10.1088/1751	10.1088/1751	NUM
ap-2083	200	4	-	-	PUNCT
ap-2083	200	5	8113/43/14/145301	8113/43/14/145301	PRON
ap-2083	201	1	[	[	X
ap-2083	201	2	18	18	NUM
ap-2083	201	3	]	]	PUNCT
ap-2083	201	4	h.	h.	PROPN
ap-2083	201	5	uncu	uncu	PROPN
ap-2083	201	6	,	,	PUNCT
ap-2083	201	7	et	et	PROPN
ap-2083	201	8	al	al	PROPN
ap-2083	201	9	.	.	PUNCT
ap-2083	201	10	bose	bose	PROPN
ap-2083	201	11	-	-	PUNCT
ap-2083	201	12	einstein	einstein	PROPN
ap-2083	201	13	condensate	condensate	NOUN
ap-2083	201	14	in	in	ADP
ap-2083	201	15	a	a	DET
ap-2083	201	16	harmonic	harmonic	ADJ
ap-2083	201	17	trap	trap	NOUN
ap-2083	201	18	with	with	ADP
ap-2083	201	19	an	an	DET
ap-2083	201	20	eccentric	eccentric	ADJ
ap-2083	201	21	dimple	dimple	ADJ
ap-2083	201	22	potential	potential	NOUN
ap-2083	201	23	.	.	PUNCT
ap-2083	202	1	las	las	PROPN
ap-2083	202	2	phys	phys	PROPN
ap-2083	202	3	18:331	18:331	NUM
ap-2083	202	4	,	,	PUNCT
ap-2083	202	5	2008	2008	NUM
ap-2083	202	6	.	.	PUNCT
ap-2083	203	1	[	[	X
ap-2083	203	2	19	19	NUM
ap-2083	203	3	]	]	X
ap-2083	203	4	v.	v.	CCONJ
ap-2083	203	5	jakubský	jakubský	PROPN
ap-2083	203	6	,	,	PUNCT
ap-2083	203	7	et	et	PROPN
ap-2083	203	8	al	al	PROPN
ap-2083	203	9	.	.	PUNCT
ap-2083	203	10	an	an	DET
ap-2083	203	11	explicitly	explicitly	ADV
ap-2083	203	12	solvable	solvable	ADJ
ap-2083	203	13	model	model	NOUN
ap-2083	203	14	of	of	ADP
ap-2083	203	15	the	the	DET
ap-2083	203	16	spontaneous	spontaneous	ADJ
ap-2083	203	17	pt	pt	PROPN
ap-2083	203	18	-symmetry	-symmetry	NOUN
ap-2083	203	19	breaking	breaking	NOUN
ap-2083	203	20	.	.	PUNCT
ap-2083	204	1	czech	czech	PROPN
ap-2083	204	2	j	j	PROPN
ap-2083	204	3	phys	phy	NOUN
ap-2083	204	4	55:1113–1116	55:1113–1116	NUM
ap-2083	204	5	,	,	PUNCT
ap-2083	204	6	2005	2005	NUM
ap-2083	204	7	.	.	PUNCT
ap-2083	205	1	doi	doi	NOUN
ap-2083	205	2	:	:	PUNCT
ap-2083	205	3	10.1007	10.1007	NUM
ap-2083	205	4	/	/	SYM
ap-2083	205	5	s10582	s10582	VERB
ap-2083	205	6	-	-	PUNCT
ap-2083	205	7	005	005	NUM
ap-2083	205	8	-	-	PUNCT
ap-2083	205	9	0115	0115	NUM
ap-2083	205	10	-	-	PUNCT
ap-2083	205	11	x	x	SYM
ap-2083	206	1	[	[	X
ap-2083	206	2	20	20	NUM
ap-2083	206	3	]	]	X
ap-2083	206	4	d.	d.	PROPN
ap-2083	206	5	krejčiřík	krejčiřík	PROPN
ap-2083	206	6	,	,	PUNCT
ap-2083	206	7	et	et	PROPN
ap-2083	206	8	al	al	PROPN
ap-2083	206	9	.	.	PROPN
ap-2083	206	10	pt	pt	PROPN
ap-2083	206	11	-symmetric	-symmetric	ADJ
ap-2083	206	12	models	model	NOUN
ap-2083	206	13	in	in	ADP
ap-2083	206	14	curved	curved	ADJ
ap-2083	206	15	manifolds	manifold	NOUN
ap-2083	206	16	.	.	PUNCT
ap-2083	207	1	j	j	PROPN
ap-2083	207	2	phys	phy	NOUN
