id	sid	tid	token	lemma	pos
ap-1797	1	1	acta	acta	PROPN
ap-1797	1	2	polytechnica	polytechnica	PROPN
ap-1797	1	3	acta	acta	PROPN
ap-1797	1	4	polytechnica	polytechnica	PROPN
ap-1797	1	5	53(3):259–267	53(3):259–267	PROPN
ap-1797	1	6	,	,	PUNCT
ap-1797	1	7	2013	2013	NUM
ap-1797	1	8	©	©	PROPN
ap-1797	1	9	czech	czech	PROPN
ap-1797	1	10	technical	technical	PROPN
ap-1797	1	11	university	university	PROPN
ap-1797	1	12	in	in	ADP
ap-1797	1	13	prague	prague	PROPN
ap-1797	1	14	,	,	PUNCT
ap-1797	1	15	2013	2013	NUM
ap-1797	1	16	available	available	ADJ
ap-1797	1	17	online	online	ADV
ap-1797	1	18	at	at	ADP
ap-1797	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1797	1	20	stationary	stationary	ADJ
ap-1797	1	21	and	and	CCONJ
ap-1797	1	22	dynamical	dynamical	ADJ
ap-1797	1	23	solutions	solution	NOUN
ap-1797	1	24	of	of	ADP
ap-1797	1	25	the	the	DET
ap-1797	1	26	gross	gross	ADJ
ap-1797	1	27	-	-	PUNCT
ap-1797	1	28	pitaevskii	pitaevskii	ADJ
ap-1797	1	29	equation	equation	NOUN
ap-1797	1	30	for	for	ADP
ap-1797	1	31	a	a	DET
ap-1797	1	32	bose	bose	NOUN
ap-1797	1	33	-	-	PUNCT
ap-1797	1	34	einstein	einstein	NOUN
ap-1797	1	35	condensate	condensate	NOUN
ap-1797	1	36	in	in	ADP
ap-1797	1	37	a	a	DET
ap-1797	1	38	pt	pt	NOUN
ap-1797	1	39	symmetric	symmetric	ADJ
ap-1797	1	40	double	double	ADJ
ap-1797	1	41	well	well	NOUN
ap-1797	1	42	holger	holger	NOUN
ap-1797	1	43	cartarius∗	cartarius∗	NOUN
ap-1797	1	44	,	,	PUNCT
ap-1797	1	45	dennis	dennis	PROPN
ap-1797	1	46	dast	dast	PROPN
ap-1797	1	47	,	,	PUNCT
ap-1797	1	48	daniel	daniel	PROPN
ap-1797	1	49	haag	haag	PROPN
ap-1797	1	50	,	,	PUNCT
ap-1797	1	51	günter	günter	PROPN
ap-1797	1	52	wunner	wunner	NOUN
ap-1797	1	53	,	,	PUNCT
ap-1797	1	54	rüdiger	rüdiger	ADJ
ap-1797	1	55	eichler	eichler	NOUN
ap-1797	1	56	,	,	PUNCT
ap-1797	1	57	jorg	jorg	PROPN
ap-1797	1	58	main	main	PROPN
ap-1797	1	59	institut	institut	PROPN
ap-1797	1	60	für	für	PROPN
ap-1797	1	61	theoretische	theoretische	PROPN
ap-1797	1	62	physik	physik	PROPN
ap-1797	1	63	1	1	NUM
ap-1797	1	64	,	,	PUNCT
ap-1797	1	65	universität	universität	PROPN
ap-1797	1	66	stuttgart	stuttgart	PROPN
ap-1797	1	67	,	,	PUNCT
ap-1797	1	68	pfaffenwaldring	pfaffenwaldre	VERB
ap-1797	1	69	57	57	NUM
ap-1797	1	70	,	,	PUNCT
ap-1797	1	71	70550	70550	NUM
ap-1797	1	72	stuttgart	stuttgart	PROPN
ap-1797	1	73	,	,	PUNCT
ap-1797	1	74	germany	germany	PROPN
ap-1797	1	75	∗	∗	NOUN
ap-1797	1	76	corresponding	correspond	VERB
ap-1797	1	77	author	author	NOUN
ap-1797	1	78	:	:	PUNCT
ap-1797	1	79	holger.cartarius@itp1.uni-stuttgart.de	holger.cartarius@itp1.uni-stuttgart.de	ADJ
ap-1797	1	80	abstract	abstract	ADJ
ap-1797	1	81	.	.	PUNCT
ap-1797	2	1	we	we	PRON
ap-1797	2	2	investigate	investigate	VERB
ap-1797	2	3	the	the	DET
ap-1797	2	4	gross	gross	ADJ
ap-1797	2	5	-	-	PUNCT
ap-1797	2	6	pitaevskii	pitaevskii	ADJ
ap-1797	2	7	equation	equation	NOUN
ap-1797	2	8	for	for	ADP
ap-1797	2	9	a	a	DET
ap-1797	2	10	bose	bose	NOUN
ap-1797	2	11	-	-	PUNCT
ap-1797	2	12	einstein	einstein	NOUN
ap-1797	2	13	condensate	condensate	NOUN
ap-1797	2	14	in	in	ADP
ap-1797	2	15	a	a	DET
ap-1797	2	16	pt	pt	NOUN
ap-1797	2	17	symmetric	symmetric	ADJ
ap-1797	2	18	double	double	ADJ
ap-1797	2	19	-	-	PUNCT
ap-1797	2	20	well	well	NOUN
ap-1797	2	21	potential	potential	NOUN
ap-1797	2	22	by	by	ADP
ap-1797	2	23	means	mean	NOUN
ap-1797	2	24	of	of	ADP
ap-1797	2	25	the	the	DET
ap-1797	2	26	time	time	NOUN
ap-1797	2	27	-	-	PUNCT
ap-1797	2	28	dependent	dependent	ADJ
ap-1797	2	29	variational	variational	ADJ
ap-1797	2	30	principle	principle	NOUN
ap-1797	2	31	and	and	CCONJ
ap-1797	2	32	numerically	numerically	ADV
ap-1797	2	33	exact	exact	ADJ
ap-1797	2	34	solutions	solution	NOUN
ap-1797	2	35	.	.	PUNCT
ap-1797	3	1	a	a	DET
ap-1797	3	2	one	one	NUM
ap-1797	3	3	-	-	PUNCT
ap-1797	3	4	dimensional	dimensional	ADJ
ap-1797	3	5	and	and	CCONJ
ap-1797	3	6	a	a	DET
ap-1797	3	7	fully	fully	ADV
ap-1797	3	8	three	three	NUM
ap-1797	3	9	-	-	PUNCT
ap-1797	3	10	dimensional	dimensional	ADJ
ap-1797	3	11	setup	setup	NOUN
ap-1797	3	12	are	be	AUX
ap-1797	3	13	used	use	VERB
ap-1797	3	14	.	.	PUNCT
ap-1797	4	1	stationary	stationary	ADJ
ap-1797	4	2	states	state	NOUN
ap-1797	4	3	are	be	AUX
ap-1797	4	4	determined	determine	VERB
ap-1797	4	5	and	and	CCONJ
ap-1797	4	6	the	the	DET
ap-1797	4	7	propagation	propagation	NOUN
ap-1797	4	8	of	of	ADP
ap-1797	4	9	wave	wave	NOUN
ap-1797	4	10	function	function	NOUN
ap-1797	4	11	is	be	AUX
ap-1797	4	12	investigated	investigate	VERB
ap-1797	4	13	using	use	VERB
ap-1797	4	14	the	the	DET
ap-1797	4	15	time	time	NOUN
ap-1797	4	16	-	-	PUNCT
ap-1797	4	17	dependent	dependent	ADJ
ap-1797	4	18	grosspitaevskii	grosspitaevskii	ADJ
ap-1797	4	19	equation	equation	NOUN
ap-1797	4	20	.	.	PUNCT
ap-1797	5	1	due	due	ADP
ap-1797	5	2	to	to	ADP
ap-1797	5	3	the	the	DET
ap-1797	5	4	nonlinearity	nonlinearity	NOUN
ap-1797	5	5	of	of	ADP
ap-1797	5	6	the	the	DET
ap-1797	5	7	gross	gross	ADJ
ap-1797	5	8	-	-	PUNCT
ap-1797	5	9	pitaevskii	pitaevskii	ADJ
ap-1797	5	10	equation	equation	NOUN
ap-1797	5	11	the	the	DET
ap-1797	5	12	potential	potential	NOUN
ap-1797	5	13	depends	depend	VERB
ap-1797	5	14	on	on	ADP
ap-1797	5	15	the	the	DET
ap-1797	5	16	wave	wave	NOUN
ap-1797	5	17	function	function	NOUN
ap-1797	5	18	and	and	CCONJ
ap-1797	5	19	its	its	PRON
ap-1797	5	20	solutions	solution	NOUN
ap-1797	5	21	decide	decide	VERB
ap-1797	5	22	whether	whether	SCONJ
ap-1797	5	23	or	or	CCONJ
ap-1797	5	24	not	not	PART
ap-1797	5	25	the	the	DET
ap-1797	5	26	hamiltonian	hamiltonian	NOUN
ap-1797	5	27	itself	itself	PRON
ap-1797	5	28	is	be	AUX
ap-1797	5	29	pt	pt	X
ap-1797	5	30	symmetric	symmetric	ADJ
ap-1797	5	31	.	.	PUNCT
ap-1797	6	1	stationary	stationary	ADJ
ap-1797	6	2	solutions	solution	NOUN
ap-1797	6	3	with	with	ADP
ap-1797	6	4	real	real	ADJ
ap-1797	6	5	energy	energy	NOUN
ap-1797	6	6	eigenvalues	eigenvalue	VERB
ap-1797	6	7	fulfilling	fulfil	VERB
ap-1797	6	8	exact	exact	ADJ
ap-1797	6	9	pt	pt	NOUN
ap-1797	6	10	symmetry	symmetry	NOUN
ap-1797	6	11	are	be	AUX
ap-1797	6	12	found	find	VERB
ap-1797	6	13	as	as	ADV
ap-1797	6	14	well	well	ADV
ap-1797	6	15	as	as	ADP
ap-1797	6	16	pt	pt	X
ap-1797	6	17	broken	break	VERB
ap-1797	6	18	eigenstates	eigenstate	NOUN
ap-1797	6	19	with	with	ADP
ap-1797	6	20	complex	complex	ADJ
ap-1797	6	21	energies	energy	NOUN
ap-1797	6	22	.	.	PUNCT
ap-1797	7	1	the	the	DET
ap-1797	7	2	latter	latter	ADJ
ap-1797	7	3	describe	describe	VERB
ap-1797	7	4	decaying	decay	VERB
ap-1797	7	5	or	or	CCONJ
ap-1797	7	6	growing	grow	VERB
ap-1797	7	7	probability	probability	NOUN
ap-1797	7	8	amplitudes	amplitude	NOUN
ap-1797	7	9	and	and	CCONJ
ap-1797	7	10	are	be	AUX
ap-1797	7	11	not	not	PART
ap-1797	7	12	true	true	ADJ
ap-1797	7	13	stationary	stationary	ADJ
ap-1797	7	14	solutions	solution	NOUN
ap-1797	7	15	of	of	ADP
ap-1797	7	16	the	the	DET
ap-1797	7	17	time	time	NOUN
ap-1797	7	18	-	-	PUNCT
ap-1797	7	19	dependent	dependent	ADJ
ap-1797	7	20	gross	gross	ADJ
ap-1797	7	21	-	-	PUNCT
ap-1797	7	22	pitaevskii	pitaevskii	ADJ
ap-1797	7	23	equation	equation	NOUN
ap-1797	7	24	.	.	PUNCT
ap-1797	8	1	however	however	ADV
ap-1797	8	2	,	,	PUNCT
ap-1797	8	3	they	they	PRON
ap-1797	8	4	still	still	ADV
ap-1797	8	5	provide	provide	VERB
ap-1797	8	6	qualitative	qualitative	ADJ
ap-1797	8	7	information	information	NOUN
ap-1797	8	8	about	about	ADP
ap-1797	8	9	the	the	DET
ap-1797	8	10	time	time	NOUN
ap-1797	8	11	evolution	evolution	NOUN
ap-1797	8	12	of	of	ADP
ap-1797	8	13	the	the	DET
ap-1797	8	14	wave	wave	NOUN
ap-1797	8	15	functions	function	NOUN
ap-1797	8	16	.	.	PUNCT
ap-1797	9	1	keywords	keyword	NOUN
ap-1797	9	2	:	:	PUNCT
ap-1797	9	3	bose	bose	NOUN
ap-1797	9	4	-	-	PUNCT
ap-1797	9	5	einstein	einstein	NOUN
ap-1797	9	6	condensates	condensate	NOUN
ap-1797	9	7	,	,	PUNCT
ap-1797	9	8	pt	pt	X
ap-1797	9	9	symmetry	symmetry	NOUN
ap-1797	9	10	,	,	PUNCT
ap-1797	9	11	gross	gross	ADJ
ap-1797	9	12	-	-	PUNCT
ap-1797	9	13	pitaevskii	pitaevskii	ADJ
ap-1797	9	14	equation	equation	NOUN
ap-1797	9	15	,	,	PUNCT
ap-1797	9	16	stationary	stationary	ADJ
ap-1797	9	17	states	state	NOUN
ap-1797	9	18	,	,	PUNCT
ap-1797	9	19	dynamics	dynamic	NOUN
ap-1797	9	20	.	.	PUNCT
ap-1797	10	1	1	1	X
ap-1797	10	2	.	.	X
ap-1797	10	3	introduction	introduction	NOUN
ap-1797	10	4	bose	bose	NOUN
ap-1797	10	5	-	-	PUNCT
ap-1797	10	6	einstein	einstein	NOUN
ap-1797	10	7	condensates	condensate	NOUN
ap-1797	10	8	can	can	AUX
ap-1797	10	9	,	,	PUNCT
ap-1797	10	10	at	at	ADP
ap-1797	10	11	extremely	extremely	ADV
ap-1797	10	12	low	low	ADJ
ap-1797	10	13	temperatures	temperature	NOUN
ap-1797	10	14	,	,	PUNCT
ap-1797	10	15	be	be	AUX
ap-1797	10	16	described	describe	VERB
ap-1797	10	17	by	by	ADP
ap-1797	10	18	the	the	DET
ap-1797	10	19	gross	gross	ADJ
ap-1797	10	20	-	-	PUNCT
ap-1797	10	21	pitaevskii	pitaevskii	ADJ
ap-1797	10	22	equation	equation	NOUN
ap-1797	10	23	[	[	X
ap-1797	10	24	1	1	NUM
ap-1797	10	25	,	,	PUNCT
ap-1797	10	26	2	2	NUM
ap-1797	10	27	]	]	PUNCT
ap-1797	10	28	,	,	PUNCT
ap-1797	10	29	which	which	PRON
ap-1797	10	30	reads	read	VERB
ap-1797	10	31	in	in	ADP
ap-1797	10	32	a	a	DET
ap-1797	10	33	particle	particle	NOUN
ap-1797	10	34	number	number	NOUN
ap-1797	10	35	scaled	scale	VERB
ap-1797	10	36	form	form	NOUN
ap-1797	10	37	and	and	CCONJ
ap-1797	10	38	in	in	ADP
ap-1797	10	39	appropriate	appropriate	ADJ
ap-1797	10	40	units	unit	NOUN
ap-1797	10	41	iψ̇(x	iψ̇(x	PROPN
ap-1797	10	42	,	,	PUNCT
ap-1797	10	43	t	t	PROPN
ap-1797	10	44	)	)	PUNCT
ap-1797	10	45	=	=	SYM
ap-1797	10	46	(	(	PUNCT
ap-1797	10	47	−∆	−∆	NOUN
ap-1797	10	48	+	+	CCONJ
ap-1797	10	49	v	v	X
ap-1797	10	50	(	(	PUNCT
ap-1797	10	51	x)−	x)−	PROPN
ap-1797	10	52	g|ψ(x	g|ψ(x	PROPN
ap-1797	10	53	,	,	PUNCT
ap-1797	10	54	t)|2	t)|2	ADJ
ap-1797	10	55	)	)	PUNCT
ap-1797	10	56	ψ(x	ψ(x	PROPN
ap-1797	10	57	,	,	PUNCT
ap-1797	10	58	t	t	PROPN
ap-1797	10	59	)	)	PUNCT
ap-1797	10	60	.	.	PUNCT
ap-1797	11	1	(	(	PUNCT
ap-1797	11	2	1	1	X
ap-1797	11	3	)	)	PUNCT
ap-1797	11	4	this	this	PRON
ap-1797	11	5	is	be	AUX
ap-1797	11	6	the	the	DET
ap-1797	11	7	hartree	hartree	ADJ
ap-1797	11	8	approximation	approximation	NOUN
ap-1797	11	9	of	of	ADP
ap-1797	11	10	the	the	DET
ap-1797	11	11	corresponding	correspond	VERB
ap-1797	11	12	many	many	ADJ
ap-1797	11	13	-	-	PUNCT
ap-1797	11	14	particle	particle	NOUN
ap-1797	11	15	equation	equation	NOUN
ap-1797	11	16	for	for	ADP
ap-1797	11	17	the	the	DET
ap-1797	11	18	dilute	dilute	ADJ
ap-1797	11	19	atomic	atomic	ADJ
ap-1797	11	20	gas	gas	NOUN
ap-1797	11	21	,	,	PUNCT
ap-1797	11	22	where	where	SCONJ
ap-1797	11	23	the	the	DET
ap-1797	11	24	assumption	assumption	NOUN
ap-1797	11	25	that	that	SCONJ
ap-1797	11	26	all	all	DET
ap-1797	11	27	atoms	atom	NOUN
ap-1797	11	28	are	be	AUX
ap-1797	11	29	in	in	ADP
ap-1797	11	30	the	the	DET
ap-1797	11	31	quantum	quantum	ADJ
ap-1797	11	32	mechanical	mechanical	ADJ
ap-1797	11	33	ground	ground	NOUN
ap-1797	11	34	state	state	NOUN
ap-1797	11	35	is	be	AUX
ap-1797	11	36	used	use	VERB
ap-1797	11	37	.	.	PUNCT
ap-1797	12	1	an	an	DET
ap-1797	12	2	external	external	ADJ
ap-1797	12	3	potential	potential	NOUN
ap-1797	12	4	,	,	PUNCT
ap-1797	12	5	in	in	ADP
ap-1797	12	6	which	which	PRON
ap-1797	12	7	the	the	DET
ap-1797	12	8	atom	atom	NOUN
ap-1797	12	9	cloud	cloud	NOUN
ap-1797	12	10	is	be	AUX
ap-1797	12	11	trapped	trap	VERB
ap-1797	12	12	,	,	PUNCT
ap-1797	12	13	is	be	AUX
ap-1797	12	14	described	describe	VERB
ap-1797	12	15	by	by	ADP
ap-1797	12	16	v	v	PROPN
ap-1797	12	17	(	(	PUNCT
ap-1797	12	18	x	x	NOUN
ap-1797	12	19	)	)	PUNCT
ap-1797	12	20	.	.	PUNCT
ap-1797	13	1	additionally	additionally	ADV
ap-1797	13	2	,	,	PUNCT
ap-1797	13	3	the	the	DET
ap-1797	13	4	atoms	atom	NOUN
ap-1797	13	5	interact	interact	VERB
ap-1797	13	6	via	via	ADP
ap-1797	13	7	the	the	DET
ap-1797	13	8	short	short	ADJ
ap-1797	13	9	-	-	PUNCT
ap-1797	13	10	range	range	NOUN
ap-1797	13	11	van	van	PROPN
ap-1797	13	12	der	der	NOUN
ap-1797	13	13	waals	waal	NOUN
ap-1797	13	14	force	force	NOUN
ap-1797	13	15	.	.	PUNCT
ap-1797	14	1	in	in	ADP
ap-1797	14	2	the	the	DET
ap-1797	14	3	dilute	dilute	NOUN
ap-1797	14	4	gas	gas	NOUN
ap-1797	14	5	it	it	PRON
ap-1797	14	6	can	can	AUX
ap-1797	14	7	be	be	AUX
ap-1797	14	8	described	describe	VERB
ap-1797	14	9	sufficiently	sufficiently	ADV
ap-1797	14	10	exact	exact	ADJ
ap-1797	14	11	by	by	ADP
ap-1797	14	12	an	an	DET
ap-1797	14	13	s	s	NOUN
ap-1797	14	14	-	-	PUNCT
ap-1797	14	15	wave	wave	NOUN
ap-1797	14	16	scattering	scattering	NOUN
ap-1797	14	17	process	process	NOUN
ap-1797	14	18	,	,	PUNCT
ap-1797	14	19	which	which	PRON
ap-1797	14	20	leads	lead	VERB
ap-1797	14	21	in	in	ADP
ap-1797	14	22	the	the	DET
ap-1797	14	23	mean	mean	ADJ
ap-1797	14	24	-	-	PUNCT
ap-1797	14	25	field	field	NOUN
ap-1797	14	26	approximation	approximation	NOUN
ap-1797	14	27	to	to	ADP
ap-1797	14	28	the	the	DET
ap-1797	14	29	nonlinear	nonlinear	ADJ
ap-1797	14	30	contribution	contribution	NOUN
ap-1797	14	31	−g|ψ(x	−g|ψ(x	NOUN
ap-1797	14	32	,	,	PUNCT
ap-1797	14	33	t)|2	t)|2	PROPN
ap-1797	14	34	.	.	PUNCT
ap-1797	15	1	the	the	DET
ap-1797	15	2	strength	strength	NOUN
ap-1797	15	3	g	g	PROPN
ap-1797	15	4	is	be	AUX
ap-1797	15	5	determined	determine	VERB
ap-1797	15	6	by	by	ADP
ap-1797	15	7	the	the	DET
ap-1797	15	8	s	s	NOUN
ap-1797	15	9	-	-	PUNCT
ap-1797	15	10	wave	wave	NOUN
ap-1797	15	11	scattering	scattering	NOUN
ap-1797	15	12	length	length	NOUN
ap-1797	15	13	.	.	PUNCT
ap-1797	16	1	using	use	VERB
ap-1797	16	2	magnetic	magnetic	ADJ
ap-1797	16	3	fields	field	NOUN
ap-1797	16	4	acting	act	VERB
ap-1797	16	5	on	on	ADP
ap-1797	16	6	the	the	DET
ap-1797	16	7	hyperfine	hyperfine	ADJ
ap-1797	16	8	levels	level	NOUN
ap-1797	16	9	of	of	ADP
ap-1797	16	10	the	the	DET
ap-1797	16	11	atoms	atom	NOUN
ap-1797	16	12	and	and	CCONJ
ap-1797	16	13	exploiting	exploit	VERB
ap-1797	16	14	feshbach	feshbach	NOUN
ap-1797	16	15	resonances	resonance	NOUN
ap-1797	16	16	,	,	PUNCT
ap-1797	16	17	the	the	DET
ap-1797	16	18	scattering	scatter	VERB
ap-1797	16	19	length	length	NOUN
ap-1797	16	20	can	can	AUX
ap-1797	16	21	be	be	AUX
ap-1797	16	22	tuned	tune	VERB
ap-1797	16	23	and	and	CCONJ
ap-1797	16	24	g	g	NOUN
ap-1797	16	25	is	be	AUX
ap-1797	16	26	a	a	DET
ap-1797	16	27	true	true	ADJ
ap-1797	16	28	parameter	parameter	NOUN
ap-1797	16	29	of	of	ADP
ap-1797	16	30	the	the	DET
ap-1797	16	31	system	system	NOUN
ap-1797	16	32	,	,	PUNCT
ap-1797	16	33	which	which	PRON
ap-1797	16	34	can	can	AUX
ap-1797	16	35	be	be	AUX
ap-1797	16	36	varied	varied	ADJ
ap-1797	16	37	.	.	PUNCT
ap-1797	17	1	bose	bose	NOUN
ap-1797	17	2	-	-	PUNCT
ap-1797	17	3	einstein	einstein	NOUN
ap-1797	17	4	condensates	condensate	NOUN
ap-1797	17	5	are	be	AUX
ap-1797	17	6	a	a	DET
ap-1797	17	7	promising	promising	ADJ
ap-1797	17	8	candidate	candidate	NOUN
ap-1797	17	9	for	for	ADP
ap-1797	17	10	a	a	DET
ap-1797	17	11	first	first	ADJ
ap-1797	17	12	experimental	experimental	ADJ
ap-1797	17	13	realization	realization	NOUN
ap-1797	17	14	of	of	ADP
ap-1797	17	15	a	a	DET
ap-1797	17	16	special	special	ADJ
ap-1797	17	17	class	class	NOUN
ap-1797	17	18	of	of	ADP
ap-1797	17	19	non	non	ADJ
ap-1797	17	20	-	-	ADJ
ap-1797	17	21	hermitian	hermitian	ADJ
ap-1797	17	22	hamiltonians	hamiltonian	NOUN
ap-1797	17	23	in	in	ADP
ap-1797	17	24	quantum	quantum	ADJ
ap-1797	17	25	mechanics	mechanic	NOUN
ap-1797	17	26	,	,	PUNCT
ap-1797	17	27	viz	viz	NOUN
ap-1797	17	28	.	.	PUNCT
ap-1797	18	1	systems	system	NOUN
ap-1797	18	2	which	which	PRON
ap-1797	18	3	possess	possess	VERB
ap-1797	18	4	a	a	DET
ap-1797	18	5	pt	pt	NOUN
ap-1797	18	6	symmetry	symmetry	NOUN
ap-1797	18	7	in	in	ADP
ap-1797	18	8	spite	spite	NOUN
ap-1797	18	9	of	of	ADP
ap-1797	18	10	their	their	PRON
ap-1797	18	11	non	non	ADJ
ap-1797	18	12	-	-	ADJ
ap-1797	18	13	hermitian	hermitian	ADJ
ap-1797	18	14	nature	nature	NOUN
ap-1797	18	15	.	.	PUNCT
ap-1797	19	1	as	as	SCONJ
ap-1797	19	2	was	be	AUX
ap-1797	19	3	shown	show	VERB
ap-1797	19	4	first	first	ADV
ap-1797	19	5	by	by	ADP
ap-1797	19	6	bender	bender	NOUN
ap-1797	19	7	and	and	CCONJ
ap-1797	19	8	boettcher	boettcher	PROPN
ap-1797	19	9	,	,	PUNCT
ap-1797	19	10	these	these	DET
ap-1797	19	11	hamiltonians	hamiltonian	NOUN
ap-1797	19	12	exhibit	exhibit	VERB
ap-1797	19	13	remarkable	remarkable	ADJ
ap-1797	19	14	properties	property	NOUN
ap-1797	19	15	[	[	X
ap-1797	19	16	3	3	X
ap-1797	19	17	]	]	PUNCT
ap-1797	19	18	such	such	ADJ
ap-1797	19	19	as	as	ADP
ap-1797	19	20	stationary	stationary	ADJ
ap-1797	19	21	states	state	NOUN
ap-1797	19	22	with	with	ADP
ap-1797	19	23	real	real	ADJ
ap-1797	19	24	eigenvalues	eigenvalue	NOUN
ap-1797	19	25	in	in	ADP
ap-1797	19	26	the	the	DET
ap-1797	19	27	presence	presence	NOUN
ap-1797	19	28	of	of	ADP
ap-1797	19	29	loss	loss	NOUN
ap-1797	19	30	and	and	CCONJ
ap-1797	19	31	gain	gain	VERB
ap-1797	19	32	terms	term	NOUN
ap-1797	19	33	in	in	ADP
ap-1797	19	34	the	the	DET
ap-1797	19	35	potential	potential	NOUN
ap-1797	19	36	.	.	PUNCT
ap-1797	20	1	with	with	ADP
ap-1797	20	2	the	the	DET
ap-1797	20	3	operators	operator	NOUN
ap-1797	20	4	of	of	ADP
ap-1797	20	5	spatial	spatial	ADJ
ap-1797	20	6	reflection	reflection	NOUN
ap-1797	20	7	p	p	X
ap-1797	20	8	:	:	PUNCT
ap-1797	20	9	x→	x→	PUNCT
ap-1797	20	10	−x	−x	PROPN
ap-1797	20	11	,	,	PUNCT
ap-1797	20	12	p	p	X
ap-1797	20	13	→	→	SYM
ap-1797	20	14	−p	−p	NOUN
ap-1797	20	15	,	,	PUNCT
ap-1797	20	16	and	and	CCONJ
ap-1797	20	17	of	of	ADP
ap-1797	20	18	time	time	NOUN
ap-1797	20	19	reversal	reversal	PROPN
ap-1797	20	20	t	t	NOUN
ap-1797	20	21	:	:	PUNCT
ap-1797	20	22	x	x	X
ap-1797	20	23	→	→	SYM
ap-1797	20	24	x	x	SYM
ap-1797	20	25	,	,	PUNCT
ap-1797	20	26	p	p	X
ap-1797	20	27	→	→	SYM
ap-1797	20	28	−p	−p	NOUN
ap-1797	20	29	,	,	PUNCT
ap-1797	20	30	i→	i→	VERB
ap-1797	20	31	−i	−i	PROPN
ap-1797	20	32	the	the	DET
ap-1797	20	33	pt	pt	PROPN
ap-1797	20	34	symmetry	symmetry	NOUN
ap-1797	20	35	of	of	ADP
ap-1797	20	36	the	the	DET
ap-1797	20	37	hamiltonian	hamiltonian	NOUN
ap-1797	20	38	can	can	AUX
ap-1797	20	39	be	be	AUX
ap-1797	20	40	expressed	express	VERB
ap-1797	20	41	in	in	ADP
ap-1797	20	42	terms	term	NOUN
ap-1797	20	43	of	of	ADP
ap-1797	20	44	the	the	DET
ap-1797	20	45	commutator	commutator	NOUN
ap-1797	20	46	relation	relation	PROPN
ap-1797	20	47	[	[	X
ap-1797	20	48	pt	pt	X
ap-1797	20	49	,	,	PUNCT
ap-1797	20	50	h	h	NOUN
ap-1797	20	51	]	]	X
ap-1797	20	52	=	=	SYM
ap-1797	21	1	0	0	X
ap-1797	21	2	.	.	PUNCT
ap-1797	22	1	(	(	PUNCT
ap-1797	22	2	2	2	X
ap-1797	22	3	)	)	PUNCT
ap-1797	22	4	since	since	SCONJ
ap-1797	22	5	the	the	DET
ap-1797	22	6	kinetic	kinetic	ADJ
ap-1797	22	7	energy	energy	NOUN
ap-1797	22	8	term	term	NOUN
ap-1797	22	9	in	in	ADP
ap-1797	22	10	the	the	DET
ap-1797	22	11	hamiltonian	hamiltonian	NOUN
ap-1797	22	12	is	be	AUX
ap-1797	22	13	always	always	ADV
ap-1797	22	14	pt	pt	INTJ
ap-1797	22	15	symmetric	symmetric	ADJ
ap-1797	22	16	one	one	NOUN
ap-1797	22	17	obtains	obtain	VERB
ap-1797	22	18	in	in	ADP
ap-1797	22	19	a	a	DET
ap-1797	22	20	simple	simple	ADJ
ap-1797	22	21	calculation	calculation	NOUN
ap-1797	22	22	from	from	ADP
ap-1797	22	23	(	(	PUNCT
ap-1797	22	24	2	2	X
ap-1797	22	25	)	)	PUNCT
ap-1797	22	26	the	the	DET
ap-1797	22	27	necessary	necessary	ADJ
ap-1797	22	28	condition	condition	NOUN
ap-1797	22	29	v	v	ADP
ap-1797	22	30	∗(−x	∗(−x	PROPN
ap-1797	22	31	)	)	PUNCT
ap-1797	22	32	=	=	SYM
ap-1797	22	33	v	v	X
ap-1797	22	34	(	(	PUNCT
ap-1797	22	35	x	x	X
ap-1797	22	36	)	)	PUNCT
ap-1797	22	37	(	(	PUNCT
ap-1797	22	38	3	3	X
ap-1797	22	39	)	)	PUNCT
ap-1797	22	40	for	for	ADP
ap-1797	22	41	the	the	DET
ap-1797	22	42	potential	potential	NOUN
ap-1797	22	43	.	.	PUNCT
ap-1797	23	1	whereas	whereas	SCONJ
ap-1797	23	2	the	the	DET
ap-1797	23	3	experimental	experimental	ADJ
ap-1797	23	4	realization	realization	NOUN
ap-1797	23	5	of	of	ADP
ap-1797	23	6	pt	pt	NOUN
ap-1797	23	7	symmetry	symmetry	NOUN
ap-1797	23	8	has	have	AUX
ap-1797	23	9	successfully	successfully	ADV
ap-1797	23	10	been	be	AUX
ap-1797	23	11	achieved	achieve	VERB
ap-1797	23	12	[	[	PUNCT
ap-1797	23	13	4	4	NUM
ap-1797	23	14	,	,	PUNCT
ap-1797	23	15	5	5	NUM
ap-1797	23	16	]	]	PUNCT
ap-1797	23	17	for	for	ADP
ap-1797	23	18	optical	optical	ADJ
ap-1797	23	19	wave	wave	NOUN
ap-1797	23	20	guides	guide	NOUN
ap-1797	23	21	[	[	X
ap-1797	23	22	6–12	6–12	NOUN
ap-1797	23	23	]	]	PUNCT
ap-1797	23	24	,	,	PUNCT
ap-1797	23	25	a	a	DET
ap-1797	23	26	verification	verification	NOUN
ap-1797	23	27	in	in	ADP
ap-1797	23	28	a	a	DET
ap-1797	23	29	genuine	genuine	ADJ
ap-1797	23	30	quantum	quantum	NOUN
ap-1797	23	31	system	system	NOUN
ap-1797	23	32	is	be	AUX
ap-1797	23	33	still	still	ADV
ap-1797	23	34	lacking	lack	VERB
ap-1797	23	35	.	.	PUNCT
ap-1797	24	1	however	however	ADV
ap-1797	24	2	,	,	PUNCT
ap-1797	24	3	a	a	DET
ap-1797	24	4	proposal	proposal	NOUN
ap-1797	24	5	for	for	ADP
ap-1797	24	6	a	a	DET
ap-1797	24	7	bose	bose	NOUN
ap-1797	24	8	-	-	PUNCT
ap-1797	24	9	einstein	einstein	NOUN
ap-1797	24	10	condensate	condensate	NOUN
ap-1797	24	11	with	with	ADP
ap-1797	24	12	a	a	DET
ap-1797	24	13	pt	pt	INTJ
ap-1797	24	14	symmetric	symmetric	ADJ
ap-1797	24	15	external	external	ADJ
ap-1797	24	16	potential	potential	NOUN
ap-1797	24	17	was	be	AUX
ap-1797	24	18	given	give	VERB
ap-1797	24	19	by	by	ADP
ap-1797	24	20	klaiman	klaiman	PROPN
ap-1797	24	21	et	et	PROPN
ap-1797	24	22	al	al	PROPN
ap-1797	24	23	.	.	PUNCT
ap-1797	25	1	[	[	X
ap-1797	25	2	11	11	NUM
ap-1797	25	3	]	]	PUNCT
ap-1797	25	4	,	,	PUNCT
ap-1797	25	5	who	who	PRON
ap-1797	25	6	suggested	suggest	VERB
ap-1797	25	7	a	a	DET
ap-1797	25	8	double	double	ADJ
ap-1797	25	9	-	-	PUNCT
ap-1797	25	10	well	well	NOUN
ap-1797	25	11	setup	setup	NOUN
ap-1797	25	12	,	,	PUNCT
ap-1797	25	13	where	where	SCONJ
ap-1797	25	14	atoms	atom	NOUN
ap-1797	25	15	are	be	AUX
ap-1797	25	16	coherently	coherently	ADV
ap-1797	25	17	incoupled	incouple	VERB
ap-1797	25	18	in	in	ADP
ap-1797	25	19	one	one	NUM
ap-1797	25	20	well	well	ADV
ap-1797	25	21	and	and	CCONJ
ap-1797	25	22	outcoupled	outcouple	VERB
ap-1797	25	23	from	from	ADP
ap-1797	25	24	the	the	DET
ap-1797	25	25	other	other	ADJ
ap-1797	25	26	.	.	PUNCT
ap-1797	26	1	in	in	ADP
ap-1797	26	2	this	this	DET
ap-1797	26	3	article	article	NOUN
ap-1797	26	4	,	,	PUNCT
ap-1797	26	5	we	we	PRON
ap-1797	26	6	will	will	AUX
ap-1797	26	7	solve	solve	VERB
ap-1797	26	8	the	the	DET
ap-1797	26	9	gross	gross	ADJ
ap-1797	26	10	-	-	PUNCT
ap-1797	26	11	pitaevskii	pitaevskii	ADJ
ap-1797	26	12	equation	equation	NOUN
ap-1797	26	13	of	of	ADP
ap-1797	26	14	such	such	DET
ap-1797	26	15	a	a	DET
ap-1797	26	16	system	system	NOUN
ap-1797	26	17	and	and	CCONJ
ap-1797	26	18	show	show	VERB
ap-1797	26	19	that	that	SCONJ
ap-1797	26	20	it	it	PRON
ap-1797	26	21	indeed	indeed	ADV
ap-1797	26	22	supports	support	VERB
ap-1797	26	23	pt	pt	PRON
ap-1797	26	24	symmetric	symmetric	ADJ
ap-1797	26	25	solutions	solution	NOUN
ap-1797	26	26	.	.	PUNCT
ap-1797	27	1	since	since	SCONJ
ap-1797	27	2	the	the	DET
ap-1797	27	3	model	model	NOUN
ap-1797	27	4	describes	describe	VERB
ap-1797	27	5	a	a	DET
ap-1797	27	6	true	true	ADJ
ap-1797	27	7	quantum	quantum	ADJ
ap-1797	27	8	system	system	NOUN
ap-1797	27	9	,	,	PUNCT
ap-1797	27	10	our	our	PRON
ap-1797	27	11	investigations	investigation	NOUN
ap-1797	27	12	provide	provide	VERB
ap-1797	27	13	a	a	DET
ap-1797	27	14	good	good	ADJ
ap-1797	27	15	starting	starting	NOUN
ap-1797	27	16	point	point	NOUN
ap-1797	27	17	for	for	ADP
ap-1797	27	18	an	an	DET
ap-1797	27	19	experimental	experimental	ADJ
ap-1797	27	20	realization	realization	NOUN
ap-1797	27	21	of	of	ADP
ap-1797	27	22	this	this	DET
ap-1797	27	23	quantum	quantum	ADJ
ap-1797	27	24	system	system	NOUN
ap-1797	27	25	with	with	ADP
ap-1797	27	26	pt	pt	PROPN
ap-1797	27	27	symmetry	symmetry	NOUN
ap-1797	27	28	.	.	PUNCT
ap-1797	28	1	however	however	ADV
ap-1797	28	2	,	,	PUNCT
ap-1797	28	3	in	in	ADP
ap-1797	28	4	the	the	DET
ap-1797	28	5	case	case	NOUN
ap-1797	28	6	of	of	ADP
ap-1797	28	7	the	the	DET
ap-1797	28	8	nonlinear	nonlinear	ADJ
ap-1797	28	9	gross	gross	ADJ
ap-1797	28	10	-	-	PUNCT
ap-1797	28	11	pitaevskii	pitaevskii	ADJ
ap-1797	28	12	equation	equation	NOUN
ap-1797	28	13	(	(	PUNCT
ap-1797	28	14	1	1	X
ap-1797	28	15	)	)	PUNCT
ap-1797	28	16	one	one	NOUN
ap-1797	28	17	has	have	VERB
ap-1797	28	18	to	to	PART
ap-1797	28	19	address	address	VERB
ap-1797	28	20	one	one	NUM
ap-1797	28	21	additional	additional	ADJ
ap-1797	28	22	critical	critical	ADJ
ap-1797	28	23	question	question	NOUN
ap-1797	28	24	.	.	PUNCT
ap-1797	29	1	the	the	DET
ap-1797	29	2	wave	wave	NOUN
ap-1797	29	3	function	function	NOUN
ap-1797	29	4	has	have	VERB
ap-1797	29	5	an	an	DET
ap-1797	29	6	influence	influence	NOUN
ap-1797	29	7	on	on	ADP
ap-1797	29	8	the	the	DET
ap-1797	29	9	nonlinear	nonlinear	ADJ
ap-1797	29	10	hamiltonian	hamiltonian	NOUN
ap-1797	29	11	’s	’s	PART
ap-1797	29	12	symmetry	symmetry	NOUN
ap-1797	29	13	.	.	PUNCT
ap-1797	30	1	along	along	ADP
ap-1797	30	2	with	with	ADP
ap-1797	30	3	the	the	DET
ap-1797	30	4	259	259	NUM
ap-1797	30	5	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1797	30	6	holger	holger	PROPN
ap-1797	30	7	cartarius	cartarius	PROPN
ap-1797	30	8	et	et	PROPN
ap-1797	30	9	al	al	PROPN
ap-1797	30	10	.	.	PROPN
ap-1797	30	11	acta	acta	PROPN
ap-1797	30	12	polytechnica	polytechnica	PROPN
ap-1797	30	13	external	external	ADJ
ap-1797	30	14	potential	potential	NOUN
ap-1797	30	15	the	the	DET
ap-1797	30	16	interaction	interaction	NOUN
ap-1797	30	17	term	term	NOUN
ap-1797	30	18	−g|ψ(x	−g|ψ(x	PROPN
ap-1797	30	19	,	,	PUNCT
ap-1797	30	20	t)|2	t)|2	PROPN
ap-1797	30	21	has	have	VERB
ap-1797	30	22	to	to	PART
ap-1797	30	23	fulfill	fulfill	VERB
ap-1797	30	24	the	the	DET
ap-1797	30	25	condition	condition	NOUN
ap-1797	30	26	(	(	PUNCT
ap-1797	30	27	3	3	NUM
ap-1797	30	28	)	)	PUNCT
ap-1797	30	29	.	.	PUNCT
ap-1797	31	1	the	the	DET
ap-1797	31	2	hamiltonian	hamiltonian	NOUN
ap-1797	31	3	is	be	AUX
ap-1797	31	4	only	only	ADV
ap-1797	31	5	pt	pt	X
ap-1797	31	6	symmetric	symmetric	NOUN
ap-1797	31	7	if	if	SCONJ
ap-1797	31	8	the	the	DET
ap-1797	31	9	square	square	ADJ
ap-1797	31	10	modulus	modulus	NOUN
ap-1797	31	11	of	of	ADP
ap-1797	31	12	its	its	PRON
ap-1797	31	13	solution	solution	NOUN
ap-1797	31	14	|ψ(x	|ψ(x	NOUN
ap-1797	31	15	,	,	PUNCT
ap-1797	31	16	t)|2	t)|2	PROPN
ap-1797	31	17	is	be	AUX
ap-1797	31	18	a	a	DET
ap-1797	31	19	symmetric	symmetric	ADJ
ap-1797	31	20	function	function	NOUN
ap-1797	31	21	of	of	ADP
ap-1797	31	22	x.	x.	NOUN
ap-1797	31	23	this	this	PRON
ap-1797	31	24	is	be	AUX
ap-1797	31	25	always	always	ADV
ap-1797	31	26	fulfilled	fulfil	VERB
ap-1797	31	27	for	for	ADP
ap-1797	31	28	pt	pt	X
ap-1797	31	29	symmetric	symmetric	ADJ
ap-1797	31	30	wave	wave	NOUN
ap-1797	31	31	functions	function	NOUN
ap-1797	31	32	.	.	PUNCT
ap-1797	32	1	thus	thus	ADV
ap-1797	32	2	,	,	PUNCT
ap-1797	32	3	one	one	PRON
ap-1797	32	4	may	may	AUX
ap-1797	32	5	state	state	VERB
ap-1797	32	6	that	that	SCONJ
ap-1797	32	7	the	the	DET
ap-1797	32	8	nonlinear	nonlinear	ADJ
ap-1797	32	9	hamiltonian	hamiltonian	NOUN
ap-1797	32	10	of	of	ADP
ap-1797	32	11	the	the	DET
ap-1797	32	12	gross	gross	ADJ
ap-1797	32	13	-	-	PUNCT
ap-1797	32	14	pitaevskii	pitaevskii	ADJ
ap-1797	32	15	equation	equation	NOUN
ap-1797	32	16	preserves	preserve	VERB
ap-1797	32	17	its	its	PRON
ap-1797	32	18	own	own	ADJ
ap-1797	32	19	symmetry	symmetry	NOUN
ap-1797	32	20	in	in	ADP
ap-1797	32	21	the	the	DET
ap-1797	32	22	case	case	NOUN
ap-1797	32	23	of	of	ADP
ap-1797	32	24	exact	exact	ADJ
ap-1797	32	25	pt	pt	NOUN
ap-1797	32	26	symmetry	symmetry	NOUN
ap-1797	32	27	.	.	PUNCT
ap-1797	33	1	but	but	CCONJ
ap-1797	33	2	does	do	AUX
ap-1797	33	3	this	this	PRON
ap-1797	33	4	happen	happen	VERB
ap-1797	33	5	also	also	ADV
ap-1797	33	6	with	with	ADP
ap-1797	33	7	nonlinearity	nonlinearity	NOUN
ap-1797	33	8	?	?	PUNCT
ap-1797	34	1	wave	wave	NOUN
ap-1797	34	2	functions	function	NOUN
ap-1797	34	3	describing	describe	VERB