ap-2083	207	3	a	a	PRON
ap-2083	207	4	43:485204	43:485204	NUM
ap-2083	207	5	,	,	PUNCT
ap-2083	207	6	2010	2010	NUM
ap-2083	207	7	.	.	PUNCT
ap-2083	208	1	doi	doi	NOUN
ap-2083	208	2	:	:	PUNCT
ap-2083	208	3	10.1088/1751	10.1088/1751	NUM
ap-2083	208	4	-	-	PUNCT
ap-2083	208	5	8113/43/48/485204	8113/43/48/485204	PROPN
ap-2083	208	6	[	[	X
ap-2083	208	7	21	21	NUM
ap-2083	208	8	]	]	PUNCT
ap-2083	208	9	p.	p.	NOUN
ap-2083	208	10	siegl	siegl	PROPN
ap-2083	208	11	.	.	PUNCT
ap-2083	209	1	pt	pt	X
ap-2083	209	2	-symmetric	-symmetric	ADJ
ap-2083	209	3	square	square	ADJ
ap-2083	209	4	well	well	ADJ
ap-2083	209	5	-	-	PUNCT
ap-2083	209	6	perturbations	perturbation	NOUN
ap-2083	209	7	and	and	CCONJ
ap-2083	209	8	the	the	DET
ap-2083	209	9	existence	existence	NOUN
ap-2083	209	10	of	of	ADP
ap-2083	209	11	metric	metric	ADJ
ap-2083	209	12	operator	operator	NOUN
ap-2083	209	13	.	.	PUNCT
ap-2083	210	1	int	int	PROPN
ap-2083	211	1	j	j	PROPN
ap-2083	211	2	theor	theor	PROPN
ap-2083	211	3	phys	phy	NOUN
ap-2083	211	4	textbf50:991	textbf50:991	PROPN
ap-2083	211	5	,	,	PUNCT
ap-2083	211	6	2011	2011	NUM
ap-2083	211	7	.	.	PUNCT
ap-2083	212	1	doi	doi	NOUN
ap-2083	212	2	:	:	PUNCT
ap-2083	212	3	10.1007	10.1007	NUM
ap-2083	212	4	/	/	SYM
ap-2083	212	5	s10773	s10773	NUM
ap-2083	212	6	-	-	PUNCT
ap-2083	212	7	010	010	NUM
ap-2083	212	8	-	-	PUNCT
ap-2083	212	9	0593	0593	NUM
ap-2083	212	10	-	-	PUNCT
ap-2083	212	11	x	x	PUNCT
ap-2083	213	1	[	[	X
ap-2083	213	2	22	22	NUM
ap-2083	213	3	]	]	PUNCT
ap-2083	213	4	s.	s.	PROPN
ap-2083	213	5	fassari	fassari	PROPN
ap-2083	213	6	,	,	PUNCT
ap-2083	213	7	et	et	PROPN
ap-2083	213	8	al	al	PROPN
ap-2083	213	9	.	.	PROPN
ap-2083	214	1	on	on	ADP
ap-2083	214	2	the	the	DET
ap-2083	214	3	spectrum	spectrum	NOUN
ap-2083	214	4	of	of	ADP
ap-2083	214	5	the	the	DET
ap-2083	214	6	schrödinger	schrödinger	ADJ
ap-2083	214	7	equation	equation	NOUN
ap-2083	214	8	of	of	ADP
ap-2083	214	9	the	the	DET
ap-2083	214	10	one	one	NUM
ap-2083	214	11	-	-	PUNCT
ap-2083	214	12	dimensional	dimensional	ADJ
ap-2083	214	13	harmonic	harmonic	ADJ
ap-2083	214	14	oscillator	oscillator	NOUN
ap-2083	214	15	perturbed	perturb	VERB
ap-2083	214	16	by	by	ADP
ap-2083	214	17	two	two	NUM
ap-2083	214	18	identical	identical	ADJ
ap-2083	214	19	attractive	attractive	ADJ
ap-2083	214	20	point	point	NOUN
ap-2083	214	21	interactions	interaction	NOUN
ap-2083	214	22	.	.	PUNCT
ap-2083	215	1	rep	rep	PROPN
ap-2083	215	2	math	math	PROPN
ap-2083	215	3	phys	phys	PROPN
ap-2083	215	4	69:353	69:353	PROPN
ap-2083	215	5	,	,	PUNCT
ap-2083	215	6	2012	2012	NUM