ap-1797	34	4	pt	pt	INTJ
ap-1797	34	5	broken	break	VERB
ap-1797	34	6	eigenstates	eigenstate	NOUN
ap-1797	34	7	usually	usually	ADV
ap-1797	34	8	do	do	AUX
ap-1797	34	9	not	not	PART
ap-1797	34	10	possess	possess	VERB
ap-1797	34	11	a	a	DET
ap-1797	34	12	symmetric	symmetric	ADJ
ap-1797	34	13	square	square	ADJ
ap-1797	34	14	modulus	modulus	NOUN
ap-1797	34	15	and	and	CCONJ
ap-1797	34	16	destroy	destroy	VERB
ap-1797	34	17	also	also	ADV
ap-1797	34	18	the	the	DET
ap-1797	34	19	pt	pt	NOUN
ap-1797	34	20	symmetry	symmetry	NOUN
ap-1797	34	21	of	of	ADP
ap-1797	34	22	the	the	DET
ap-1797	34	23	hamiltonian	hamiltonian	NOUN
ap-1797	34	24	.	.	PUNCT
ap-1797	35	1	previous	previous	ADJ
ap-1797	35	2	studies	study	NOUN
ap-1797	35	3	of	of	ADP
ap-1797	35	4	pt	pt	NOUN
ap-1797	35	5	symmetric	symmetric	ADJ
ap-1797	35	6	systems	system	NOUN
ap-1797	35	7	with	with	ADP
ap-1797	35	8	nonlinearity	nonlinearity	NOUN
ap-1797	35	9	indicate	indicate	VERB
ap-1797	35	10	that	that	SCONJ
ap-1797	35	11	the	the	DET
ap-1797	35	12	nonlinearity	nonlinearity	NOUN
ap-1797	35	13	does	do	AUX
ap-1797	35	14	not	not	PART
ap-1797	35	15	destroy	destroy	VERB
ap-1797	35	16	the	the	DET
ap-1797	35	17	relevant	relevant	ADJ
ap-1797	35	18	effects	effect	NOUN
ap-1797	35	19	known	know	VERB
ap-1797	35	20	from	from	ADP
ap-1797	35	21	linear	linear	PROPN
ap-1797	35	22	pt	pt	INTJ
ap-1797	35	23	symmetric	symmetric	ADJ
ap-1797	35	24	hamiltonians	hamiltonian	NOUN
ap-1797	35	25	.	.	PUNCT
ap-1797	36	1	an	an	DET
ap-1797	36	2	investigation	investigation	NOUN
ap-1797	36	3	of	of	ADP
ap-1797	36	4	a	a	DET
ap-1797	36	5	boseeinstein	boseeinstein	NOUN
ap-1797	36	6	condensate	condensate	NOUN
ap-1797	36	7	in	in	ADP
ap-1797	36	8	a	a	DET
ap-1797	36	9	two	two	NUM
ap-1797	36	10	-	-	PUNCT
ap-1797	36	11	mode	mode	NOUN
ap-1797	36	12	approximation	approximation	NOUN
ap-1797	36	13	using	use	VERB
ap-1797	36	14	a	a	DET
ap-1797	36	15	non	non	ADJ
ap-1797	36	16	-	-	ADJ
ap-1797	36	17	hermitian	hermitian	ADJ
ap-1797	36	18	bose	bose	PROPN
ap-1797	36	19	-	-	PUNCT
ap-1797	36	20	hubbard	hubbard	NOUN
ap-1797	36	21	model	model	NOUN
ap-1797	36	22	was	be	AUX
ap-1797	36	23	made	make	VERB
ap-1797	36	24	by	by	ADP
ap-1797	36	25	graefe	graefe	PROPN
ap-1797	36	26	et	et	PROPN
ap-1797	36	27	al	al	PROPN
ap-1797	36	28	.	.	PUNCT
ap-1797	37	1	[	[	X
ap-1797	37	2	13–15	13–15	NUM
ap-1797	37	3	]	]	PUNCT
ap-1797	37	4	.	.	PUNCT
ap-1797	38	1	furthermore	furthermore	ADV
ap-1797	38	2	,	,	PUNCT
ap-1797	38	3	the	the	DET
ap-1797	38	4	combination	combination	NOUN
ap-1797	38	5	of	of	ADP
ap-1797	38	6	pt	pt	NOUN
ap-1797	38	7	symmetry	symmetry	NOUN
ap-1797	38	8	and	and	CCONJ
ap-1797	38	9	nonlinearity	nonlinearity	NOUN
ap-1797	38	10	has	have	AUX
ap-1797	38	11	been	be	AUX
ap-1797	38	12	studied	study	VERB
ap-1797	38	13	in	in	ADP
ap-1797	38	14	quantum	quantum	ADJ
ap-1797	38	15	mechanical	mechanical	ADJ
ap-1797	38	16	model	model	NOUN
ap-1797	38	17	potentials	potential	VERB
ap-1797	39	1	[	[	X
ap-1797	39	2	10	10	NUM
ap-1797	39	3	,	,	PUNCT
ap-1797	39	4	16	16	NUM
ap-1797	39	5	]	]	PUNCT
ap-1797	39	6	,	,	PUNCT
ap-1797	39	7	in	in	ADP
ap-1797	39	8	optics	optic	NOUN
ap-1797	39	9	[	[	X
ap-1797	39	10	17	17	NUM
ap-1797	39	11	]	]	PUNCT
ap-1797	39	12	or	or	CCONJ
ap-1797	39	13	for	for	ADP
ap-1797	39	14	a	a	DET
ap-1797	39	15	bose	bose	NOUN
ap-1797	39	16	-	-	PUNCT
ap-1797	39	17	einstein	einstein	NOUN
ap-1797	39	18	condensate	condensate	NOUN
ap-1797	39	19	with	with	ADP
ap-1797	39	20	an	an	DET
ap-1797	39	21	idealized	idealized	ADJ
ap-1797	39	22	double	double	ADJ
ap-1797	39	23	-	-	PUNCT
ap-1797	39	24	δ	δ	NOUN
ap-1797	39	25	trap	trap	NOUN
ap-1797	40	1	[	[	X
ap-1797	40	2	18	18	NUM
ap-1797	40	3	]	]	PUNCT
ap-1797	40	4	,	,	PUNCT
ap-1797	40	5	a	a	DET
ap-1797	40	6	system	system	NOUN
ap-1797	40	7	of	of	ADP
ap-1797	40	8	which	which	PRON
ap-1797	40	9	the	the	DET
ap-1797	40	10	linear	linear	ADJ
ap-1797	40	11	variant	variant	NOUN
ap-1797	40	12	already	already	ADV
ap-1797	40	13	attracted	attract	VERB
ap-1797	40	14	much	much	ADJ
ap-1797	40	15	interest	interest	NOUN
ap-1797	40	16	[	[	X
ap-1797	40	17	19–23	19–23	NUM
ap-1797	40	18	]	]	PUNCT
ap-1797	40	19	.	.	PUNCT
ap-1797	41	1	to	to	PART
ap-1797	41	2	investigate	investigate	VERB
ap-1797	41	3	bose	bose	NOUN
ap-1797	41	4	-	-	PUNCT
ap-1797	41	5	einstein	einstein	NOUN
ap-1797	41	6	condensates	condensate	NOUN
ap-1797	41	7	in	in	ADP
ap-1797	41	8	a	a	DET
ap-1797	41	9	pt	pt	NOUN
ap-1797	41	10	symmetric	symmetric	ADJ
ap-1797	41	11	double	double	ADJ
ap-1797	41	12	well	well	INTJ
ap-1797	41	13	we	we	PRON
ap-1797	41	14	first	first	ADV
ap-1797	41	15	introduce	introduce	VERB
ap-1797	41	16	our	our	PRON
ap-1797	41	17	numerical	numerical	ADJ
ap-1797	41	18	approach	approach	NOUN
ap-1797	41	19	in	in	ADP
ap-1797	41	20	section	section	NOUN
ap-1797	41	21	2	2	NUM
ap-1797	41	22	.	.	PUNCT
ap-1797	42	1	then	then	ADV
ap-1797	42	2	we	we	PRON
ap-1797	42	3	present	present	VERB
ap-1797	42	4	and	and	CCONJ
ap-1797	42	5	discuss	discuss	VERB
ap-1797	42	6	the	the	DET
ap-1797	42	7	numerical	numerical	ADJ
ap-1797	42	8	results	result	NOUN
ap-1797	42	9	for	for	ADP
ap-1797	42	10	the	the	DET
ap-1797	42	11	energy	energy	NOUN
ap-1797	42	12	eigenvalues	eigenvalue	NOUN
ap-1797	42	13	,	,	PUNCT
ap-1797	42	14	the	the	DET
ap-1797	42	15	stationary	stationary	ADJ
ap-1797	42	16	wave	wave	NOUN
ap-1797	42	17	functions	function	NOUN
ap-1797	42	18	and	and	CCONJ
ap-1797	42	19	the	the	DET
ap-1797	42	20	time	time	NOUN
ap-1797	42	21	evolution	evolution	NOUN
ap-1797	42	22	of	of	ADP
ap-1797	42	23	non	non	ADJ
ap-1797	42	24	-	-	ADJ
ap-1797	42	25	stationary	stationary	ADJ
ap-1797	42	26	initial	initial	ADJ
ap-1797	42	27	wave	wave	NOUN
ap-1797	42	28	packets	packet	NOUN
ap-1797	42	29	in	in	ADP
ap-1797	42	30	section	section	NOUN
ap-1797	42	31	3	3	NUM
ap-1797	42	32	.	.	PUNCT
ap-1797	43	1	conclusions	conclusion	NOUN
ap-1797	43	2	are	be	AUX
ap-1797	43	3	drawn	draw	VERB
ap-1797	43	4	in	in	ADP
ap-1797	43	5	section	section	NOUN
ap-1797	43	6	4	4	NUM
ap-1797	43	7	.	.	NOUN
ap-1797	43	8	2	2	NUM
ap-1797	43	9	.	.	NOUN
ap-1797	43	10	numerical	numerical	ADJ
ap-1797	43	11	approach	approach	NOUN
ap-1797	43	12	to	to	ADP
ap-1797	43	13	bose	bose	NOUN
ap-1797	43	14	-	-	PUNCT
ap-1797	43	15	einstein	einstein	NOUN
ap-1797	43	16	condensates	condensate	NOUN
ap-1797	43	17	in	in	ADP
ap-1797	43	18	a	a	DET
ap-1797	43	19	pt	pt	NOUN
ap-1797	43	20	symmetric	symmetric	ADJ
ap-1797	43	21	double	double	ADJ
ap-1797	43	22	well	well	NOUN
ap-1797	43	23	2.1	2.1	NUM
ap-1797	43	24	.	.	PUNCT
ap-1797	44	1	gross	gross	ADJ
ap-1797	44	2	-	-	PUNCT
ap-1797	44	3	pitaevskii	pitaevskii	ADJ
ap-1797	44	4	equation	equation	NOUN
ap-1797	44	5	we	we	PRON
ap-1797	44	6	consider	consider	VERB
ap-1797	44	7	a	a	DET
ap-1797	44	8	bose	bose	NOUN
ap-1797	44	9	-	-	PUNCT
ap-1797	44	10	einstein	einstein	NOUN
ap-1797	44	11	condensate	condensate	NOUN
ap-1797	44	12	of	of	ADP
ap-1797	44	13	particles	particle	NOUN
ap-1797	44	14	with	with	ADP
ap-1797	44	15	mass	mass	NOUN
ap-1797	44	16	m	m	NOUN
ap-1797	44	17	in	in	ADP
ap-1797	44	18	a	a	DET
ap-1797	44	19	double	double	ADJ
ap-1797	44	20	-	-	PUNCT
ap-1797	44	21	well	well	NOUN
ap-1797	44	22	setup	setup	NOUN
ap-1797	44	23	described	describe	VERB
ap-1797	44	24	by	by	ADP
ap-1797	44	25	the	the	DET
ap-1797	44	26	external	external	ADJ
ap-1797	44	27	potential	potential	ADJ
ap-1797	44	28	v	v	NOUN
ap-1797	44	29	(	(	PUNCT
ap-1797	44	30	x	x	NOUN
ap-1797	44	31	)	)	PUNCT
ap-1797	45	1	=	=	SYM
ap-1797	45	2	m	m	VERB
ap-1797	45	3	2	2	NUM
ap-1797	45	4	ω	ω	NUM
ap-1797	45	5	2	2	NUM
ap-1797	45	6	xx	xx	NUM
ap-1797	45	7	2	2	NUM
ap-1797	45	8	+	+	CCONJ
ap-1797	45	9	m	m	VERB
ap-1797	45	10	2	2	NUM
ap-1797	45	11	ω	ω	NUM
ap-1797	45	12	2	2	NUM
ap-1797	45	13	y	y	PROPN
ap-1797	45	14	,	,	PUNCT
ap-1797	45	15	z(y2	z(y2	PROPN
ap-1797	45	16	+	+	CCONJ
ap-1797	45	17	z2	z2	PROPN
ap-1797	45	18	)	)	PUNCT
ap-1797	45	19	+	+	CCONJ
ap-1797	45	20	v0e	v0e	X
ap-1797	45	21	−σx2	−σx2	VERB
ap-1797	45	22	+	+	NUM
ap-1797	45	23	iγxe−ρx	iγxe−ρx	NOUN
ap-1797	45	24	2	2	NUM
ap-1797	45	25	,	,	PUNCT
ap-1797	45	26	(	(	PUNCT
ap-1797	45	27	4	4	NUM
ap-1797	45	28	)	)	PUNCT
ap-1797	45	29	where	where	SCONJ
ap-1797	45	30	a	a	DET
ap-1797	45	31	three	three	NUM
ap-1797	45	32	-	-	PUNCT
ap-1797	45	33	dimensional	dimensional	ADJ
ap-1797	45	34	harmonic	harmonic	ADJ
ap-1797	45	35	trap	trap	NOUN
ap-1797	45	36	is	be	AUX
ap-1797	45	37	superimposed	superimpose	VERB
ap-1797	45	38	by	by	ADP
ap-1797	45	39	a	a	DET
ap-1797	45	40	gaussian	gaussian	ADJ
ap-1797	45	41	barrier	barrier	NOUN
ap-1797	45	42	in	in	ADP
ap-1797	45	43	the	the	DET
ap-1797	45	44	x	x	NOUN
ap-1797	45	45	direction	direction	NOUN
ap-1797	45	46	(	(	PUNCT
ap-1797	45	47	cf	cf	NOUN
ap-1797	45	48	.	.	PUNCT
ap-1797	45	49	figure	figure	NOUN
ap-1797	45	50	1	1	NUM
ap-1797	45	51	)	)	PUNCT
ap-1797	45	52	.	.	PUNCT
ap-1797	46	1	the	the	DET
ap-1797	46	2	trapping	trap	VERB
ap-1797	46	3	frequencies	frequency	NOUN
ap-1797	46	4	are	be	AUX
ap-1797	46	5	ωx	ωx	PRON
ap-1797	46	6	for	for	ADP
ap-1797	46	7	the	the	DET
ap-1797	46	8	direction	direction	NOUN
ap-1797	46	9	of	of	ADP
ap-1797	46	10	the	the	DET
ap-1797	46	11	double	double	ADJ
ap-1797	46	12	-	-	PUNCT
ap-1797	46	13	well	well	NOUN
ap-1797	46	14	structure	structure	NOUN
ap-1797	46	15	and	and	CCONJ
ap-1797	46	16	ωy	ωy	PROPN
ap-1797	46	17	,	,	PUNCT
ap-1797	46	18	z	z	NOUN
ap-1797	46	19	for	for	ADP
ap-1797	46	20	the	the	DET
ap-1797	46	21	two	two	NUM
ap-1797	46	22	remaining	remain	VERB
ap-1797	46	23	directions	direction	NOUN
ap-1797	46	24	.	.	PUNCT
ap-1797	47	1	the	the	DET
ap-1797	47	2	barrier	barrier	NOUN
ap-1797	47	3	has	have	VERB
ap-1797	47	4	its	its	PRON
ap-1797	47	5	maximum	maximum	NOUN
ap-1797	47	6	at	at	ADP
ap-1797	47	7	x	x	X
ap-1797	47	8	=	=	SYM
ap-1797	47	9	0	0	NUM
ap-1797	47	10	,	,	PUNCT
ap-1797	47	11	the	the	DET
ap-1797	47	12	height	height	NOUN
ap-1797	47	13	v0	v0	NOUN
ap-1797	47	14	,	,	PUNCT
ap-1797	47	15	and	and	CCONJ
ap-1797	47	16	its	its	PRON
ap-1797	47	17	width	width	NOUN
ap-1797	47	18	is	be	AUX
ap-1797	47	19	determined	determine	VERB
ap-1797	47	20	by	by	ADP
ap-1797	47	21	σ	σ	PROPN
ap-1797	47	22	.	.	PUNCT
ap-1797	48	1	an	an	DET
ap-1797	48	2	outcoupling	outcoupling	NOUN
ap-1797	48	3	(	(	PUNCT
ap-1797	48	4	incoupling	incouple	VERB
ap-1797	48	5	)	)	PUNCT
ap-1797	48	6	of	of	ADP
ap-1797	48	7	atoms	atom	NOUN
ap-1797	48	8	is	be	AUX
ap-1797	48	9	reflected	reflect	VERB
ap-1797	48	10	by	by	ADP
ap-1797	48	11	a	a	DET
ap-1797	48	12	negative	negative	ADJ
ap-1797	48	13	(	(	PUNCT
ap-1797	48	14	positive	positive	ADJ
ap-1797	48	15	)	)	PUNCT
ap-1797	48	16	imaginary	imaginary	ADJ
ap-1797	48	17	potential	potential	ADJ
ap-1797	48	18	contribution	contribution	NOUN
ap-1797	48	19	in	in	ADP
ap-1797	48	20	the	the	DET
ap-1797	48	21	left	left	NOUN
ap-1797	48	22	(	(	PUNCT
ap-1797	48	23	right	right	ADJ
ap-1797	48	24	)	)	PUNCT
ap-1797	48	25	well	well	INTJ
ap-1797	48	26	.	.	PUNCT
ap-1797	49	1	its	its	PRON
ap-1797	49	2	strength	strength	NOUN
ap-1797	49	3	is	be	AUX
ap-1797	49	4	determined	determine	VERB
ap-1797	49	5	by	by	ADP
ap-1797	49	6	the	the	DET
ap-1797	49	7	gain	gain	NOUN
ap-1797	49	8	-	-	PUNCT
ap-1797	49	9	loss	loss	NOUN
ap-1797	49	10	parameter	parameter	NOUN
ap-1797	49	11	γ	γ	PROPN
ap-1797	49	12	.	.	PROPN
ap-1797	50	1	since	since	SCONJ
ap-1797	50	2	it	it	PRON
ap-1797	50	3	affects	affect	VERB
ap-1797	50	4	the	the	DET
ap-1797	50	5	probability	probability	NOUN
ap-1797	50	6	amplitude	amplitude	NOUN
ap-1797	50	7	of	of	ADP
ap-1797	50	8	the	the	DET
ap-1797	50	9	whole	whole	ADJ
ap-1797	50	10	condensate	condensate	NOUN
ap-1797	50	11	,	,	PUNCT
ap-1797	50	12	the	the	DET
ap-1797	50	13	physical	physical	ADJ
ap-1797	50	14	interpretation	interpretation	NOUN
ap-1797	50	15	is	be	AUX
ap-1797	50	16	a	a	DET
ap-1797	50	17	coherent	coherent	ADJ
ap-1797	50	18	out-/incoupling	out-/incoupling	NOUN
ap-1797	50	19	.	.	PUNCT
ap-1797	51	1	with	with	ADP
ap-1797	51	2	this	this	DET
ap-1797	51	3	ansatz	ansatz	ADV
ap-1797	51	4	we	we	PRON
ap-1797	51	5	are	be	AUX
ap-1797	51	6	not	not	PART
ap-1797	51	7	considering	consider	VERB
ap-1797	51	8	individual	individual	ADJ
ap-1797	51	9	atoms	atom	NOUN
ap-1797	51	10	but	but	CCONJ
ap-1797	51	11	the	the	DET
ap-1797	51	12	macroscopic	macroscopic	ADJ
ap-1797	51	13	wave	wave	NOUN
ap-1797	51	14	function	function	NOUN
ap-1797	51	15	of	of	ADP
ap-1797	51	16	the	the	DET
ap-1797	51	17	condensed	condense	VERB
ap-1797	51	18	phase	phase	NOUN
ap-1797	51	19	.	.	PUNCT
ap-1797	52	1	the	the	DET
ap-1797	52	2	potential	potential	ADJ
ap-1797	52	3	(	(	PUNCT
ap-1797	52	4	4	4	NUM
ap-1797	52	5	)	)	SYM
ap-1797	52	6	1	1	NUM
ap-1797	52	7	2	2	NUM
ap-1797	52	8	3	3	NUM
ap-1797	52	9	4	4	NUM
ap-1797	52	10	5	5	NUM
ap-1797	52	11	6	6	NUM
ap-1797	52	12	7	7	NUM
ap-1797	52	13	8	8	NUM
ap-1797	52	14	9	9	NUM
ap-1797	52	15	−6	−6	NOUN
ap-1797	52	16	−4	−4	NOUN
ap-1797	52	17	−2	−2	NOUN
ap-1797	52	18	0	0	NUM
ap-1797	52	19	2	2	NUM
ap-1797	52	20	4	4	NUM
ap-1797	52	21	6	6	NUM
ap-1797	52	22	−4	−4	NOUN
ap-1797	52	23	−3	−3	NOUN
ap-1797	52	24	−2	−2	PROPN
ap-1797	52	25	−1	−1	NOUN
ap-1797	52	26	0	0	NUM
ap-1797	52	27	1	1	NUM
ap-1797	52	28	2	2	NUM
ap-1797	52	29	3	3	NUM
ap-1797	52	30	4	4	NUM
ap-1797	52	31	r	r	NOUN
ap-1797	52	32	e	e	NOUN
ap-1797	52	33	v	v	NOUN
ap-1797	52	34	(	(	PUNCT
ap-1797	52	35	x	x	X
ap-1797	52	36	)	)	PUNCT
ap-1797	52	37	i	i	PRON
ap-1797	52	38	m	m	VERB
ap-1797	52	39	v	v	INTJ
ap-1797	52	40	(	(	PUNCT
ap-1797	52	41	x	x	X
ap-1797	52	42	)	)	PUNCT
ap-1797	52	43	x	x	SYM
ap-1797	52	44	rev	rev	X
ap-1797	52	45	(	(	PUNCT
ap-1797	52	46	x	x	X
ap-1797	52	47	)	)	PUNCT
ap-1797	52	48	imv	imv	NOUN
ap-1797	52	49	(	(	PUNCT
ap-1797	52	50	x	x	NOUN
ap-1797	52	51	)	)	PUNCT
ap-1797	52	52	figure	figure	NOUN
ap-1797	52	53	1	1	NUM
ap-1797	52	54	.	.	PUNCT
ap-1797	52	55	pt	pt	PROPN
ap-1797	52	56	symmetric	symmetric	ADJ
ap-1797	52	57	external	external	ADJ
ap-1797	52	58	potential	potential	NOUN
ap-1797	52	59	.	.	PUNCT
ap-1797	53	1	the	the	DET
ap-1797	53	2	real	real	ADJ
ap-1797	53	3	part	part	NOUN
ap-1797	53	4	(	(	PUNCT
ap-1797	53	5	solid	solid	ADJ
ap-1797	53	6	line	line	NOUN
ap-1797	53	7	)	)	PUNCT
ap-1797	53	8	defines	define	VERB
ap-1797	53	9	the	the	DET
ap-1797	53	10	confinement	confinement	NOUN
ap-1797	53	11	of	of	ADP
ap-1797	53	12	the	the	DET
ap-1797	53	13	condensed	condense	VERB
ap-1797	53	14	atom	atom	NOUN
ap-1797	53	15	cloud	cloud	NOUN
ap-1797	53	16	and	and	CCONJ
ap-1797	53	17	the	the	DET
ap-1797	53	18	imaginary	imaginary	ADJ
ap-1797	53	19	part	part	NOUN
ap-1797	53	20	(	(	PUNCT
ap-1797	53	21	dashed	dash	VERB
ap-1797	53	22	line	line	NOUN
ap-1797	53	23	)	)	PUNCT
ap-1797	53	24	describes	describe	VERB
ap-1797	53	25	the	the	DET
ap-1797	53	26	gain	gain	NOUN
ap-1797	53	27	-	-	PUNCT
ap-1797	53	28	loss	loss	NOUN
ap-1797	53	29	contributions	contribution	NOUN
ap-1797	53	30	due	due	ADP
ap-1797	53	31	to	to	ADP
ap-1797	53	32	the	the	DET
ap-1797	53	33	coherent	coherent	ADJ
ap-1797	53	34	inand	inand	ADJ
ap-1797	53	35	outcoupling	outcoupling	NOUN
ap-1797	53	36	of	of	ADP
ap-1797	53	37	atoms	atom	NOUN
ap-1797	53	38	.	.	PUNCT
ap-1797	54	1	has	have	AUX
ap-1797	54	2	been	be	AUX
ap-1797	54	3	chosen	choose	VERB
ap-1797	54	4	such	such	ADJ
ap-1797	54	5	that	that	SCONJ
ap-1797	54	6	it	it	PRON
ap-1797	54	7	fulfills	fulfill	VERB
ap-1797	54	8	the	the	DET
ap-1797	54	9	condition	condition	NOUN
ap-1797	54	10	(	(	PUNCT
ap-1797	54	11	3	3	NUM
ap-1797	54	12	)	)	PUNCT
ap-1797	54	13	,	,	PUNCT
ap-1797	54	14	i.e.	i.e.	X
ap-1797	54	15	its	its	PRON
ap-1797	54	16	real	real	ADJ
ap-1797	54	17	part	part	NOUN
ap-1797	54	18	is	be	AUX
ap-1797	54	19	a	a	DET
ap-1797	54	20	symmetric	symmetric	ADJ
ap-1797	54	21	function	function	NOUN
ap-1797	54	22	of	of	ADP
ap-1797	54	23	x	x	PRON
ap-1797	54	24	,	,	PUNCT
ap-1797	54	25	while	while	SCONJ
ap-1797	54	26	its	its	PRON
ap-1797	54	27	imaginary	imaginary	ADJ
ap-1797	54	28	part	part	NOUN
ap-1797	54	29	is	be	AUX
ap-1797	54	30	antisymmetric	antisymmetric	ADJ
ap-1797	54	31	.	.	PUNCT
ap-1797	55	1	thus	thus	ADV
ap-1797	55	2	,	,	PUNCT
ap-1797	55	3	the	the	DET
ap-1797	55	4	linear	linear	ADJ
ap-1797	55	5	external	external	ADJ
ap-1797	55	6	potential	potential	NOUN
ap-1797	55	7	(	(	PUNCT
ap-1797	55	8	4	4	NUM
ap-1797	55	9	)	)	PUNCT
ap-1797	55	10	is	be	AUX
ap-1797	55	11	pt	pt	X
ap-1797	55	12	symmetric	symmetric	NOUN
ap-1797	55	13	.	.	PUNCT
ap-1797	56	1	introducing	introduce	VERB
ap-1797	56	2	the	the	DET
ap-1797	56	3	length	length	NOUN
ap-1797	56	4	scale	scale	NOUN
ap-1797	56	5	a0	a0	PROPN
ap-1797	56	6	=	=	PUNCT
ap-1797	56	7	√	√	PROPN
ap-1797	56	8	~/mωy	~/mωy	NUM
ap-1797	56	9	,	,	PUNCT
ap-1797	56	10	z	z	NOUN
ap-1797	56	11	defined	define	VERB
ap-1797	56	12	by	by	ADP
ap-1797	56	13	the	the	DET
ap-1797	56	14	trap	trap	NOUN
ap-1797	56	15	frequency	frequency	NOUN
ap-1797	56	16	in	in	ADP
ap-1797	56	17	the	the	DET
ap-1797	56	18	direction	direction	NOUN
ap-1797	56	19	perpendicular	perpendicular	NOUN
ap-1797	56	20	to	to	ADP
ap-1797	56	21	the	the	DET
ap-1797	56	22	double	double	ADJ
ap-1797	56	23	-	-	PUNCT
ap-1797	56	24	well	well	NOUN
ap-1797	56	25	shape	shape	NOUN
ap-1797	56	26	and	and	CCONJ
ap-1797	56	27	the	the	DET
ap-1797	56	28	unit	unit	NOUN
ap-1797	56	29	of	of	ADP
ap-1797	56	30	energy	energy	NOUN
ap-1797	56	31	e0	e0	PROPN
ap-1797	56	32	=	=	PUNCT
ap-1797	57	1	~2/2ma2	~2/2ma2	PROPN
ap-1797	57	2	0	0	PUNCT
ap-1797	58	1	the	the	DET
ap-1797	58	2	dimensionless	dimensionless	ADJ
ap-1797	58	3	potential	potential	NOUN
ap-1797	58	4	reads	read	VERB
ap-1797	58	5	v	v	NOUN
ap-1797	58	6	(	(	PUNCT
ap-1797	58	7	x	x	NOUN
ap-1797	58	8	)	)	PUNCT
ap-1797	58	9	=	=	SYM
ap-1797	59	1	ω2	ω2	ADJ
ap-1797	59	2	xx	xx	NUM
ap-1797	59	3	2	2	NUM
ap-1797	59	4	+	+	CCONJ
ap-1797	59	5	y2	y2	PROPN
ap-1797	59	6	+	+	CCONJ
ap-1797	59	7	z2	z2	PROPN
ap-1797	59	8	+	+	CCONJ
ap-1797	59	9	v0e	v0e	PROPN
ap-1797	59	10	−σx2	−σx2	VERB
ap-1797	59	11	+	+	NUM
ap-1797	59	12	iγxe−ρx	iγxe−ρx	NOUN
ap-1797	59	13	2	2	NUM
ap-1797	59	14	,	,	PUNCT
ap-1797	59	15	(	(	PUNCT
ap-1797	59	16	5	5	NUM
ap-1797	59	17	)	)	PUNCT
ap-1797	59	18	and	and	CCONJ
ap-1797	59	19	the	the	DET
ap-1797	59	20	evolution	evolution	NOUN
ap-1797	59	21	of	of	ADP
ap-1797	59	22	the	the	DET
ap-1797	59	23	condensate	condensate	NOUN
ap-1797	59	24	is	be	AUX
ap-1797	59	25	described	describe	VERB
ap-1797	59	26	by	by	ADP
ap-1797	59	27	the	the	DET
ap-1797	59	28	gross	gross	ADJ
ap-1797	59	29	-	-	PUNCT
ap-1797	59	30	pitaevskii	pitaevskii	ADJ
ap-1797	59	31	equation	equation	NOUN
ap-1797	59	32	(	(	PUNCT
ap-1797	59	33	1	1	NUM
ap-1797	59	34	)	)	PUNCT
ap-1797	59	35	.	.	PUNCT
ap-1797	60	1	with	with	ADP
ap-1797	60	2	the	the	DET
ap-1797	60	3	chemical	chemical	ADJ
ap-1797	60	4	potential	potential	NOUN
ap-1797	60	5	µ	µ	NOUN
ap-1797	60	6	and	and	CCONJ
ap-1797	60	7	the	the	DET
ap-1797	60	8	usual	usual	ADJ
ap-1797	60	9	separation	separation	NOUN
ap-1797	60	10	ansatz	ansatz	ADJ
ap-1797	60	11	ψ(x	ψ(x	PROPN
ap-1797	60	12	,	,	PUNCT
ap-1797	60	13	t	t	PROPN
ap-1797	60	14	)	)	PUNCT
ap-1797	60	15	=	=	PUNCT
ap-1797	60	16	φ(x)e−iµt	φ(x)e−iµt	NOUN
ap-1797	60	17	in	in	ADP
ap-1797	60	18	the	the	DET
ap-1797	60	19	units	unit	NOUN
ap-1797	60	20	defined	define	VERB
ap-1797	60	21	above	above	ADP
ap-1797	60	22	one	one	NUM
ap-1797	60	23	obtains	obtain	VERB
ap-1797	60	24	the	the	DET
ap-1797	60	25	time	time	NOUN
ap-1797	60	26	-	-	PUNCT
ap-1797	60	27	independent	independent	ADJ
ap-1797	60	28	gross	gross	ADJ
ap-1797	60	29	-	-	PUNCT
ap-1797	60	30	pitaevskii	pitaevskii	ADJ
ap-1797	60	31	equation	equation	NOUN
ap-1797	60	32	(	(	PUNCT
ap-1797	60	33	−∆	−∆	NOUN
ap-1797	60	34	+	+	CCONJ
ap-1797	60	35	v	v	X
ap-1797	60	36	(	(	PUNCT
ap-1797	60	37	x)−	x)−	PROPN
ap-1797	60	38	g|φ(x)|2	g|φ(x)|2	PROPN
ap-1797	60	39	)	)	PUNCT
ap-1797	60	40	φ(x	φ(x	PROPN
ap-1797	60	41	)	)	PUNCT
ap-1797	60	42	=	=	PUNCT
ap-1797	60	43	µφ(x	µφ(x	NOUN
ap-1797	60	44	)	)	PUNCT
ap-1797	60	45	.	.	PUNCT
ap-1797	61	1	(	(	PUNCT
ap-1797	61	2	6	6	NUM
ap-1797	61	3	)	)	PUNCT
ap-1797	61	4	in	in	ADP
ap-1797	61	5	our	our	PRON
ap-1797	61	6	calculations	calculation	NOUN
ap-1797	61	7	we	we	PRON
ap-1797	61	8	use	use	VERB
ap-1797	61	9	the	the	DET
ap-1797	61	10	potential	potential	ADJ
ap-1797	61	11	parameters	parameter	NOUN
ap-1797	61	12	ωx	ωx	VERB
ap-1797	61	13	=	=	SYM
ap-1797	61	14	0.5	0.5	NUM
ap-1797	61	15	,	,	PUNCT
ap-1797	61	16	v0	v0	NOUN
ap-1797	61	17	=	=	SYM
ap-1797	61	18	4	4	NUM
ap-1797	61	19	,	,	PUNCT
ap-1797	61	20	and	and	CCONJ
ap-1797	61	21	σ	σ	X
ap-1797	61	22	=	=	SYM
ap-1797	61	23	0.5	0.5	NUM
ap-1797	61	24	.	.	PUNCT
ap-1797	62	1	the	the	DET
ap-1797	62	2	width	width	ADJ
ap-1797	62	3	parameter	parameter	NOUN
ap-1797	62	4	ρ	ρ	PROPN
ap-1797	62	5	=	=	PROPN
ap-1797	62	6	σ	σ	PROPN
ap-1797	62	7	2	2	NUM
ap-1797	62	8	ln(v0σ	ln(v0σ	PROPN
ap-1797	62	9	/	/	SYM
ap-1797	62	10	ω2	ω2	PROPN
ap-1797	62	11	x	x	X
ap-1797	62	12	)	)	PUNCT
ap-1797	62	13	(	(	PUNCT
ap-1797	62	14	7	7	X
ap-1797	62	15	)	)	PUNCT
ap-1797	62	16	of	of	ADP
ap-1797	62	17	the	the	DET
ap-1797	62	18	gain	gain	NOUN
ap-1797	62	19	-	-	PUNCT
ap-1797	62	20	loss	loss	NOUN
ap-1797	62	21	potential	potential	NOUN
ap-1797	62	22	is	be	AUX
ap-1797	62	23	chosen	choose	VERB
ap-1797	62	24	such	such	ADJ
ap-1797	62	25	that	that	SCONJ
ap-1797	62	26	the	the	DET
ap-1797	62	27	extrema	extrema	NOUN
ap-1797	62	28	of	of	ADP
ap-1797	62	29	the	the	DET
ap-1797	62	30	real	real	ADJ
ap-1797	62	31	and	and	CCONJ
ap-1797	62	32	imaginary	imaginary	ADJ
ap-1797	62	33	potential	potential	ADJ
ap-1797	62	34	parts	part	NOUN
ap-1797	62	35	coincide	coincide	NOUN
ap-1797	62	36	,	,	PUNCT
ap-1797	62	37	cf	cf	NOUN
ap-1797	62	38	.	.	PUNCT
ap-1797	62	39	figure	figure	NOUN
ap-1797	62	40	1	1	NUM
ap-1797	62	41	.	.	PUNCT
ap-1797	63	1	if	if	SCONJ
ap-1797	63	2	only	only	ADV
ap-1797	63	3	the	the	DET
ap-1797	63	4	x	x	NOUN
ap-1797	63	5	direction	direction	NOUN
ap-1797	63	6	is	be	AUX
ap-1797	63	7	considered	consider	VERB
ap-1797	63	8	and	and	CCONJ
ap-1797	63	9	all	all	DET
ap-1797	63	10	y	y	PROPN
ap-1797	63	11	and	and	CCONJ
ap-1797	63	12	z	z	NOUN
ap-1797	63	13	terms	term	NOUN
ap-1797	63	14	are	be	AUX
ap-1797	63	15	removed	remove	VERB
ap-1797	63	16	from	from	ADP
ap-1797	63	17	the	the	DET
ap-1797	63	18	potential	potential	NOUN
ap-1797	63	19	and	and	CCONJ
ap-1797	63	20	the	the	DET
ap-1797	63	21	wave	wave	NOUN
ap-1797	63	22	function	function	NOUN
ap-1797	63	23	,	,	PUNCT
ap-1797	63	24	we	we	PRON
ap-1797	63	25	can	can	AUX
ap-1797	63	26	reduce	reduce	VERB
ap-1797	63	27	the	the	DET
ap-1797	63	28	model	model	NOUN
ap-1797	63	29	to	to	ADP
ap-1797	63	30	one	one	NUM
ap-1797	63	31	dimension	dimension	NOUN
ap-1797	63	32	that	that	PRON
ap-1797	63	33	contains	contain	VERB
ap-1797	63	34	the	the	DET
ap-1797	63	35	relevant	relevant	ADJ
ap-1797	63	36	pt	pt	X
ap-1797	63	37	symmetric	symmetric	ADJ
ap-1797	63	38	information	information	NOUN
ap-1797	63	39	.	.	PUNCT
ap-1797	64	1	2.2	2.2	NUM
ap-1797	64	2	.	.	PUNCT
ap-1797	65	1	two	two	NUM
ap-1797	65	2	methods	method	NOUN
ap-1797	65	3	:	:	PUNCT
ap-1797	65	4	variational	variational	ADJ
ap-1797	65	5	gaussian	gaussian	NOUN
ap-1797	65	6	and	and	CCONJ
ap-1797	65	7	numerically	numerically	ADV
ap-1797	65	8	exact	exact	ADJ
ap-1797	65	9	we	we	PRON
ap-1797	65	10	use	use	VERB
ap-1797	65	11	two	two	NUM
ap-1797	65	12	methods	method	NOUN
ap-1797	65	13	to	to	PART
ap-1797	65	14	solve	solve	VERB
ap-1797	65	15	the	the	DET
ap-1797	65	16	time	time	NOUN
ap-1797	65	17	-	-	PUNCT
ap-1797	65	18	dependent	dependent	ADJ
ap-1797	65	19	and	and	CCONJ
ap-1797	65	20	time	time	NOUN
ap-1797	65	21	-	-	PUNCT
ap-1797	65	22	independent	independent	ADJ
ap-1797	65	23	gross	gross	ADJ
ap-1797	65	24	-	-	PUNCT
ap-1797	65	25	pitaevskii	pitaevskii	ADJ
ap-1797	65	26	equations	equation	NOUN
ap-1797	65	27	(	(	PUNCT
ap-1797	65	28	1	1	NUM
ap-1797	65	29	)	)	PUNCT
ap-1797	65	30	and	and	CCONJ
ap-1797	65	31	(	(	PUNCT
ap-1797	65	32	6	6	NUM
ap-1797	65	33	)	)	PUNCT
ap-1797	65	34	.	.	PUNCT
ap-1797	66	1	the	the	DET
ap-1797	66	2	gaussian	gaussian	ADJ
ap-1797	66	3	variational	variational	ADJ
ap-1797	66	4	method	method	NOUN
ap-1797	66	5	has	have	AUX
ap-1797	66	6	been	be	AUX
ap-1797	66	7	shown	show	VERB
ap-1797	66	8	to	to	PART
ap-1797	66	9	provide	provide	VERB
ap-1797	66	10	highly	highly	ADV
ap-1797	66	11	precise	precise	ADJ
ap-1797	66	12	solutions	solution	NOUN
ap-1797	66	13	with	with	ADP
ap-1797	66	14	low	low	ADJ
ap-1797	66	15	numerical	numerical	ADJ
ap-1797	66	16	effort	effort	NOUN
ap-1797	66	17	[	[	X
ap-1797	66	18	24–26	24–26	NUM
ap-1797	66	19	]	]	PUNCT
ap-1797	66	20	.	.	PUNCT
ap-1797	67	1	since	since	SCONJ
ap-1797	67	2	in	in	ADP
ap-1797	67	3	our	our	PRON
ap-1797	67	4	work	work	NOUN
ap-1797	67	5	it	it	PRON
ap-1797	67	6	is	be	AUX
ap-1797	67	7	applied	apply	VERB
ap-1797	67	8	260	260	NUM
ap-1797	67	9	vol	vol	NOUN
ap-1797	67	10	.	.	PUNCT
ap-1797	68	1	53	53	NUM
ap-1797	68	2	no	no	NOUN
ap-1797	68	3	.	.	PUNCT
ap-1797	69	1	3/2013	3/2013	PROPN
ap-1797	69	2	stationary	stationary	ADJ
ap-1797	69	3	and	and	CCONJ
ap-1797	69	4	dynamical	dynamical	ADJ
ap-1797	69	5	solutions	solution	NOUN
ap-1797	69	6	of	of	ADP
ap-1797	69	7	the	the	DET
ap-1797	69	8	gross	gross	ADJ
ap-1797	69	9	-	-	PUNCT
ap-1797	69	10	pitaevskii	pitaevskii	ADJ
ap-1797	69	11	equation	equation	NOUN
ap-1797	69	12	for	for	ADP
ap-1797	69	13	the	the	DET
ap-1797	69	14	first	first	ADJ
ap-1797	69	15	time	time	NOUN
ap-1797	69	16	to	to	ADP
ap-1797	69	17	bose	bose	NOUN
ap-1797	69	18	-	-	PUNCT
ap-1797	69	19	einstein	einstein	NOUN
ap-1797	69	20	condensates	condensate	NOUN
ap-1797	69	21	in	in	ADP
ap-1797	69	22	a	a	DET
ap-1797	69	23	pt	pt	NOUN
ap-1797	69	24	symmetric	symmetric	ADJ
ap-1797	69	25	complex	complex	ADJ
ap-1797	69	26	potential	potential	NOUN
ap-1797	69	27	,	,	PUNCT
ap-1797	69	28	we	we	PRON
ap-1797	69	29	compare	compare	VERB
ap-1797	69	30	it	it	PRON
ap-1797	69	31	to	to	ADP
ap-1797	69	32	numerically	numerically	ADV
ap-1797	69	33	exact	exact	ADJ
ap-1797	69	34	solutions	solution	NOUN
ap-1797	69	35	of	of	ADP
ap-1797	69	36	the	the	DET
ap-1797	69	37	gross	gross	ADJ
ap-1797	69	38	-	-	PUNCT
ap-1797	69	39	pitaevskii	pitaevskii	ADJ
ap-1797	69	40	equation	equation	NOUN
ap-1797	69	41	in	in	ADP
ap-1797	69	42	the	the	DET
ap-1797	69	43	one	one	NUM
ap-1797	69	44	-	-	PUNCT
ap-1797	69	45	dimensional	dimensional	ADJ
ap-1797	69	46	case	case	NOUN
ap-1797	69	47	.	.	PUNCT
ap-1797	70	1	the	the	DET
ap-1797	70	2	idea	idea	NOUN
ap-1797	70	3	of	of	ADP
ap-1797	70	4	the	the	DET
ap-1797	70	5	gaussian	gaussian	ADJ
ap-1797	70	6	variational	variational	ADJ
ap-1797	70	7	method	method	NOUN
ap-1797	70	8	consists	consist	VERB
ap-1797	70	9	of	of	ADP
ap-1797	70	10	the	the	DET
ap-1797	70	11	restriction	restriction	NOUN
ap-1797	70	12	to	to	ADP
ap-1797	70	13	a	a	DET
ap-1797	70	14	gaussian	gaussian	ADJ
ap-1797	70	15	shaped	shape	VERB
ap-1797	70	16	wave	wave	NOUN
ap-1797	70	17	function	function	NOUN
ap-1797	70	18	ψ(z	ψ(z	PROPN
ap-1797	70	19	,	,	PUNCT
ap-1797	70	20	x	x	X
ap-1797	70	21	)	)	PUNCT
ap-1797	70	22	=	=	SYM
ap-1797	71	1	2∑	2∑	NOUN
ap-1797	71	2	k=1	k=1	PUNCT
ap-1797	71	3	e−[ak	e−[ak	PROPN
ap-1797	71	4	x(x−qk	x(x−qk	PROPN
ap-1797	72	1	x)2+ak	x)2+ak	PROPN
ap-1797	72	2	y	y	PROPN
ap-1797	72	3	,	,	PUNCT
ap-1797	72	4	z(y2+z2	z(y2+z2	PROPN
ap-1797	72	5	)	)	PUNCT
ap-1797	72	6	]	]	PUNCT
ap-1797	73	1	×	×	PROPN
ap-1797	73	2	eipk	eipk	NOUN
ap-1797	73	3	x(x−qk	x(x−qk	PROPN
ap-1797	73	4	x)−ϕk	x)−ϕk	PROPN
ap-1797	73	5	(	(	PUNCT
ap-1797	73	6	8)	8)	NUM
ap-1797	73	7	described	describe	VERB
ap-1797	73	8	by	by	ADP
ap-1797	73	9	a	a	DET
ap-1797	73	10	small	small	ADJ
ap-1797	73	11	set	set	NOUN
ap-1797	73	12	of	of	ADP
ap-1797	73	13	variational	variational	ADJ
ap-1797	73	14	parameters	parameter	NOUN
ap-1797	73	15	,	,	PUNCT
ap-1797	73	16	viz	viz	NOUN
ap-1797	73	17	.	.	PUNCT
ap-1797	74	1	z(t	z(t	NOUN
ap-1797	74	2	)	)	PUNCT