ap-2083	215	7	.	.	PUNCT
ap-2083	216	1	[	[	X
ap-2083	216	2	23	23	NUM
ap-2083	216	3	]	]	PUNCT
ap-2083	216	4	e.	e.	PROPN
ap-2083	216	5	p.	p.	PROPN
ap-2083	216	6	gross	gross	PROPN
ap-2083	216	7	.	.	PUNCT
ap-2083	216	8	structure	structure	NOUN
ap-2083	216	9	of	of	ADP
ap-2083	216	10	a	a	DET
ap-2083	216	11	quantized	quantize	VERB
ap-2083	216	12	vortex	vortex	NOUN
ap-2083	216	13	in	in	ADP
ap-2083	216	14	boson	boson	NOUN
ap-2083	216	15	systems	system	NOUN
ap-2083	216	16	.	.	PUNCT
ap-2083	217	1	nuovo	nuovo	PROPN
ap-2083	217	2	cimento	cimento	PROPN
ap-2083	217	3	20:454	20:454	NUM
ap-2083	217	4	,	,	PUNCT
ap-2083	217	5	1961	1961	NUM
ap-2083	217	6	.	.	PUNCT
ap-2083	218	1	[	[	X
ap-2083	218	2	24	24	NUM
ap-2083	218	3	]	]	PUNCT
ap-2083	218	4	l.	l.	PROPN
ap-2083	218	5	p.	p.	PROPN
ap-2083	218	6	pitaevskii	pitaevskii	PROPN
ap-2083	218	7	.	.	PUNCT
ap-2083	219	1	vortex	vortex	NOUN
ap-2083	219	2	lines	line	NOUN
ap-2083	219	3	in	in	ADP
ap-2083	219	4	an	an	DET
ap-2083	219	5	imperfect	imperfect	ADJ
ap-2083	219	6	bose	bose	NOUN
ap-2083	219	7	gas	gas	NOUN
ap-2083	219	8	.	.	PUNCT
ap-2083	220	1	sov	sov	PROPN
ap-2083	220	2	phys	phy	NOUN
ap-2083	220	3	jetp	jetp	VERB
ap-2083	220	4	13:451	13:451	NUM
ap-2083	220	5	,	,	PUNCT
ap-2083	220	6	1961	1961	NUM
ap-2083	220	7	.	.	PUNCT
ap-2083	221	1	[	[	X
ap-2083	221	2	25	25	NUM
ap-2083	221	3	]	]	X
ap-2083	221	4	w.	w.	PROPN
ap-2083	221	5	d.	d.	PROPN
ap-2083	221	6	heiss	heiss	PROPN
ap-2083	221	7	,	,	PUNCT
ap-2083	221	8	et	et	PROPN
ap-2083	221	9	al	al	PROPN
ap-2083	221	10	.	.	PUNCT
ap-2083	221	11	spectral	spectral	ADJ
ap-2083	221	12	singularities	singularity	NOUN
ap-2083	221	13	in	in	ADP
ap-2083	221	14	pt	pt	X
ap-2083	221	15	-symmetric	-symmetric	ADJ
ap-2083	221	16	bose	bose	NOUN
ap-2083	221	17	-	-	PUNCT
ap-2083	221	18	einstein	einstein	NOUN
ap-2083	221	19	condensates	condensate	NOUN
ap-2083	221	20	.	.	PUNCT
ap-2083	222	1	j	j	PROPN
ap-2083	222	2	phys	phy	NOUN
ap-2083	222	3	a	a	DET
ap-2083	222	4	46:275307	46:275307	NUM
ap-2083	222	5	,	,	PUNCT
ap-2083	222	6	2013	2013	NUM
ap-2083	222	7	.	.	PUNCT
ap-2083	223	1	doi	doi	NOUN
ap-2083	223	2	:	:	PUNCT
ap-2083	223	3	10.1088/1751	10.1088/1751	NUM
ap-2083	223	4	-	-	SYM
ap-2083	223	5	8113/46/27/275307	8113/46/27/275307	NUM
ap-2083	223	6	121	121	NUM
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ap-2083	223	8	http://dx.doi.org/10.1103/physreva.86.013612	http://dx.doi.org/10.1103/physreva.86.013612	PROPN
ap-2083	223	9	http://dx.doi.org/10.1088/1751-8113/45/44/444008	http://dx.doi.org/10.1088/1751-8113/45/44/444008	PROPN