ap-1797	75	1	=	=	PRON
ap-1797	75	2	{	{	PUNCT
ap-1797	75	3	akx(t	akx(t	PROPN
ap-1797	75	4	)	)	PUNCT
ap-1797	75	5	,	,	PUNCT
ap-1797	75	6	aky	aky	PROPN
ap-1797	75	7	,	,	PUNCT
ap-1797	75	8	z(t	z(t	NOUN
ap-1797	75	9	)	)	PUNCT
ap-1797	75	10	,	,	PUNCT
ap-1797	75	11	qkx(t	qkx(t	NOUN
ap-1797	75	12	)	)	PUNCT
ap-1797	75	13	,	,	PUNCT
ap-1797	75	14	pkx(t	pkx(t	PROPN
ap-1797	75	15	)	)	PUNCT
ap-1797	75	16	,	,	PUNCT
ap-1797	75	17	ϕk	ϕk	ADV
ap-1797	75	18	}	}	PUNCT
ap-1797	75	19	.	.	PUNCT
ap-1797	76	1	(	(	PUNCT
ap-1797	76	2	9	9	X
ap-1797	76	3	)	)	PUNCT
ap-1797	76	4	in	in	ADP
ap-1797	76	5	the	the	DET
ap-1797	76	6	case	case	NOUN
ap-1797	76	7	of	of	ADP
ap-1797	76	8	the	the	DET
ap-1797	76	9	pt	pt	PROPN
ap-1797	76	10	symmetric	symmetric	ADJ
ap-1797	76	11	double	double	ADJ
ap-1797	76	12	-	-	PUNCT
ap-1797	76	13	well	well	NOUN
ap-1797	76	14	setup	setup	NOUN
ap-1797	76	15	it	it	PRON
ap-1797	76	16	is	be	AUX
ap-1797	76	17	reasonable	reasonable	ADJ
ap-1797	76	18	to	to	PART
ap-1797	76	19	start	start	VERB
ap-1797	76	20	with	with	ADP
ap-1797	76	21	two	two	NUM
ap-1797	76	22	gaussian	gaussian	ADJ
ap-1797	76	23	wave	wave	NOUN
ap-1797	76	24	functions	function	NOUN
ap-1797	76	25	,	,	PUNCT
ap-1797	76	26	where	where	SCONJ
ap-1797	76	27	each	each	PRON
ap-1797	76	28	of	of	ADP
ap-1797	76	29	them	they	PRON
ap-1797	76	30	is	be	AUX
ap-1797	76	31	located	locate	VERB
ap-1797	76	32	in	in	ADP
ap-1797	76	33	one	one	NUM
ap-1797	76	34	of	of	ADP
ap-1797	76	35	the	the	DET
ap-1797	76	36	wells	well	NOUN
ap-1797	76	37	.	.	PUNCT
ap-1797	77	1	the	the	DET
ap-1797	77	2	widths	width	NOUN
ap-1797	77	3	of	of	ADP
ap-1797	77	4	the	the	DET
ap-1797	77	5	gaussians	gaussian	NOUN
ap-1797	77	6	are	be	AUX
ap-1797	77	7	determined	determine	VERB
ap-1797	77	8	by	by	ADP
ap-1797	77	9	the	the	DET
ap-1797	77	10	complex	complex	ADJ
ap-1797	77	11	parameters	parameter	NOUN
ap-1797	77	12	a1	a1	PROPN
ap-1797	77	13	x	x	X
ap-1797	77	14	,	,	PUNCT
ap-1797	77	15	a2	a2	PROPN
ap-1797	77	16	x	x	PROPN
ap-1797	77	17	,	,	PUNCT
ap-1797	77	18	a1	a1	PROPN
ap-1797	77	19	y	y	PROPN
ap-1797	77	20	,	,	PUNCT
ap-1797	77	21	z	z	PROPN
ap-1797	77	22	and	and	CCONJ
ap-1797	77	23	a2	a2	PROPN
ap-1797	77	24	y	y	PROPN
ap-1797	77	25	,	,	PUNCT
ap-1797	77	26	z.	z.	PROPN
ap-1797	77	27	since	since	SCONJ
ap-1797	77	28	the	the	DET
ap-1797	77	29	relevant	relevant	ADJ
ap-1797	77	30	dynamics	dynamic	NOUN
ap-1797	77	31	only	only	ADV
ap-1797	77	32	affects	affect	VERB
ap-1797	77	33	the	the	DET
ap-1797	77	34	x	x	NOUN
ap-1797	77	35	coordinate	coordinate	NOUN
ap-1797	77	36	and	and	CCONJ
ap-1797	77	37	the	the	DET
ap-1797	77	38	trap	trap	NOUN
ap-1797	77	39	was	be	AUX
ap-1797	77	40	assumed	assume	VERB
ap-1797	77	41	to	to	PART
ap-1797	77	42	be	be	AUX
ap-1797	77	43	symmetric	symmetric	ADJ
ap-1797	77	44	in	in	ADP
ap-1797	77	45	y	y	PROPN
ap-1797	77	46	and	and	CCONJ
ap-1797	77	47	z	z	NOUN
ap-1797	77	48	directions	direction	NOUN
ap-1797	77	49	,	,	PUNCT
ap-1797	77	50	we	we	PRON
ap-1797	77	51	include	include	VERB
ap-1797	77	52	in	in	ADP
ap-1797	77	53	our	our	PRON
ap-1797	77	54	ansatz	ansatz	NOUN
ap-1797	77	55	the	the	DET
ap-1797	77	56	same	same	ADJ
ap-1797	77	57	symmetry	symmetry	NOUN
ap-1797	77	58	for	for	ADP
ap-1797	77	59	the	the	DET
ap-1797	77	60	gaussian	gaussian	ADJ
ap-1797	77	61	wave	wave	NOUN
ap-1797	77	62	functions	function	NOUN
ap-1797	77	63	.	.	PUNCT
ap-1797	78	1	the	the	DET
ap-1797	78	2	positions	position	NOUN
ap-1797	78	3	and	and	CCONJ
ap-1797	78	4	the	the	DET
ap-1797	78	5	corresponding	corresponding	ADJ
ap-1797	78	6	momenta	momenta	NOUN
ap-1797	78	7	of	of	ADP
ap-1797	78	8	both	both	DET
ap-1797	78	9	gaussians	gaussian	NOUN
ap-1797	78	10	are	be	AUX
ap-1797	78	11	determined	determine	VERB
ap-1797	78	12	by	by	ADP
ap-1797	78	13	the	the	DET
ap-1797	78	14	real	real	ADJ
ap-1797	78	15	coordinates	coordinate	NOUN
ap-1797	78	16	q1	q1	PROPN
ap-1797	78	17	x	x	SYM
ap-1797	78	18	,	,	PUNCT
ap-1797	78	19	q2	q2	PROPN
ap-1797	78	20	x	x	PROPN
ap-1797	78	21	,	,	PUNCT
ap-1797	78	22	p1	p1	PROPN
ap-1797	78	23	x	x	PUNCT
ap-1797	78	24	and	and	CCONJ
ap-1797	78	25	p2	p2	PROPN
ap-1797	78	26	x.	x.	NOUN
ap-1797	79	1	the	the	DET
ap-1797	79	2	amplitudes	amplitude	NOUN
ap-1797	79	3	and	and	CCONJ
ap-1797	79	4	phases	phase	NOUN
ap-1797	79	5	are	be	AUX
ap-1797	79	6	introduced	introduce	VERB
ap-1797	79	7	via	via	ADP
ap-1797	79	8	the	the	DET
ap-1797	79	9	complex	complex	ADJ
ap-1797	79	10	variables	variable	NOUN
ap-1797	79	11	ϕ1	ϕ1	NOUN
ap-1797	79	12	and	and	CCONJ
ap-1797	79	13	ϕ2	ϕ2	ADV
ap-1797	79	14	.	.	PUNCT
ap-1797	80	1	this	this	PRON
ap-1797	80	2	leads	lead	VERB
ap-1797	80	3	in	in	ADP
ap-1797	80	4	total	total	NOUN
ap-1797	80	5	to	to	ADP
ap-1797	80	6	16	16	NUM
ap-1797	80	7	real	real	ADJ
ap-1797	80	8	parameters	parameter	NOUN
ap-1797	80	9	completely	completely	ADV
ap-1797	80	10	defining	define	VERB
ap-1797	80	11	the	the	DET
ap-1797	80	12	condensate	condensate	NOUN
ap-1797	80	13	wave	wave	NOUN
ap-1797	80	14	function	function	NOUN
ap-1797	80	15	.	.	PUNCT
ap-1797	81	1	reducing	reduce	VERB
ap-1797	81	2	the	the	DET
ap-1797	81	3	model	model	NOUN
ap-1797	81	4	to	to	ADP
ap-1797	81	5	one	one	NUM
ap-1797	81	6	dimension	dimension	NOUN
ap-1797	81	7	we	we	PRON
ap-1797	81	8	end	end	VERB
ap-1797	81	9	up	up	ADP
ap-1797	81	10	with	with	ADP
ap-1797	81	11	twelve	twelve	NUM
ap-1797	81	12	real	real	ADJ
ap-1797	81	13	variables	variable	NOUN
ap-1797	81	14	.	.	PUNCT
ap-1797	82	1	certainly	certainly	ADV
ap-1797	82	2	,	,	PUNCT
ap-1797	82	3	the	the	DET
ap-1797	82	4	ansatz	ansatz	ADJ
ap-1797	82	5	(	(	PUNCT
ap-1797	82	6	8)	8)	NUM
ap-1797	82	7	can	can	AUX
ap-1797	82	8	not	not	PART
ap-1797	82	9	solve	solve	VERB
ap-1797	82	10	the	the	DET
ap-1797	82	11	timedependent	timedependent	NOUN
ap-1797	82	12	gross	gross	ADJ
ap-1797	82	13	-	-	PUNCT
ap-1797	82	14	pitaevskii	pitaevskii	ADJ
ap-1797	82	15	equation	equation	NOUN
ap-1797	82	16	(	(	PUNCT
ap-1797	82	17	1	1	X
ap-1797	82	18	)	)	PUNCT
ap-1797	82	19	exactly	exactly	ADV
ap-1797	82	20	.	.	PUNCT
ap-1797	83	1	one	one	NUM
ap-1797	83	2	way	way	NOUN
ap-1797	83	3	to	to	PART
ap-1797	83	4	find	find	VERB
ap-1797	83	5	the	the	DET
ap-1797	83	6	“	"	PUNCT
ap-1797	83	7	best	good	ADJ
ap-1797	83	8	”	"	PUNCT
ap-1797	83	9	approximative	approximative	ADJ
ap-1797	83	10	solution	solution	NOUN
ap-1797	83	11	with	with	ADP
ap-1797	83	12	a	a	DET
ap-1797	83	13	wave	wave	NOUN
ap-1797	83	14	function	function	NOUN
ap-1797	83	15	restricted	restrict	VERB
ap-1797	83	16	to	to	ADP
ap-1797	83	17	the	the	DET
ap-1797	83	18	gaussian	gaussian	ADJ
ap-1797	83	19	form	form	NOUN
ap-1797	83	20	(	(	PUNCT
ap-1797	83	21	8)	8)	NUM
ap-1797	83	22	is	be	AUX
ap-1797	83	23	the	the	DET
ap-1797	83	24	application	application	NOUN
ap-1797	83	25	of	of	ADP
ap-1797	83	26	the	the	DET
ap-1797	83	27	mclachlan	mclachlan	PROPN
ap-1797	83	28	time	time	NOUN
ap-1797	83	29	-	-	PUNCT
ap-1797	83	30	dependent	dependent	ADJ
ap-1797	83	31	variational	variational	ADJ
ap-1797	83	32	principle	principle	NOUN
ap-1797	83	33	[	[	X
ap-1797	83	34	27	27	NUM
ap-1797	83	35	]	]	PUNCT
ap-1797	83	36	,	,	PUNCT
ap-1797	83	37	δi	δi	PRON
ap-1797	83	38	=	=	SYM
ap-1797	83	39	δ	δ	PROPN
ap-1797	83	40	∥∥iχ(z(t),x)−hψ(z(t),x	∥∥iχ(z(t),x)−hψ(z(t),x	NOUN
ap-1797	83	41	)	)	PUNCT
ap-1797	83	42	∥∥2	∥∥2	PROPN
ap-1797	83	43	!	!	PUNCT
ap-1797	84	1	=	=	PUNCT
ap-1797	85	1	0	0	X
ap-1797	85	2	.	.	PUNCT
ap-1797	86	1	(	(	PUNCT
ap-1797	86	2	10	10	NUM
ap-1797	86	3	)	)	PUNCT
ap-1797	86	4	in	in	ADP
ap-1797	86	5	this	this	DET
ap-1797	86	6	procedure	procedure	NOUN
ap-1797	86	7	the	the	DET
ap-1797	86	8	variation	variation	NOUN
ap-1797	86	9	with	with	ADP
ap-1797	86	10	respect	respect	NOUN
ap-1797	86	11	to	to	ADP
ap-1797	86	12	the	the	DET
ap-1797	86	13	parameters	parameter	NOUN
ap-1797	86	14	in	in	ADP
ap-1797	86	15	the	the	DET
ap-1797	86	16	wave	wave	NOUN
ap-1797	86	17	function	function	NOUN
ap-1797	86	18	χ	χ	NOUN
ap-1797	86	19	is	be	AUX
ap-1797	86	20	performed	perform	VERB
ap-1797	86	21	such	such	ADJ
ap-1797	86	22	that	that	SCONJ
ap-1797	86	23	the	the	DET
ap-1797	86	24	functional	functional	ADJ
ap-1797	86	25	i	i	PRON
ap-1797	86	26	is	be	AUX
ap-1797	86	27	minimized	minimize	VERB
ap-1797	86	28	.	.	PUNCT
ap-1797	87	1	in	in	ADP
ap-1797	87	2	a	a	DET
ap-1797	87	3	second	second	ADJ
ap-1797	87	4	step	step	NOUN
ap-1797	87	5	one	one	NUM
ap-1797	87	6	sets	set	VERB
ap-1797	87	7	ψ̇	ψ̇	NOUN
ap-1797	87	8	≡	≡	PROPN
ap-1797	87	9	χ	χ	NOUN
ap-1797	87	10	and	and	CCONJ
ap-1797	87	11	obtains	obtain	VERB
ap-1797	87	12	the	the	DET
ap-1797	87	13	equations	equation	NOUN
ap-1797	87	14	of	of	ADP
ap-1797	87	15	motion	motion	NOUN
ap-1797	87	16	,	,	PUNCT
ap-1797	87	17	which	which	PRON
ap-1797	87	18	in	in	ADP
ap-1797	87	19	our	our	PRON
ap-1797	87	20	case	case	NOUN
ap-1797	87	21	are	be	AUX
ap-1797	87	22	of	of	ADP
ap-1797	87	23	the	the	DET
ap-1797	87	24	form	form	NOUN
ap-1797	87	25	ȧkx	ȧkx	NOUN
ap-1797	87	26	=	=	SYM
ap-1797	87	27	−4i	−4i	PRON
ap-1797	87	28	(	(	PUNCT
ap-1797	87	29	(	(	PUNCT
ap-1797	87	30	akx)2	akx)2	NOUN
ap-1797	87	31	+	+	CCONJ
ap-1797	87	32	(	(	PUNCT
ap-1797	87	33	aky	aky	X
ap-1797	87	34	,	,	PUNCT
ap-1797	87	35	z)2)+	z)2)+	PROPN
ap-1797	87	36	iv	iv	NUM
ap-1797	87	37	k2;x	k2;x	PROPN
ap-1797	87	38	,	,	PUNCT
ap-1797	87	39	(	(	PUNCT
ap-1797	87	40	11a	11a	NOUN
ap-1797	87	41	)	)	PUNCT
ap-1797	87	42	ȧky	ȧky	NOUN
ap-1797	87	43	,	,	PUNCT
ap-1797	87	44	z	z	NOUN
ap-1797	87	45	=	=	SYM
ap-1797	87	46	−4i	−4i	PROPN
ap-1797	87	47	(	(	PUNCT
ap-1797	87	48	(	(	PUNCT
ap-1797	87	49	akx)2	akx)2	NOUN
ap-1797	87	50	+	+	CCONJ
ap-1797	87	51	(	(	PUNCT
ap-1797	87	52	aky	aky	X
ap-1797	87	53	,	,	PUNCT
ap-1797	87	54	z)2)+	z)2)+	PROPN
ap-1797	87	55	iv	iv	NUM
ap-1797	87	56	k2;y	k2;y	PROPN
ap-1797	87	57	,	,	PUNCT
ap-1797	87	58	z	z	PROPN
ap-1797	87	59	,	,	PUNCT
ap-1797	87	60	(	(	PUNCT
ap-1797	87	61	11b	11b	NOUN
ap-1797	87	62	)	)	PUNCT
ap-1797	87	63	q̇kx	q̇kx	SCONJ
ap-1797	87	64	=	=	SYM
ap-1797	87	65	2pkx	2pkx	NUM
ap-1797	87	66	+	+	NUM
ap-1797	87	67	skx	skx	PROPN
ap-1797	87	68	,	,	PUNCT
ap-1797	87	69	(	(	PUNCT
ap-1797	87	70	11c	11c	NOUN
ap-1797	87	71	)	)	PUNCT
ap-1797	87	72	ṗkx	ṗkx	NOUN
ap-1797	88	1	=	=	SYM
ap-1797	89	1	−re	−re	PROPN
ap-1797	90	1	vk1;x	vk1;x	NUM
ap-1797	91	1	−	−	PROPN
ap-1797	91	2	2	2	NUM
ap-1797	91	3	imakxs	imakxs	NOUN
ap-1797	92	1	k	k	NOUN
ap-1797	92	2	x	x	NOUN
ap-1797	92	3	−	−	PROPN
ap-1797	92	4	2	2	NUM
ap-1797	92	5	rev	rev	VERB
ap-1797	92	6	k2;xq	k2;xq	NOUN
ap-1797	92	7	k	k	PROPN
ap-1797	92	8	x	x	PROPN
ap-1797	92	9	,	,	PUNCT
ap-1797	92	10	(	(	PUNCT
ap-1797	92	11	11d	11d	NOUN
ap-1797	92	12	)	)	PUNCT
ap-1797	92	13	ϕ̇k	ϕ̇k	NOUN
ap-1797	93	1	=	=	SYM
ap-1797	93	2	ivk0	ivk0	VERB
ap-1797	93	3	+	+	NUM
ap-1797	93	4	2i(akx	2i(akx	NUM
ap-1797	94	1	+	+	SYM
ap-1797	94	2	aky	aky	X
ap-1797	94	3	,	,	PUNCT
ap-1797	94	4	z)−	z)−	PROPN
ap-1797	94	5	i(pkx)2	i(pkx)2	VERB
ap-1797	94	6	−	−	NOUN
ap-1797	94	7	ipkxskx	ipkxskx	VERB
ap-1797	94	8	+	+	CCONJ
ap-1797	94	9	iqkxvk1;x	iqkxvk1;x	NOUN
ap-1797	94	10	+	+	CCONJ
ap-1797	94	11	iqkxv	iqkxv	NOUN
ap-1797	94	12	k2;xq	k2;xq	NOUN
ap-1797	94	13	k	k	PROPN
ap-1797	94	14	x	x	PROPN
ap-1797	94	15	,	,	PUNCT
ap-1797	94	16	(	(	PUNCT
ap-1797	94	17	11e	11e	NUM
ap-1797	94	18	)	)	PUNCT
ap-1797	94	19	with	with	ADP
ap-1797	94	20	skx	skx	PROPN
ap-1797	94	21	=	=	SYM
ap-1797	94	22	1	1	NUM
ap-1797	94	23	2(reakx)−1(im	2(reakx)−1(im	NUM
ap-1797	94	24	vk1;x	vk1;x	NOUN
ap-1797	94	25	+	+	SYM
ap-1797	94	26	2	2	NUM
ap-1797	94	27	imv	imv	NOUN
ap-1797	94	28	k2;xq	k2;xq	NOUN
ap-1797	94	29	k	k	PROPN
ap-1797	94	30	x	x	PROPN
ap-1797	94	31	)	)	PUNCT
ap-1797	94	32	.	.	PUNCT
ap-1797	95	1	(	(	PUNCT
ap-1797	95	2	11f	11f	NUM
ap-1797	95	3	)	)	PUNCT
ap-1797	95	4	the	the	DET
ap-1797	95	5	equations	equation	NOUN
ap-1797	95	6	of	of	ADP
ap-1797	95	7	motion	motion	NOUN
ap-1797	95	8	(	(	PUNCT
ap-1797	95	9	11a)-(11f	11a)-(11f	NOUN
ap-1797	95	10	)	)	PUNCT
ap-1797	95	11	contain	contain	VERB
ap-1797	95	12	effective	effective	ADJ
ap-1797	95	13	potential	potential	ADJ
ap-1797	95	14	terms	term	NOUN
ap-1797	95	15	v	v	ADP
ap-1797	95	16	=	=	SYM
ap-1797	95	17	(	(	PUNCT
ap-1797	95	18	v1	v1	PROPN
ap-1797	95	19	0	0	NUM
ap-1797	95	20	,	,	PUNCT
ap-1797	95	21	.	.	PUNCT
ap-1797	95	22	.	.	PUNCT
ap-1797	96	1	.	.	PUNCT
ap-1797	97	1	,	,	PUNCT
ap-1797	97	2	v	v	X
ap-1797	97	3	1	1	NUM
ap-1797	97	4	1;x	1;x	NUM
ap-1797	97	5	,	,	PUNCT
ap-1797	97	6	.	.	PUNCT
ap-1797	97	7	.	.	PUNCT
ap-1797	97	8	.	.	PUNCT
ap-1797	98	1	,	,	PUNCT
ap-1797	98	2	v	v	X
ap-1797	98	3	1	1	NUM
ap-1797	98	4	2;x	2;x	NUM
ap-1797	98	5	,	,	PUNCT
ap-1797	98	6	.	.	PUNCT
ap-1797	98	7	.	.	PUNCT
ap-1797	98	8	.	.	PUNCT
ap-1797	98	9	)	)	PUNCT
ap-1797	99	1	,	,	PUNCT
ap-1797	99	2	which	which	PRON
ap-1797	99	3	are	be	AUX
ap-1797	99	4	obtained	obtain	VERB
ap-1797	99	5	from	from	ADP
ap-1797	99	6	a	a	DET
ap-1797	99	7	system	system	NOUN
ap-1797	99	8	of	of	ADP
ap-1797	99	9	linear	linear	PROPN
ap-1797	99	10	equations	equation	NOUN
ap-1797	99	11	,	,	PUNCT
ap-1797	99	12	kv	kv	PROPN
ap-1797	99	13	=	=	SYM
ap-1797	99	14	r	r	NOUN
ap-1797	99	15	,	,	PUNCT
ap-1797	99	16	where	where	SCONJ
ap-1797	99	17	the	the	DET
ap-1797	99	18	matrix	matrix	NOUN
ap-1797	99	19	k	k	PROPN
ap-1797	99	20	contains	contain	VERB
ap-1797	99	21	weighted	weight	VERB
ap-1797	99	22	overlap	overlap	NOUN
ap-1797	99	23	integrals	integral	NOUN
ap-1797	99	24	of	of	ADP
ap-1797	99	25	the	the	DET
ap-1797	99	26	gaussians	gaussian	NOUN
ap-1797	99	27	and	and	CCONJ
ap-1797	99	28	the	the	DET
ap-1797	99	29	vector	vector	NOUN
ap-1797	99	30	r	r	NOUN
ap-1797	99	31	consists	consist	VERB
ap-1797	99	32	of	of	ADP
ap-1797	99	33	weighted	weight	VERB
ap-1797	99	34	gaussian	gaussian	ADJ
ap-1797	99	35	averages	average	NOUN
ap-1797	99	36	of	of	ADP
ap-1797	99	37	all	all	DET
ap-1797	99	38	potential	potential	ADJ
ap-1797	99	39	terms	term	NOUN
ap-1797	99	40	including	include	VERB
ap-1797	99	41	the	the	DET
ap-1797	99	42	nonlinearity	nonlinearity	NOUN
ap-1797	99	43	.	.	PUNCT
ap-1797	100	1	the	the	DET
ap-1797	100	2	detailed	detailed	ADJ
ap-1797	100	3	form	form	NOUN
ap-1797	100	4	can	can	AUX
ap-1797	100	5	be	be	AUX
ap-1797	100	6	found	find	VERB
ap-1797	100	7	in	in	ADP
ap-1797	100	8	[	[	X
ap-1797	100	9	28	28	NUM
ap-1797	100	10	]	]	PUNCT
ap-1797	100	11	.	.	PUNCT
ap-1797	101	1	the	the	DET
ap-1797	101	2	dynamics	dynamic	NOUN
ap-1797	101	3	of	of	ADP
ap-1797	101	4	the	the	DET
ap-1797	101	5	condensate	condensate	NOUN
ap-1797	101	6	wave	wave	NOUN
ap-1797	101	7	function	function	NOUN
ap-1797	101	8	is	be	AUX
ap-1797	101	9	found	find	VERB
ap-1797	101	10	by	by	ADP
ap-1797	101	11	solving	solve	VERB
ap-1797	101	12	the	the	DET
ap-1797	101	13	ordinary	ordinary	ADJ
ap-1797	101	14	differential	differential	ADJ
ap-1797	101	15	equations	equation	NOUN
ap-1797	101	16	(	(	PUNCT
ap-1797	101	17	11a)-(11f	11a)-(11f	NUM
ap-1797	101	18	)	)	PUNCT
ap-1797	101	19	with	with	ADP
ap-1797	101	20	a	a	DET
ap-1797	101	21	runge	runge	NOUN
ap-1797	101	22	-	-	PUNCT
ap-1797	101	23	kutta	kutta	NOUN
ap-1797	101	24	algorithm	algorithm	NOUN
ap-1797	101	25	[	[	X
ap-1797	101	26	29	29	NUM
ap-1797	101	27	]	]	PUNCT
ap-1797	101	28	.	.	PUNCT
ap-1797	102	1	stationary	stationary	ADJ
ap-1797	102	2	states	state	NOUN
ap-1797	102	3	or	or	CCONJ
ap-1797	102	4	solutions	solution	NOUN
ap-1797	102	5	of	of	ADP
ap-1797	102	6	the	the	DET
ap-1797	102	7	time	time	NOUN
ap-1797	102	8	-	-	PUNCT
ap-1797	102	9	independent	independent	ADJ
ap-1797	102	10	gross	gross	ADJ
ap-1797	102	11	-	-	PUNCT
ap-1797	102	12	pitaevskii	pitaevskii	ADJ
ap-1797	102	13	equation	equation	NOUN
ap-1797	102	14	are	be	AUX
ap-1797	102	15	found	find	VERB
ap-1797	102	16	by	by	ADP
ap-1797	102	17	the	the	DET
ap-1797	102	18	requirements	requirement	NOUN
ap-1797	102	19	ȧkx	ȧkx	PROPN
ap-1797	102	20	=	=	SYM
ap-1797	102	21	ȧky	ȧky	PROPN
ap-1797	102	22	,	,	PUNCT
ap-1797	102	23	z	z	NOUN
ap-1797	102	24	=	=	SYM
ap-1797	102	25	q̇kx	q̇kx	NOUN
ap-1797	102	26	=	=	X
ap-1797	102	27	ṗkx	ṗkx	PROPN
ap-1797	102	28	=	=	SYM
ap-1797	102	29	0	0	PUNCT
ap-1797	103	1	(	(	PUNCT
ap-1797	103	2	12	12	NUM
ap-1797	103	3	conditions	condition	NOUN
ap-1797	103	4	for	for	ADP
ap-1797	103	5	real	real	ADJ
ap-1797	103	6	numbers	number	NOUN
ap-1797	103	7	)	)	PUNCT
ap-1797	103	8	,	,	PUNCT
ap-1797	103	9	ϕ̇1	ϕ̇1	PROPN
ap-1797	103	10	=	=	SYM
ap-1797	103	11	ϕ̇2	ϕ̇2	PROPN
ap-1797	103	12	(	(	PUNCT
ap-1797	103	13	2	2	NUM
ap-1797	103	14	conditions	condition	NOUN
ap-1797	103	15	)	)	PUNCT
ap-1797	103	16	.	.	PUNCT
ap-1797	104	1	these	these	DET
ap-1797	104	2	states	state	NOUN
ap-1797	104	3	have	have	VERB
ap-1797	104	4	to	to	PART
ap-1797	104	5	be	be	AUX
ap-1797	104	6	normalized	normalize	VERB
ap-1797	104	7	,	,	PUNCT
ap-1797	104	8	‖ψ‖	‖ψ‖	PROPN
ap-1797	104	9	=	=	SYM
ap-1797	104	10	1	1	NUM
ap-1797	104	11	,	,	PUNCT
ap-1797	104	12	which	which	PRON
ap-1797	104	13	is	be	AUX
ap-1797	104	14	important	important	ADJ
ap-1797	104	15	in	in	ADP
ap-1797	104	16	the	the	DET
ap-1797	104	17	nonlinear	nonlinear	ADJ
ap-1797	104	18	gross	gross	ADJ
ap-1797	104	19	-	-	PUNCT
ap-1797	104	20	pitaevskii	pitaevskii	ADJ
ap-1797	104	21	equation	equation	NOUN
ap-1797	104	22	and	and	CCONJ
ap-1797	104	23	adds	add	VERB
ap-1797	104	24	an	an	DET
ap-1797	104	25	additional	additional	ADJ
ap-1797	104	26	constraint	constraint	NOUN
ap-1797	104	27	.	.	PUNCT
ap-1797	105	1	due	due	ADP
ap-1797	105	2	to	to	ADP
ap-1797	105	3	the	the	DET
ap-1797	105	4	arbitrary	arbitrary	ADJ
ap-1797	105	5	global	global	ADJ
ap-1797	105	6	phase	phase	NOUN
ap-1797	105	7	one	one	NUM
ap-1797	105	8	of	of	ADP
ap-1797	105	9	the	the	DET
ap-1797	105	10	16	16	NUM
ap-1797	105	11	gaussian	gaussian	ADJ
ap-1797	105	12	parameters	parameter	NOUN
ap-1797	105	13	introduced	introduce	VERB
ap-1797	105	14	above	above	ADV
ap-1797	105	15	is	be	AUX
ap-1797	105	16	free	free	ADJ
ap-1797	105	17	and	and	CCONJ
ap-1797	105	18	15	15	NUM
ap-1797	105	19	parameters	parameter	NOUN
ap-1797	105	20	must	must	AUX
ap-1797	105	21	be	be	AUX
ap-1797	105	22	varied	varied	ADJ
ap-1797	105	23	to	to	PART
ap-1797	105	24	fulfill	fulfill	VERB
ap-1797	105	25	the	the	DET
ap-1797	105	26	15	15	NUM
ap-1797	105	27	conditions	condition	NOUN
ap-1797	105	28	.	.	PUNCT
ap-1797	106	1	this	this	PRON
ap-1797	106	2	is	be	AUX
ap-1797	106	3	done	do	VERB
ap-1797	106	4	with	with	ADP
ap-1797	106	5	a	a	DET
ap-1797	106	6	15	15	NUM
ap-1797	106	7	-	-	PUNCT
ap-1797	106	8	dimensional	dimensional	ADJ
ap-1797	106	9	root	root	NOUN
ap-1797	106	10	search	search	NOUN
ap-1797	106	11	by	by	ADP
ap-1797	106	12	applying	apply	VERB
ap-1797	106	13	a	a	DET
ap-1797	106	14	powell	powell	NOUN
ap-1797	106	15	hybrid	hybrid	NOUN
ap-1797	106	16	method	method	NOUN
ap-1797	106	17	[	[	X
ap-1797	106	18	29	29	NUM
ap-1797	106	19	]	]	PUNCT
ap-1797	106	20	.	.	PUNCT
ap-1797	107	1	if	if	SCONJ
ap-1797	107	2	we	we	PRON
ap-1797	107	3	consider	consider	VERB
ap-1797	107	4	a	a	DET
ap-1797	107	5	one	one	NUM
ap-1797	107	6	-	-	PUNCT
ap-1797	107	7	dimensional	dimensional	ADJ
ap-1797	107	8	condensate	condensate	NOUN
ap-1797	107	9	the	the	DET
ap-1797	107	10	root	root	NOUN
ap-1797	107	11	search	search	NOUN
ap-1797	107	12	reduces	reduce	VERB
ap-1797	107	13	to	to	ADP
ap-1797	107	14	11	11	NUM
ap-1797	107	15	conditions	condition	NOUN
ap-1797	107	16	,	,	PUNCT
ap-1797	107	17	which	which	PRON
ap-1797	107	18	have	have	VERB
ap-1797	107	19	to	to	PART
ap-1797	107	20	be	be	AUX
ap-1797	107	21	fulfilled	fulfil	VERB
ap-1797	107	22	by	by	ADP
ap-1797	107	23	11	11	NUM
ap-1797	107	24	appropriately	appropriately	ADV
ap-1797	107	25	chosen	choose	VERB
ap-1797	107	26	parameters	parameter	NOUN
ap-1797	107	27	.	.	PUNCT
ap-1797	108	1	this	this	DET
ap-1797	108	2	small	small	ADJ
ap-1797	108	3	difference	difference	NOUN
ap-1797	108	4	exemplifies	exemplify	VERB
ap-1797	108	5	the	the	DET
ap-1797	108	6	high	high	ADJ
ap-1797	108	7	scalability	scalability	NOUN
ap-1797	108	8	of	of	ADP
ap-1797	108	9	the	the	DET
ap-1797	108	10	variational	variational	ADJ
ap-1797	108	11	gaussian	gaussian	NOUN
ap-1797	108	12	method	method	NOUN
ap-1797	108	13	.	.	PUNCT
ap-1797	109	1	an	an	DET
ap-1797	109	2	increase	increase	NOUN
ap-1797	109	3	of	of	ADP
ap-1797	109	4	the	the	DET
ap-1797	109	5	dimension	dimension	NOUN
ap-1797	109	6	or	or	CCONJ
ap-1797	109	7	the	the	DET
ap-1797	109	8	flexibility	flexibility	NOUN
ap-1797	109	9	of	of	ADP
ap-1797	109	10	the	the	DET
ap-1797	109	11	wave	wave	NOUN
ap-1797	109	12	function	function	NOUN
ap-1797	109	13	leads	lead	VERB
ap-1797	109	14	only	only	ADV
ap-1797	109	15	to	to	ADP
ap-1797	109	16	a	a	DET
ap-1797	109	17	moderate	moderate	ADJ
ap-1797	109	18	increase	increase	NOUN
ap-1797	109	19	of	of	ADP
ap-1797	109	20	the	the	DET
ap-1797	109	21	numerical	numerical	ADJ
ap-1797	109	22	effort	effort	NOUN
ap-1797	109	23	.	.	PUNCT
ap-1797	110	1	the	the	DET
ap-1797	110	2	numerically	numerically	ADV
ap-1797	110	3	exact	exact	ADJ
ap-1797	110	4	integrations	integration	NOUN
ap-1797	110	5	of	of	ADP
ap-1797	110	6	the	the	DET
ap-1797	110	7	grosspitaevskii	grosspitaevskii	ADJ
ap-1797	110	8	equations	equation	NOUN
ap-1797	110	9	(	(	PUNCT
ap-1797	110	10	1	1	NUM
ap-1797	110	11	)	)	PUNCT
ap-1797	110	12	and	and	CCONJ
ap-1797	110	13	(	(	PUNCT
ap-1797	110	14	6	6	X
ap-1797	110	15	)	)	PUNCT
ap-1797	110	16	presented	present	VERB
ap-1797	110	17	in	in	ADP
ap-1797	110	18	this	this	DET
ap-1797	110	19	paper	paper	NOUN
ap-1797	110	20	are	be	AUX
ap-1797	110	21	carried	carry	VERB
ap-1797	110	22	out	out	ADP
ap-1797	110	23	for	for	ADP
ap-1797	110	24	the	the	DET
ap-1797	110	25	one	one	NUM
ap-1797	110	26	-	-	PUNCT
ap-1797	110	27	dimensional	dimensional	ADJ
ap-1797	110	28	setup	setup	NOUN
ap-1797	110	29	,	,	PUNCT
ap-1797	110	30	where	where	SCONJ
ap-1797	110	31	the	the	DET
ap-1797	110	32	computational	computational	ADJ
ap-1797	110	33	costs	cost	NOUN
ap-1797	110	34	are	be	AUX
ap-1797	110	35	reasonable	reasonable	ADJ
ap-1797	110	36	.	.	PUNCT
ap-1797	111	1	the	the	DET
ap-1797	111	2	stationary	stationary	ADJ
ap-1797	111	3	wave	wave	NOUN
ap-1797	111	4	functions	function	NOUN
ap-1797	111	5	are	be	AUX
ap-1797	111	6	integrated	integrate	VERB
ap-1797	111	7	outward	outward	ADV
ap-1797	111	8	from	from	ADP
ap-1797	111	9	x	x	X
ap-1797	111	10	=	=	SYM
ap-1797	111	11	0	0	NUM
ap-1797	111	12	in	in	ADP
ap-1797	111	13	positive	positive	ADJ
ap-1797	111	14	and	and	CCONJ
ap-1797	111	15	negative	negative	ADJ
ap-1797	111	16	direction	direction	NOUN
ap-1797	111	17	using	use	VERB
ap-1797	111	18	a	a	DET
ap-1797	111	19	rungekutta	rungekutta	ADJ
ap-1797	111	20	algorithm	algorithm	NOUN
ap-1797	111	21	with	with	ADP
ap-1797	111	22	initial	initial	ADJ
ap-1797	111	23	values	value	NOUN
ap-1797	111	24	reψ(0	reψ(0	NOUN
ap-1797	111	25	)	)	PUNCT
ap-1797	111	26	,	,	PUNCT
ap-1797	111	27	ψ′(0	ψ′(0	PRON
ap-1797	111	28	)	)	PUNCT
ap-1797	111	29	∈	∈	PROPN
ap-1797	111	30	c	c	NOUN
ap-1797	111	31	,	,	PUNCT
ap-1797	111	32	and	and	CCONJ
ap-1797	111	33	µ	µ	PROPN
ap-1797	111	34	∈	∈	PROPN
ap-1797	111	35	c.	c.	NOUN
ap-1797	111	36	they	they	PRON
ap-1797	111	37	have	have	VERB
ap-1797	111	38	to	to	PART
ap-1797	111	39	be	be	AUX
ap-1797	111	40	chosen	choose	VERB
ap-1797	111	41	such	such	ADJ
ap-1797	111	42	that	that	SCONJ
ap-1797	111	43	the	the	DET
ap-1797	111	44	five	five	NUM
ap-1797	111	45	conditions	condition	NOUN
ap-1797	111	46	ψ(∞	ψ(∞	NOUN
ap-1797	111	47	)	)	PUNCT
ap-1797	111	48	→	→	SYM
ap-1797	111	49	0	0	NUM
ap-1797	111	50	,	,	PUNCT
ap-1797	111	51	ψ(−∞	ψ(−∞	ADJ
ap-1797	111	52	)	)	PUNCT
ap-1797	111	53	→	→	SYM
ap-1797	111	54	0	0	NUM
ap-1797	111	55	,	,	PUNCT
ap-1797	111	56	and	and	CCONJ
ap-1797	111	57	‖ψ‖	‖ψ‖	PROPN
ap-1797	111	58	=	=	NOUN
ap-1797	111	59	1	1	NUM
ap-1797	111	60	are	be	AUX
ap-1797	111	61	satisfied	satisfied	ADJ
ap-1797	111	62	.	.	PUNCT
ap-1797	112	1	the	the	DET
ap-1797	112	2	conditions	condition	NOUN
ap-1797	112	3	define	define	VERB
ap-1797	112	4	square	square	NOUN
ap-1797	112	5	-	-	PUNCT
ap-1797	112	6	integrable	integrable	ADJ
ap-1797	112	7	and	and	CCONJ
ap-1797	112	8	normalized	normalize	VERB
ap-1797	112	9	wave	wave	NOUN
ap-1797	112	10	functions	function	NOUN
ap-1797	112	11	,	,	PUNCT
ap-1797	112	12	i.e.	i.e.	X
ap-1797	112	13	the	the	DET
ap-1797	112	14	stationary	stationary	ADJ
ap-1797	112	15	states	state	NOUN
ap-1797	112	16	we	we	PRON
ap-1797	112	17	are	be	AUX
ap-1797	112	18	interested	interested	ADJ
ap-1797	112	19	in	in	ADP
ap-1797	112	20	.	.	PUNCT
ap-1797	113	1	note	note	VERB
ap-1797	113	2	that	that	SCONJ
ap-1797	113	3	the	the	DET
ap-1797	113	4	arbitrary	arbitrary	ADJ
ap-1797	113	5	global	global	ADJ
ap-1797	113	6	phase	phase	NOUN
ap-1797	113	7	has	have	AUX
ap-1797	113	8	been	be	AUX
ap-1797	113	9	exploited	exploit	VERB
ap-1797	113	10	by	by	ADP
ap-1797	113	11	setting	set	VERB
ap-1797	113	12	imψ(0	imψ(0	NOUN
ap-1797	113	13	)	)	PUNCT
ap-1797	114	1	=	=	SYM
ap-1797	114	2	0	0	NUM
ap-1797	114	3	for	for	ADP
ap-1797	114	4	the	the	DET
ap-1797	114	5	initial	initial	ADJ
ap-1797	114	6	values	value	NOUN
ap-1797	114	7	of	of	ADP
ap-1797	114	8	the	the	DET
ap-1797	114	9	integration	integration	NOUN
ap-1797	114	10	.	.	PUNCT
ap-1797	115	1	for	for	ADP
ap-1797	115	2	dynamical	dynamical	ADJ
ap-1797	115	3	calculations	calculation	NOUN
ap-1797	115	4	the	the	DET
ap-1797	115	5	split	split	ADJ
ap-1797	115	6	operator	operator	NOUN
ap-1797	115	7	method	method	NOUN
ap-1797	115	8	is	be	AUX
ap-1797	115	9	used	use	VERB
ap-1797	115	10	,	,	PUNCT
ap-1797	115	11	as	as	SCONJ
ap-1797	115	12	explained	explain	VERB
ap-1797	115	13	in	in	ADP
ap-1797	115	14	[	[	X
ap-1797	115	15	28	28	NUM
ap-1797	115	16	]	]	PUNCT
ap-1797	115	17	.	.	PUNCT
ap-1797	116	1	3	3	X
ap-1797	116	2	.	.	X
ap-1797	116	3	numerical	numerical	PROPN
ap-1797	116	4	solutions	solution	NOUN
ap-1797	116	5	3.1	3.1	NUM
ap-1797	116	6	.	.	PUNCT
ap-1797	117	1	energy	energy	NOUN
ap-1797	117	2	eigenvalues	eigenvalues	PROPN
ap-1797	117	3	figure	figure	NOUN
ap-1797	117	4	2	2	NUM
ap-1797	117	5	shows	show	VERB
ap-1797	117	6	a	a	DET
ap-1797	117	7	typical	typical	ADJ
ap-1797	117	8	example	example	NOUN
ap-1797	117	9	for	for	ADP
ap-1797	117	10	the	the	DET
ap-1797	117	11	eigenvalues	eigenvalue	NOUN
ap-1797	117	12	of	of	ADP
ap-1797	117	13	the	the	DET
ap-1797	117	14	time	time	NOUN
ap-1797	117	15	-	-	PUNCT
ap-1797	117	16	independent	independent	ADJ
ap-1797	117	17	gross	gross	ADJ
ap-1797	117	18	-	-	PUNCT
ap-1797	117	19	pitaevskii	pitaevskii	ADJ
ap-1797	117	20	equation	equation	NOUN
ap-1797	117	21	(	(	PUNCT
ap-1797	117	22	6	6	NUM
ap-1797	117	23	)	)	PUNCT
ap-1797	117	24	.	.	PUNCT
ap-1797	118	1	first	first	ADV
ap-1797	118	2	,	,	PUNCT
ap-1797	118	3	one	one	PRON
ap-1797	118	4	observes	observe	VERB
ap-1797	118	5	that	that	SCONJ
ap-1797	118	6	the	the	DET
ap-1797	118	7	linear	linear	ADJ
ap-1797	118	8	system	system	NOUN
ap-1797	118	9	(	(	PUNCT
ap-1797	118	10	g	g	NOUN
ap-1797	118	11	=	=	SYM
ap-1797	118	12	0	0	NUM
ap-1797	118	13	)	)	PUNCT
ap-1797	118	14	reveals	reveal	VERB
ap-1797	118	15	the	the	DET
ap-1797	118	16	known	know	VERB
ap-1797	118	17	features	feature	NOUN
ap-1797	118	18	of	of	ADP
ap-1797	118	19	complex	complex	ADJ
ap-1797	118	20	hamiltonians	hamiltonian	NOUN
ap-1797	118	21	with	with	ADP
ap-1797	118	22	pt	pt	PROPN
ap-1797	118	23	symmetry	symmetry	NOUN
ap-1797	118	24	.	.	PUNCT
ap-1797	119	1	two	two	NUM
ap-1797	119	2	real	real	ADJ
ap-1797	119	3	eigenvalue	eigenvalue	NOUN
ap-1797	119	4	solutions	solution	NOUN
ap-1797	119	5	are	be	AUX
ap-1797	119	6	found	find	VERB
ap-1797	119	7	below	below	ADP
ap-1797	119	8	a	a	DET
ap-1797	119	9	value	value	NOUN
ap-1797	119	10	γep	γep	NOUN
ap-1797	119	11	,	,	PUNCT
ap-1797	119	12	where	where	SCONJ
ap-1797	119	13	they	they	PRON
ap-1797	119	14	merge	merge	VERB
ap-1797	119	15	in	in	ADP
ap-1797	119	16	an	an	DET
ap-1797	119	17	exceptional	exceptional	ADJ
ap-1797	119	18	point	point	NOUN
ap-1797	119	19	.	.	PUNCT
ap-1797	120	1	for	for	ADP
ap-1797	120	2	larger	large	ADJ