ap-2083	223	10	http://dx.doi.org/10.1002/prop.201200080	http://dx.doi.org/10.1002/prop.201200080	NOUN
ap-2083	223	11	http://dx.doi.org/10.1088/1751-8113/46/37/375301	http://dx.doi.org/10.1088/1751-8113/46/37/375301	PROPN
ap-2083	223	12	http://dx.doi.org/10.1103/physreva.87.051601	http://dx.doi.org/10.1103/physreva.87.051601	PROPN
ap-2083	223	13	http://dx.doi.org/10.2478/s11533-011-0139-3	http://dx.doi.org/10.2478/s11533-011-0139-3	PUNCT
ap-2083	223	14	http://dx.doi.org/10.1016/s0375-9601(99)00672-6	http://dx.doi.org/10.1016/s0375-9601(99)00672-6	PROPN
ap-2083	223	15	http://dx.doi.org/10.1088/0305-4470/38/22/003	http://dx.doi.org/10.1088/0305-4470/38/22/003	PROPN
ap-2083	223	16	http://dx.doi.org/10.1007/s10582-005-0110-2	http://dx.doi.org/10.1007/s10582-005-0110-2	X
ap-2083	223	17	http://dx.doi.org/10.1088/0305-4470/39/43/008	http://dx.doi.org/10.1088/0305-4470/39/43/008	PROPN
ap-2083	223	18	http://dx.doi.org/10.1088/1751-8113/42/12/12503	http://dx.doi.org/10.1088/1751-8113/42/12/12503	ADP
ap-2083	223	19	http://dx.doi.org/10.1088/1751-8113/43/14/145301	http://dx.doi.org/10.1088/1751-8113/43/14/145301	PROPN
ap-2083	223	20	http://dx.doi.org/10.1007/s10582-005-0115-x	http://dx.doi.org/10.1007/s10582-005-0115-x	PROPN
ap-2083	223	21	http://dx.doi.org/10.1088/1751-8113/43/48/485204	http://dx.doi.org/10.1088/1751-8113/43/48/485204	NOUN
ap-2083	223	22	http://dx.doi.org/10.1007/s10773-010-0593-x	http://dx.doi.org/10.1007/s10773-010-0593-x	NOUN
ap-2083	223	23	http://dx.doi.org/10.1088/1751-8113/46/27/275307	http://dx.doi.org/10.1088/1751-8113/46/27/275307	X
ap-2083	223	24	acta	acta	PROPN
ap-2083	223	25	polytechnica	polytechnica	PROPN
ap-2083	223	26	54(2):116–121	54(2):116–121	NUM
ap-2083	223	27	,	,	PUNCT
ap-2083	223	28	2014	2014	NUM
ap-2083	223	29	1	1	NUM
ap-2083	223	30	introduction	introduction	NOUN
ap-2083	223	31	2	2	NUM
ap-2083	223	32	bose	bose	NOUN
ap-2083	223	33	-	-	PUNCT
ap-2083	223	34	einstein	einstein	NOUN
ap-2083	223	35	condensate	condensate	NOUN
ap-2083	223	36	in	in	ADP
ap-2083	223	37	a	a	DET
ap-2083	223	38	pt	pt	ADJ
ap-2083	223	39	-	-	ADJ
ap-2083	223	40	symmetric	symmetric	ADJ
ap-2083	223	41	harmonic	harmonic	ADJ
ap-2083	223	42	trap	trap	NOUN
ap-2083	223	43	3	3	NUM
ap-2083	223	44	eigenvalue	eigenvalue	NOUN
ap-2083	223	45	spectra	spectra	ADJ
ap-2083	223	46	4	4	NUM
ap-2083	223	47	eigenvalue	eigenvalue	ADJ
ap-2083	223	48	shifts	shift	NOUN
ap-2083	223	49	5	5	NUM
ap-2083	223	50	conclusions	conclusion	NOUN
ap-2083	223	51	acknowledgements	acknowledgement	NOUN
ap-2083	223	52	references	reference	NOUN