ap-1797	120	3	values	value	NOUN
ap-1797	120	4	of	of	ADP
ap-1797	120	5	γ	γ	PROPN
ap-1797	120	6	two	two	NUM
ap-1797	120	7	complex	complex	ADJ
ap-1797	120	8	and	and	CCONJ
ap-1797	120	9	complex	complex	ADJ
ap-1797	120	10	conjugate	conjugate	ADJ
ap-1797	120	11	solutions	solution	NOUN
ap-1797	120	12	are	be	AUX
ap-1797	120	13	found	find	VERB
ap-1797	120	14	.	.	PUNCT
ap-1797	121	1	the	the	DET
ap-1797	121	2	agreement	agreement	NOUN
ap-1797	121	3	between	between	ADP
ap-1797	121	4	the	the	DET
ap-1797	121	5	gaussian	gaussian	ADJ
ap-1797	121	6	approximation	approximation	NOUN
ap-1797	121	7	(	(	PUNCT
ap-1797	121	8	solid	solid	ADJ
ap-1797	121	9	261	261	NUM
ap-1797	121	10	holger	holger	NOUN
ap-1797	121	11	cartarius	cartarius	NOUN
ap-1797	121	12	et	et	PROPN
ap-1797	121	13	al	al	PROPN
ap-1797	121	14	.	.	PROPN
ap-1797	122	1	acta	acta	PROPN
ap-1797	122	2	polytechnica	polytechnica	PROPN
ap-1797	122	3	2.34	2.34	NUM
ap-1797	122	4	2.36	2.36	NUM
ap-1797	122	5	2.38	2.38	NUM
ap-1797	122	6	2.40	2.40	NUM
ap-1797	122	7	2.42	2.42	NUM
ap-1797	122	8	2.44	2.44	NUM
ap-1797	122	9	2.46	2.46	NUM
ap-1797	122	10	2.48	2.48	NUM
ap-1797	122	11	2.50	2.50	NUM
ap-1797	122	12	2.52	2.52	NUM
ap-1797	122	13	0	0	NUM
ap-1797	122	14	0.01	0.01	NUM
ap-1797	122	15	0.02	0.02	NUM
ap-1797	122	16	0.03	0.03	NUM
ap-1797	122	17	0.04	0.04	NUM
ap-1797	122	18	0.05	0.05	NUM
ap-1797	122	19	0.06	0.06	NUM
ap-1797	122	20	0.07	0.07	NUM
ap-1797	122	21	0.08	0.08	NUM
ap-1797	122	22	r	r	NOUN
ap-1797	122	23	e	e	X
ap-1797	122	24	µ	µ	X
ap-1797	122	25	γ	γ	X
ap-1797	122	26	(	(	PUNCT
ap-1797	122	27	a	a	PROPN
ap-1797	122	28	)	)	PUNCT
ap-1797	122	29	−0.08	−0.08	PROPN
ap-1797	123	1	−0.06	−0.06	ADP
ap-1797	123	2	−0.04	−0.04	PROPN
ap-1797	123	3	−0.02	−0.02	NOUN
ap-1797	123	4	0.00	0.00	NUM
ap-1797	123	5	0.02	0.02	NUM
ap-1797	123	6	0.04	0.04	NUM
ap-1797	123	7	0.06	0.06	NUM
ap-1797	123	8	0.08	0.08	NUM
ap-1797	123	9	0	0	NUM
ap-1797	123	10	0.01	0.01	NUM
ap-1797	123	11	0.02	0.02	NUM
ap-1797	123	12	0.03	0.03	NUM
ap-1797	123	13	0.04	0.04	NUM
ap-1797	123	14	0.05	0.05	NUM
ap-1797	123	15	0.06	0.06	NUM
ap-1797	123	16	0.07	0.07	NUM
ap-1797	123	17	0.08	0.08	NUM
ap-1797	124	1	i	i	PRON
ap-1797	124	2	m	m	VERB
ap-1797	124	3	µ	µ	VERB
ap-1797	124	4	γ	γ	X
ap-1797	124	5	(	(	PUNCT
ap-1797	124	6	b	b	NOUN
ap-1797	124	7	)	)	PUNCT
ap-1797	124	8	g	g	NOUN
ap-1797	124	9	=	=	SYM
ap-1797	124	10	0	0	NUM
ap-1797	124	11	g	g	NOUN
ap-1797	124	12	=	=	NOUN
ap-1797	124	13	0.1	0.1	NUM
ap-1797	124	14	g	g	NOUN
ap-1797	124	15	=	=	NOUN
ap-1797	124	16	0.2	0.2	NUM
ap-1797	124	17	g	g	NOUN
ap-1797	124	18	=	=	NOUN
ap-1797	124	19	0.3	0.3	NUM
ap-1797	124	20	figure	figure	NOUN
ap-1797	124	21	2	2	NUM
ap-1797	124	22	.	.	PUNCT
ap-1797	125	1	eigenvalues	eigenvalue	NOUN
ap-1797	125	2	of	of	ADP
ap-1797	125	3	the	the	DET
ap-1797	125	4	time	time	NOUN
ap-1797	125	5	-	-	PUNCT
ap-1797	125	6	independent	independent	ADJ
ap-1797	125	7	grosspitaevskii	grosspitaevskii	ADJ
ap-1797	125	8	equation	equation	NOUN
ap-1797	125	9	(	(	PUNCT
ap-1797	125	10	6	6	NUM
ap-1797	125	11	)	)	PUNCT
ap-1797	125	12	for	for	ADP
ap-1797	125	13	different	different	ADJ
ap-1797	125	14	values	value	NOUN
ap-1797	125	15	of	of	ADP
ap-1797	125	16	the	the	DET
ap-1797	125	17	nonlinearity	nonlinearity	NOUN
ap-1797	125	18	g	g	NOUN
ap-1797	125	19	in	in	ADP
ap-1797	125	20	dependence	dependence	NOUN
ap-1797	125	21	on	on	ADP
ap-1797	125	22	the	the	DET
ap-1797	125	23	gain	gain	NOUN
ap-1797	125	24	-	-	PUNCT
ap-1797	125	25	loss	loss	NOUN
ap-1797	125	26	parameter	parameter	NOUN
ap-1797	125	27	γ	γ	PROPN
ap-1797	125	28	.	.	PROPN
ap-1797	125	29	with	with	ADP
ap-1797	125	30	increasing	increase	VERB
ap-1797	125	31	g	g	ADP
ap-1797	125	32	the	the	DET
ap-1797	125	33	real	real	ADJ
ap-1797	125	34	part	part	NOUN
ap-1797	125	35	of	of	ADP
ap-1797	125	36	the	the	DET
ap-1797	125	37	energies	energy	NOUN
ap-1797	125	38	decreases	decrease	VERB
ap-1797	125	39	.	.	PUNCT
ap-1797	126	1	the	the	DET
ap-1797	126	2	gaussian	gaussian	ADJ
ap-1797	126	3	approximation	approximation	NOUN
ap-1797	126	4	(	(	PUNCT
ap-1797	126	5	solid	solid	ADJ
ap-1797	126	6	lines	line	NOUN
ap-1797	126	7	)	)	PUNCT
ap-1797	126	8	and	and	CCONJ
ap-1797	126	9	the	the	DET
ap-1797	126	10	numerically	numerically	ADV
ap-1797	126	11	exact	exact	ADJ
ap-1797	126	12	solutions	solution	NOUN
ap-1797	126	13	(	(	PUNCT
ap-1797	126	14	dashed	dash	VERB
ap-1797	126	15	lines	line	NOUN
ap-1797	126	16	)	)	PUNCT
ap-1797	126	17	are	be	AUX
ap-1797	126	18	shown	show	VERB
ap-1797	126	19	.	.	PUNCT
ap-1797	127	1	vanishing	vanish	VERB
ap-1797	127	2	imaginary	imaginary	ADJ
ap-1797	127	3	parts	part	NOUN
ap-1797	127	4	are	be	AUX
ap-1797	127	5	not	not	PART
ap-1797	127	6	plotted	plot	VERB
ap-1797	127	7	.	.	PUNCT
ap-1797	128	1	two	two	NUM
ap-1797	128	2	solutions	solution	NOUN
ap-1797	128	3	with	with	ADP
ap-1797	128	4	real	real	ADJ
ap-1797	128	5	eigenvalues	eigenvalue	NOUN
ap-1797	128	6	are	be	AUX
ap-1797	128	7	obtained	obtain	VERB
ap-1797	128	8	up	up	ADP
ap-1797	128	9	to	to	ADP
ap-1797	128	10	a	a	DET
ap-1797	128	11	value	value	NOUN
ap-1797	128	12	γep	γep	X
ap-1797	129	1	≈	≈	NOUN
ap-1797	129	2	0.04	0.04	NUM
ap-1797	129	3	,	,	PUNCT
ap-1797	129	4	where	where	SCONJ
ap-1797	129	5	they	they	PRON
ap-1797	129	6	merge	merge	VERB
ap-1797	129	7	in	in	ADP
ap-1797	129	8	an	an	DET
ap-1797	129	9	exceptional	exceptional	ADJ
ap-1797	129	10	point	point	NOUN
ap-1797	129	11	.	.	PUNCT
ap-1797	130	1	two	two	NUM
ap-1797	130	2	additional	additional	ADJ
ap-1797	130	3	solutions	solution	NOUN
ap-1797	130	4	with	with	ADP
ap-1797	130	5	complex	complex	ADJ
ap-1797	130	6	eigenvalues	eigenvalue	NOUN
ap-1797	130	7	are	be	AUX
ap-1797	130	8	obtained	obtain	VERB
ap-1797	130	9	,	,	PUNCT
ap-1797	130	10	starting	start	VERB
ap-1797	130	11	at	at	ADP
ap-1797	130	12	a	a	DET
ap-1797	130	13	critical	critical	ADJ
ap-1797	130	14	value	value	NOUN
ap-1797	130	15	γc	γc	PROPN
ap-1797	130	16	,	,	PUNCT
ap-1797	130	17	where	where	SCONJ
ap-1797	130	18	γc	γc	PROPN
ap-1797	130	19	<	<	X
ap-1797	130	20	γep	γep	PROPN
ap-1797	130	21	for	for	ADP
ap-1797	130	22	g	g	PROPN
ap-1797	130	23	6=	6=	PROPN
ap-1797	130	24	0	0	NUM
ap-1797	130	25	.	.	PUNCT
ap-1797	131	1	lines	line	NOUN
ap-1797	131	2	)	)	PUNCT
ap-1797	131	3	and	and	CCONJ
ap-1797	131	4	the	the	DET
ap-1797	131	5	numerically	numerically	ADV
ap-1797	131	6	exact	exact	ADJ
ap-1797	131	7	solution	solution	NOUN
ap-1797	131	8	(	(	PUNCT
ap-1797	131	9	dashed	dash	VERB
ap-1797	131	10	lines	line	NOUN
ap-1797	131	11	)	)	PUNCT
ap-1797	131	12	is	be	AUX
ap-1797	131	13	excellent	excellent	ADJ
ap-1797	131	14	.	.	PUNCT
ap-1797	132	1	an	an	DET
ap-1797	132	2	important	important	ADJ
ap-1797	132	3	result	result	NOUN
ap-1797	132	4	is	be	AUX
ap-1797	132	5	the	the	DET
ap-1797	132	6	persistence	persistence	NOUN
ap-1797	132	7	of	of	ADP
ap-1797	132	8	real	real	ADJ
ap-1797	132	9	eigenvalue	eigenvalue	NOUN
ap-1797	132	10	solutions	solution	NOUN
ap-1797	132	11	for	for	ADP
ap-1797	132	12	nonvanishing	nonvanishe	VERB
ap-1797	132	13	values	value	NOUN
ap-1797	132	14	of	of	ADP
ap-1797	132	15	the	the	DET
ap-1797	132	16	gain	gain	NOUN
ap-1797	132	17	-	-	PUNCT
ap-1797	132	18	loss	loss	NOUN
ap-1797	132	19	parameter	parameter	NOUN
ap-1797	132	20	γ	γ	NOUN
ap-1797	132	21	in	in	ADP
ap-1797	132	22	the	the	DET
ap-1797	132	23	case	case	NOUN
ap-1797	132	24	g	g	ADP
ap-1797	132	25	6=	6=	PROPN
ap-1797	132	26	0	0	NUM
ap-1797	132	27	.	.	PUNCT
ap-1797	133	1	this	this	PRON
ap-1797	133	2	demonstrates	demonstrate	VERB
ap-1797	133	3	that	that	SCONJ
ap-1797	133	4	the	the	DET
ap-1797	133	5	gross	gross	ADJ
ap-1797	133	6	-	-	PUNCT
ap-1797	133	7	pitaevskii	pitaevskii	ADJ
ap-1797	133	8	equation	equation	NOUN
ap-1797	133	9	with	with	ADP
ap-1797	133	10	a	a	DET
ap-1797	133	11	nonlinearity	nonlinearity	NOUN
ap-1797	133	12	in	in	ADP
ap-1797	133	13	the	the	DET
ap-1797	133	14	potential	potential	NOUN
ap-1797	133	15	still	still	ADV
ap-1797	133	16	supports	support	VERB
ap-1797	133	17	real	real	ADJ
ap-1797	133	18	eigenvalue	eigenvalue	NOUN
ap-1797	133	19	solutions	solution	NOUN
ap-1797	133	20	,	,	PUNCT
ap-1797	133	21	i.e.	i.e.	X
ap-1797	133	22	non	non	ADJ
ap-1797	133	23	-	-	ADJ
ap-1797	133	24	decaying	decaying	ADJ
ap-1797	133	25	states	state	NOUN
ap-1797	133	26	.	.	PUNCT
ap-1797	134	1	there	there	PRON
ap-1797	134	2	are	be	VERB
ap-1797	134	3	,	,	PUNCT
ap-1797	134	4	however	however	ADV
ap-1797	134	5	,	,	PUNCT
ap-1797	134	6	a	a	DET
ap-1797	134	7	few	few	ADJ
ap-1797	134	8	crucial	crucial	ADJ
ap-1797	134	9	differences	difference	NOUN
ap-1797	134	10	between	between	ADP
ap-1797	134	11	the	the	DET
ap-1797	134	12	linear	linear	NOUN
ap-1797	134	13	and	and	CCONJ
ap-1797	134	14	the	the	DET
ap-1797	134	15	nonlinear	nonlinear	ADJ
ap-1797	134	16	system	system	NOUN
ap-1797	134	17	.	.	PUNCT
ap-1797	135	1	the	the	DET
ap-1797	135	2	complex	complex	ADJ
ap-1797	135	3	eigenvalue	eigenvalue	ADJ
ap-1797	135	4	solutions	solution	NOUN
ap-1797	135	5	are	be	AUX
ap-1797	135	6	now	now	ADV
ap-1797	135	7	born	bear	VERB
ap-1797	135	8	at	at	ADP
ap-1797	135	9	a	a	DET
ap-1797	135	10	value	value	NOUN
ap-1797	135	11	γc	γc	X
ap-1797	135	12	<	<	X
ap-1797	135	13	γep	γep	NOUN
ap-1797	135	14	,	,	PUNCT
ap-1797	135	15	whereas	whereas	SCONJ
ap-1797	135	16	at	at	ADP
ap-1797	135	17	the	the	DET
ap-1797	135	18	exceptional	exceptional	ADJ
ap-1797	135	19	point	point	NOUN
ap-1797	135	20	γep	γep	VERB
ap-1797	135	21	only	only	ADV
ap-1797	135	22	the	the	DET
ap-1797	135	23	real	real	ADJ
ap-1797	135	24	eigenvalue	eigenvalue	PROPN
ap-1797	135	25	states	state	NOUN
ap-1797	135	26	vanish	vanish	VERB
ap-1797	135	27	and	and	CCONJ
ap-1797	135	28	new	new	ADJ
ap-1797	135	29	complex	complex	ADJ
ap-1797	135	30	solutions	solution	NOUN
ap-1797	135	31	do	do	AUX
ap-1797	135	32	not	not	PART
ap-1797	135	33	appear	appear	VERB
ap-1797	135	34	.	.	PUNCT
ap-1797	136	1	the	the	DET
ap-1797	136	2	bifurcation	bifurcation	NOUN
ap-1797	136	3	scenario	scenario	NOUN
ap-1797	136	4	of	of	ADP
ap-1797	136	5	the	the	DET
ap-1797	136	6	linear	linear	ADJ
ap-1797	136	7	system	system	NOUN
ap-1797	136	8	seems	seem	VERB
ap-1797	136	9	to	to	PART
ap-1797	136	10	be	be	AUX
ap-1797	136	11	split	split	VERB
ap-1797	136	12	between	between	ADP
ap-1797	136	13	the	the	DET
ap-1797	136	14	emergence	emergence	NOUN
ap-1797	136	15	of	of	ADP
ap-1797	136	16	complex	complex	ADJ
ap-1797	136	17	eigenvalue	eigenvalue	ADJ
ap-1797	136	18	solutions	solution	NOUN
ap-1797	136	19	at	at	ADP
ap-1797	136	20	γc	γc	PROPN
ap-1797	136	21	and	and	CCONJ
ap-1797	136	22	the	the	DET
ap-1797	136	23	disappearance	disappearance	NOUN
ap-1797	136	24	of	of	ADP
ap-1797	136	25	the	the	DET
ap-1797	136	26	real	real	ADJ
ap-1797	136	27	eigenvalue	eigenvalue	NOUN
ap-1797	136	28	states	state	NOUN
ap-1797	136	29	at	at	ADP
ap-1797	136	30	γep	γep	PRON
ap-1797	136	31	6=	6=	SYM
ap-1797	136	32	γc	γc	PROPN
ap-1797	136	33	.	.	PUNCT
ap-1797	137	1	it	it	PRON
ap-1797	137	2	is	be	AUX
ap-1797	137	3	possible	possible	ADJ
ap-1797	137	4	to	to	PART
ap-1797	137	5	explain	explain	VERB
ap-1797	137	6	this	this	DET
ap-1797	137	7	unusual	unusual	ADJ
ap-1797	137	8	characteristics	characteristic	NOUN
ap-1797	137	9	by	by	ADP
ap-1797	137	10	the	the	DET
ap-1797	137	11	non	non	NOUN
ap-1797	137	12	-	-	NOUN
ap-1797	137	13	analyticity	analyticity	NOUN
ap-1797	137	14	of	of	ADP
ap-1797	137	15	the	the	DET
ap-1797	137	16	grosspitaevskii	grosspitaevskii	ADJ
ap-1797	137	17	equation	equation	NOUN
ap-1797	137	18	[	[	X
ap-1797	137	19	28	28	NUM
ap-1797	137	20	]	]	PUNCT
ap-1797	137	21	.	.	PUNCT
ap-1797	138	1	for	for	ADP
ap-1797	138	2	sufficiently	sufficiently	ADV
ap-1797	138	3	high	high	ADJ
ap-1797	138	4	values	value	NOUN
ap-1797	138	5	of	of	ADP
ap-1797	138	6	g	g	NOUN
ap-1797	138	7	the	the	DET
ap-1797	138	8	complex	complex	ADJ
ap-1797	138	9	eigenvalues	eigenvalue	NOUN
ap-1797	138	10	exist	exist	VERB
ap-1797	138	11	down	down	ADP
ap-1797	138	12	to	to	ADP
ap-1797	138	13	γ→	γ→	PROPN
ap-1797	138	14	0	0	NUM
ap-1797	138	15	and	and	CCONJ
ap-1797	138	16	only	only	ADV
ap-1797	138	17	lose	lose	VERB
ap-1797	138	18	their	their	PRON
ap-1797	138	19	imaginary	imaginary	ADJ
ap-1797	138	20	contribution	contribution	NOUN
ap-1797	138	21	for	for	ADP
ap-1797	138	22	γ	γ	X
ap-1797	138	23	=	=	SYM
ap-1797	138	24	0	0	NUM
ap-1797	138	25	.	.	PUNCT
ap-1797	139	1	the	the	DET
ap-1797	139	2	one	one	NUM
ap-1797	139	3	-	-	PUNCT
ap-1797	139	4	dimensional	dimensional	ADJ
ap-1797	139	5	model	model	NOUN
ap-1797	139	6	already	already	ADV
ap-1797	139	7	contains	contain	VERB
ap-1797	139	8	the	the	DET
ap-1797	139	9	whole	whole	ADJ
ap-1797	139	10	important	important	ADJ
ap-1797	139	11	potential	potential	ADJ
ap-1797	139	12	shape	shape	NOUN
ap-1797	139	13	for	for	ADP
ap-1797	139	14	the	the	DET
ap-1797	139	15	analysis	analysis	NOUN
ap-1797	139	16	of	of	ADP
ap-1797	139	17	a	a	DET
ap-1797	139	18	pt	pt	NOUN
ap-1797	139	19	symmetric	symmetric	ADJ
ap-1797	139	20	condensate	condensate	NOUN
ap-1797	139	21	.	.	PUNCT
ap-1797	140	1	thus	thus	ADV
ap-1797	140	2	,	,	PUNCT
ap-1797	140	3	one	one	PRON
ap-1797	140	4	can	can	AUX
ap-1797	140	5	expect	expect	VERB
ap-1797	140	6	that	that	SCONJ
ap-1797	140	7	it	it	PRON
ap-1797	140	8	includes	include	VERB
ap-1797	140	9	all	all	DET
ap-1797	140	10	important	important	ADJ
ap-1797	140	11	features	feature	NOUN
ap-1797	140	12	in	in	ADP
ap-1797	140	13	the	the	DET
ap-1797	140	14	eigenvalue	eigenvalue	NOUN
ap-1797	140	15	structure	structure	NOUN
ap-1797	140	16	.	.	PUNCT
ap-1797	141	1	this	this	PRON
ap-1797	141	2	is	be	AUX
ap-1797	141	3	confirmed	confirm	VERB
ap-1797	141	4	by	by	ADP
ap-1797	141	5	the	the	DET
ap-1797	141	6	comparison	comparison	NOUN
ap-1797	141	7	4.34	4.34	NUM
ap-1797	141	8	4.36	4.36	NUM
ap-1797	141	9	4.38	4.38	NUM
ap-1797	141	10	4.40	4.40	NUM
ap-1797	141	11	4.42	4.42	NUM
ap-1797	141	12	4.44	4.44	NUM
ap-1797	141	13	4.46	4.46	NUM
ap-1797	141	14	4.48	4.48	NUM
ap-1797	141	15	4.50	4.50	NUM
ap-1797	141	16	4.52	4.52	NUM
ap-1797	141	17	0	0	NUM
ap-1797	141	18	0.01	0.01	NUM
ap-1797	141	19	0.02	0.02	NUM
ap-1797	141	20	0.03	0.03	NUM
ap-1797	141	21	0.04	0.04	NUM
ap-1797	141	22	0.05	0.05	NUM
ap-1797	141	23	0.06	0.06	NUM
ap-1797	141	24	0.07	0.07	NUM
ap-1797	141	25	0.08	0.08	NUM
ap-1797	141	26	r	r	NOUN
ap-1797	141	27	e	e	X
ap-1797	141	28	µ	µ	X
ap-1797	141	29	γ	γ	X
ap-1797	141	30	(	(	PUNCT
ap-1797	141	31	a	a	PROPN
ap-1797	141	32	)	)	PUNCT
ap-1797	141	33	−0.08	−0.08	PROPN
ap-1797	142	1	−0.06	−0.06	ADP
ap-1797	142	2	−0.04	−0.04	PROPN
ap-1797	142	3	−0.02	−0.02	NOUN
ap-1797	142	4	0.00	0.00	NUM
ap-1797	142	5	0.02	0.02	NUM
ap-1797	142	6	0.04	0.04	NUM
ap-1797	142	7	0.06	0.06	NUM
ap-1797	142	8	0.08	0.08	NUM
ap-1797	142	9	0	0	NUM
ap-1797	142	10	0.01	0.01	NUM
ap-1797	142	11	0.02	0.02	NUM
ap-1797	142	12	0.03	0.03	NUM
ap-1797	142	13	0.04	0.04	NUM
ap-1797	142	14	0.05	0.05	NUM
ap-1797	142	15	0.06	0.06	NUM
ap-1797	142	16	0.07	0.07	NUM
ap-1797	142	17	0.08	0.08	NUM
ap-1797	142	18	i	i	PRON
ap-1797	142	19	m	m	VERB
ap-1797	142	20	µ	µ	VERB
ap-1797	142	21	γ	γ	X
ap-1797	142	22	(	(	PUNCT
ap-1797	142	23	b	b	NOUN
ap-1797	142	24	)	)	PUNCT
ap-1797	142	25	g3d	g3d	PROPN
ap-1797	143	1	=	=	PUNCT
ap-1797	143	2	0	0	PUNCT
ap-1797	144	1	g3d	g3d	PROPN
ap-1797	144	2	=	=	PUNCT
ap-1797	144	3	0.2π	0.2π	PROPN
ap-1797	144	4	g3d	g3d	PROPN
ap-1797	144	5	=	=	PUNCT
ap-1797	144	6	0.4π	0.4π	NUM
ap-1797	144	7	g3d	g3d	PROPN
ap-1797	144	8	=	=	SYM
ap-1797	144	9	0.6π	0.6π	NUM
ap-1797	144	10	figure	figure	NOUN
ap-1797	144	11	3	3	NUM
ap-1797	144	12	.	.	PUNCT
ap-1797	145	1	real	real	ADJ
ap-1797	145	2	(	(	PUNCT
ap-1797	145	3	a	a	NOUN
ap-1797	145	4	)	)	PUNCT
ap-1797	145	5	and	and	CCONJ
ap-1797	145	6	nonvanishing	nonvanishe	VERB
ap-1797	145	7	imaginary	imaginary	ADJ
ap-1797	145	8	(	(	PUNCT
ap-1797	145	9	b	b	NOUN
ap-1797	145	10	)	)	PUNCT
ap-1797	145	11	parts	part	NOUN
ap-1797	145	12	of	of	ADP
ap-1797	145	13	the	the	DET
ap-1797	145	14	energy	energy	NOUN
ap-1797	145	15	eigenvalues	eigenvalue	NOUN
ap-1797	145	16	of	of	ADP
ap-1797	145	17	the	the	DET
ap-1797	145	18	time	time	NOUN
ap-1797	145	19	-	-	PUNCT
ap-1797	145	20	independent	independent	ADJ
ap-1797	145	21	gross	gross	ADJ
ap-1797	145	22	-	-	PUNCT
ap-1797	145	23	pitaevskii	pitaevskii	ADJ
ap-1797	145	24	equation	equation	NOUN
ap-1797	145	25	in	in	ADP
ap-1797	145	26	the	the	DET
ap-1797	145	27	one(dashed	one(dashe	VERB
ap-1797	145	28	lines	line	NOUN
ap-1797	145	29	)	)	PUNCT
ap-1797	145	30	and	and	CCONJ
ap-1797	145	31	three	three	NUM
ap-1797	145	32	-	-	PUNCT
ap-1797	145	33	dimensional	dimensional	ADJ
ap-1797	145	34	(	(	PUNCT
ap-1797	145	35	solid	solid	ADJ
ap-1797	145	36	lines	line	NOUN
ap-1797	145	37	)	)	PUNCT
ap-1797	145	38	models	model	NOUN
ap-1797	145	39	.	.	PUNCT
ap-1797	146	1	the	the	DET
ap-1797	146	2	comparison	comparison	NOUN
ap-1797	146	3	shows	show	VERB
ap-1797	146	4	that	that	SCONJ
ap-1797	146	5	,	,	PUNCT
ap-1797	146	6	by	by	ADP
ap-1797	146	7	applying	apply	VERB
ap-1797	146	8	an	an	DET
ap-1797	146	9	appropriate	appropriate	ADJ
ap-1797	146	10	rescaling	rescaling	NOUN
ap-1797	146	11	of	of	ADP
ap-1797	146	12	the	the	DET
ap-1797	146	13	nonlinearity	nonlinearity	NOUN
ap-1797	146	14	parameter	parameter	NOUN
ap-1797	146	15	g	g	PROPN
ap-1797	146	16	and	and	CCONJ
ap-1797	146	17	an	an	DET
ap-1797	146	18	energy	energy	NOUN
ap-1797	146	19	shift	shift	NOUN
ap-1797	146	20	for	for	ADP
ap-1797	146	21	the	the	DET
ap-1797	146	22	energy	energy	NOUN
ap-1797	146	23	contributions	contribution	NOUN
ap-1797	146	24	from	from	ADP
ap-1797	146	25	the	the	DET
ap-1797	146	26	two	two	NUM
ap-1797	146	27	additional	additional	ADJ
ap-1797	146	28	directions	direction	NOUN
ap-1797	146	29	,	,	PUNCT
ap-1797	146	30	the	the	DET
ap-1797	146	31	one	one	NUM
ap-1797	146	32	-	-	PUNCT
ap-1797	146	33	dimensional	dimensional	ADJ
ap-1797	146	34	model	model	NOUN
ap-1797	146	35	already	already	ADV
ap-1797	146	36	provides	provide	VERB
ap-1797	146	37	a	a	DET
ap-1797	146	38	very	very	ADV
ap-1797	146	39	good	good	ADJ
ap-1797	146	40	quantitative	quantitative	ADJ
ap-1797	146	41	description	description	NOUN
ap-1797	146	42	of	of	ADP
ap-1797	146	43	the	the	DET
ap-1797	146	44	fully	fully	ADV
ap-1797	146	45	three	three	NUM
ap-1797	146	46	-	-	PUNCT
ap-1797	146	47	dimensional	dimensional	ADJ
ap-1797	146	48	setup	setup	NOUN
ap-1797	146	49	.	.	PUNCT
ap-1797	147	1	it	it	PRON
ap-1797	147	2	is	be	AUX
ap-1797	147	3	almost	almost	ADV
ap-1797	147	4	impossible	impossible	ADJ
ap-1797	147	5	to	to	PART
ap-1797	147	6	identify	identify	VERB
ap-1797	147	7	the	the	DET
ap-1797	147	8	differences	difference	NOUN
ap-1797	147	9	in	in	ADP
ap-1797	147	10	the	the	DET
ap-1797	147	11	graph	graph	NOUN
ap-1797	147	12	.	.	PUNCT
ap-1797	148	1	of	of	ADP
ap-1797	148	2	the	the	DET
ap-1797	148	3	eigenvalues	eigenvalue	NOUN
ap-1797	148	4	obtained	obtain	VERB
ap-1797	148	5	with	with	ADP
ap-1797	148	6	the	the	DET
ap-1797	148	7	one(dashed	one(dashed	NUM
ap-1797	148	8	)	)	PUNCT
ap-1797	148	9	and	and	CCONJ
ap-1797	148	10	three	three	NUM
ap-1797	148	11	-	-	PUNCT
ap-1797	148	12	dimensional	dimensional	ADJ
ap-1797	148	13	(	(	PUNCT
ap-1797	148	14	solid	solid	ADJ
ap-1797	148	15	)	)	PUNCT
ap-1797	148	16	potentials	potential	NOUN
ap-1797	148	17	in	in	ADP
ap-1797	148	18	figure	figure	NOUN
ap-1797	148	19	3	3	NUM
ap-1797	148	20	.	.	PUNCT
ap-1797	149	1	the	the	DET
ap-1797	149	2	three	three	NUM
ap-1797	149	3	-	-	PUNCT
ap-1797	149	4	dimensional	dimensional	ADJ
ap-1797	149	5	setup	setup	NOUN
ap-1797	149	6	contains	contain	VERB
ap-1797	149	7	two	two	NUM
ap-1797	149	8	additional	additional	ADJ
ap-1797	149	9	directions	direction	NOUN
ap-1797	149	10	in	in	ADP
ap-1797	149	11	which	which	PRON
ap-1797	149	12	an	an	DET
ap-1797	149	13	external	external	ADJ
ap-1797	149	14	harmonic	harmonic	ADJ
ap-1797	149	15	oscillator	oscillator	NOUN
ap-1797	149	16	potential	potential	NOUN
ap-1797	149	17	is	be	AUX
ap-1797	149	18	present	present	ADJ
ap-1797	149	19	.	.	PUNCT
ap-1797	150	1	this	this	PRON
ap-1797	150	2	leads	lead	VERB
ap-1797	150	3	to	to	ADP
ap-1797	150	4	the	the	DET
ap-1797	150	5	assumption	assumption	NOUN
ap-1797	150	6	that	that	SCONJ
ap-1797	150	7	,	,	PUNCT
ap-1797	150	8	in	in	ADP
ap-1797	150	9	the	the	DET
ap-1797	150	10	ground	ground	NOUN
ap-1797	150	11	state	state	NOUN
ap-1797	150	12	,	,	PUNCT
ap-1797	150	13	the	the	DET
ap-1797	150	14	energy	energy	NOUN
ap-1797	150	15	is	be	AUX
ap-1797	150	16	shifted	shift	VERB
ap-1797	150	17	by	by	ADP
ap-1797	150	18	a	a	DET
ap-1797	150	19	value	value	NOUN
ap-1797	150	20	of	of	ADP
ap-1797	150	21	∆µ	∆µ	PROPN
ap-1797	150	22	=	=	SYM
ap-1797	150	23	2	2	NUM
ap-1797	150	24	in	in	ADP
ap-1797	150	25	the	the	DET
ap-1797	150	26	units	unit	NOUN
ap-1797	150	27	introduced	introduce	VERB
ap-1797	150	28	above	above	ADV
ap-1797	150	29	.	.	PUNCT
ap-1797	151	1	furthermore	furthermore	ADV
ap-1797	151	2	,	,	PUNCT
ap-1797	151	3	the	the	DET
ap-1797	151	4	spatial	spatial	ADJ
ap-1797	151	5	extension	extension	NOUN
ap-1797	151	6	in	in	ADP
ap-1797	151	7	y	y	PROPN
ap-1797	151	8	and	and	CCONJ
ap-1797	151	9	z	z	PROPN
ap-1797	151	10	directions	direction	NOUN
ap-1797	151	11	leads	lead	VERB
ap-1797	151	12	to	to	ADP
ap-1797	151	13	additional	additional	ADJ
ap-1797	151	14	energy	energy	NOUN
ap-1797	151	15	contributions	contribution	NOUN
ap-1797	151	16	from	from	ADP
ap-1797	151	17	the	the	DET
ap-1797	151	18	contact	contact	NOUN
ap-1797	151	19	interaction	interaction	NOUN
ap-1797	151	20	.	.	PUNCT
ap-1797	152	1	the	the	DET
ap-1797	152	2	difference	difference	NOUN
ap-1797	152	3	can	can	AUX
ap-1797	152	4	be	be	AUX
ap-1797	152	5	estimated	estimate	VERB
ap-1797	152	6	from	from	ADP
ap-1797	152	7	the	the	DET
ap-1797	152	8	expectation	expectation	NOUN
ap-1797	152	9	value	value	NOUN
ap-1797	152	10	of	of	ADP
ap-1797	152	11	the	the	DET
ap-1797	152	12	contact	contact	NOUN
ap-1797	152	13	energy	energy	NOUN
ap-1797	152	14	.	.	PUNCT
ap-1797	153	1	we	we	PRON
ap-1797	153	2	demand	demand	VERB
ap-1797	153	3	that	that	SCONJ
ap-1797	153	4	the	the	DET
ap-1797	153	5	expectation	expectation	NOUN
ap-1797	153	6	values	value	NOUN
ap-1797	153	7	of	of	ADP
ap-1797	153	8	both	both	DET
ap-1797	153	9	models	model	NOUN
ap-1797	153	10	are	be	AUX
ap-1797	153	11	identical,∫	identical,∫	ADJ
ap-1797	153	12	r3	r3	PROPN
ap-1797	153	13	dxdy	dxdy	PROPN
ap-1797	153	14	dz	dz	PROPN
ap-1797	153	15	g3d|ψ3d(x)|4	g3d|ψ3d(x)|4	PROPN
ap-1797	153	16	!	!	PUNCT
ap-1797	154	1	=	=	PUNCT
ap-1797	155	1	∫	∫	PROPN
ap-1797	155	2	r	r	NOUN
ap-1797	155	3	dx	dx	PROPN
ap-1797	155	4	g1d|ψ1d(x)|4	g1d|ψ1d(x)|4	PROPN
ap-1797	155	5	(	(	PUNCT
ap-1797	155	6	12	12	NUM
ap-1797	155	7	)	)	PUNCT
ap-1797	155	8	and	and	CCONJ
ap-1797	155	9	obtain	obtain	VERB
ap-1797	155	10	the	the	DET
ap-1797	155	11	condition	condition	NOUN
ap-1797	155	12	g3d	g3d	PROPN
ap-1797	156	1	=	=	PUNCT
ap-1797	157	1	2πg1d	2πg1d	NUM
ap-1797	157	2	(	(	PUNCT
ap-1797	157	3	13	13	NUM
ap-1797	157	4	)	)	PUNCT
ap-1797	157	5	for	for	ADP
ap-1797	157	6	a	a	DET
ap-1797	157	7	rescaled	rescaled	ADJ
ap-1797	157	8	g1d	g1d	NOUN
ap-1797	157	9	of	of	ADP
ap-1797	157	10	the	the	DET
ap-1797	157	11	one	one	NUM
ap-1797	157	12	-	-	PUNCT
ap-1797	157	13	dimensional	dimensional	ADJ
ap-1797	157	14	model	model	NOUN
ap-1797	157	15	which	which	PRON
ap-1797	157	16	leads	lead	VERB
ap-1797	157	17	to	to	ADP
ap-1797	157	18	the	the	DET
ap-1797	157	19	same	same	ADJ
ap-1797	157	20	contact	contact	NOUN
ap-1797	157	21	energy	energy	NOUN
ap-1797	157	22	as	as	ADP
ap-1797	157	23	a	a	DET
ap-1797	157	24	threedimensional	threedimensional	ADJ
ap-1797	157	25	wave	wave	NOUN
ap-1797	157	26	function	function	NOUN
ap-1797	157	27	with	with	ADP
ap-1797	157	28	g3d	g3d	PROPN
ap-1797	157	29	.	.	PUNCT
ap-1797	158	1	in	in	ADP
ap-1797	158	2	this	this	DET
ap-1797	158	3	calculation	calculation	NOUN
ap-1797	158	4	we	we	PRON
ap-1797	158	5	used	use	VERB
ap-1797	158	6	a	a	DET
ap-1797	158	7	product	product	NOUN
ap-1797	158	8	ansatz	ansatz	ADJ
ap-1797	158	9	ψ3d(x	ψ3d(x	PROPN
ap-1797	158	10	)	)	PUNCT
ap-1797	159	1	≈	≈	PROPN
ap-1797	159	2	ψ1d(x)ψ0(y)ψ0(z	ψ1d(x)ψ0(y)ψ0(z	NOUN
ap-1797	159	3	)	)	PUNCT
ap-1797	159	4	of	of	ADP
ap-1797	159	5	the	the	DET
ap-1797	159	6	wave	wave	NOUN
ap-1797	159	7	function	function	NOUN
ap-1797	159	8	,	,	PUNCT
ap-1797	159	9	where	where	SCONJ
ap-1797	159	10	ψ0	ψ0	PROPN
ap-1797	159	11	describes	describe	VERB
ap-1797	159	12	the	the	DET
ap-1797	159	13	harmonic	harmonic	ADJ
ap-1797	159	14	oscillator	oscillator	NOUN
ap-1797	159	15	ground	ground	NOUN
ap-1797	159	16	state	state	NOUN
ap-1797	159	17	[	[	X
ap-1797	159	18	28	28	NUM
ap-1797	159	19	]	]	PUNCT
ap-1797	159	20	.	.	PUNCT
ap-1797	160	1	this	this	DET
ap-1797	160	2	assumption	assumption	NOUN
ap-1797	160	3	is	be	AUX
ap-1797	160	4	only	only	ADV
ap-1797	160	5	correct	correct	ADJ
ap-1797	160	6	in	in	ADP
ap-1797	160	7	the	the	DET
ap-1797	160	8	linear	linear	ADJ
ap-1797	160	9	case	case	NOUN
ap-1797	160	10	without	without	ADP
ap-1797	160	11	262	262	NUM
ap-1797	160	12	vol	vol	NOUN
ap-1797	160	13	.	.	PUNCT
ap-1797	161	1	53	53	NUM
ap-1797	161	2	no	no	NOUN
ap-1797	161	3	.	.	PUNCT
ap-1797	162	1	3/2013	3/2013	PROPN
ap-1797	162	2	stationary	stationary	ADJ
ap-1797	162	3	and	and	CCONJ
ap-1797	162	4	dynamical	dynamical	ADJ
ap-1797	162	5	solutions	solution	NOUN
ap-1797	162	6	of	of	ADP
ap-1797	162	7	the	the	DET
ap-1797	162	8	gross	gross	ADJ
ap-1797	162	9	-	-	PUNCT
ap-1797	162	10	pitaevskii	pitaevskii	ADJ
ap-1797	162	11	equation	equation	NOUN
ap-1797	162	12	−0.3	−0.3	PROPN
ap-1797	163	1	−0.2	−0.2	PROPN
ap-1797	164	1	−0.1	−0.1	NOUN
ap-1797	164	2	0	0	NUM
ap-1797	164	3	0.1	0.1	NUM
ap-1797	164	4	0.2	0.2	NUM
ap-1797	164	5	0.3	0.3	NUM
ap-1797	164	6	0.4	0.4	NUM
ap-1797	164	7	0.5	0.5	NUM
ap-1797	164	8	−6	−6	NOUN
ap-1797	164	9	−4	−4	PROPN
ap-1797	164	10	−2	−2	NOUN
ap-1797	164	11	0	0	NUM
ap-1797	164	12	2	2	NUM
ap-1797	164	13	4	4	NUM
ap-1797	164	14	6	6	NUM
ap-1797	164	15	φ	φ	NUM
ap-1797	164	16	x	x	SYM
ap-1797	164	17	(	(	PUNCT
ap-1797	164	18	a	a	X
ap-1797	164	19	)	)	PUNCT
ap-1797	164	20	−0.5	−0.5	NUM
ap-1797	164	21	−0.4	−0.4	NUM
ap-1797	165	1	−0.3	−0.3	NOUN
ap-1797	165	2	−0.2	−0.2	PROPN
ap-1797	166	1	−0.1	−0.1	NOUN
ap-1797	166	2	0	0	NUM
ap-1797	166	3	0.1	0.1	NUM
ap-1797	166	4	0.2	0.2	NUM
ap-1797	166	5	0.3	0.3	NUM
ap-1797	166	6	0.4	0.4	NUM
ap-1797	166	7	0.5	0.5	NUM
ap-1797	166	8	−6	−6	NOUN
ap-1797	166	9	−4	−4	PROPN
ap-1797	166	10	−2	−2	NOUN
ap-1797	166	11	0	0	NUM
ap-1797	166	12	2	2	NUM
ap-1797	166	13	4	4	NUM
ap-1797	166	14	6	6	NUM
ap-1797	166	15	φ	φ	NUM
ap-1797	166	16	x	x	SYM
ap-1797	166	17	(	(	PUNCT
ap-1797	166	18	b	b	NOUN
ap-1797	166	19	)	)	PUNCT
ap-1797	166	20	reφ	reφ	NOUN
ap-1797	166	21	imφ	imφ	PROPN
ap-1797	166	22	|φ|2	|φ|2	PROPN
ap-1797	166	23	figure	figure	NOUN
ap-1797	166	24	4	4	NUM
ap-1797	166	25	.	.	NOUN
ap-1797	166	26	wave	wave	NOUN
ap-1797	166	27	functions	function	NOUN
ap-1797	166	28	of	of	ADP
ap-1797	166	29	the	the	DET
ap-1797	166	30	ground	ground	NOUN
ap-1797	166	31	(	(	PUNCT
ap-1797	166	32	a	a	X
ap-1797	166	33	)	)	PUNCT
ap-1797	166	34	and	and	CCONJ
ap-1797	166	35	excited	excited	ADJ
ap-1797	166	36	(	(	PUNCT
ap-1797	166	37	b	b	NOUN
ap-1797	166	38	)	)	PUNCT
ap-1797	166	39	eigenstates	eigenstate	NOUN
ap-1797	166	40	with	with	ADP
ap-1797	166	41	real	real	ADJ
ap-1797	166	42	eigenvalues	eigenvalue	NOUN
ap-1797	166	43	in	in	ADP
ap-1797	166	44	the	the	DET
ap-1797	166	45	case	case	NOUN
ap-1797	166	46	g	g	NOUN
ap-1797	166	47	=	=	NOUN
ap-1797	166	48	0.2	0.2	NUM
ap-1797	166	49	and	and	CCONJ
ap-1797	166	50	γ	γ	X
ap-1797	166	51	=	=	SYM
ap-1797	166	52	0.03	0.03	NUM
ap-1797	166	53	.	.	PUNCT
ap-1797	167	1	only	only	ADV
ap-1797	167	2	the	the	DET
ap-1797	167	3	gaussian	gaussian	ADJ
ap-1797	167	4	solutions	solution	NOUN
ap-1797	167	5	are	be	AUX
ap-1797	167	6	shown	show	VERB
ap-1797	167	7	since	since	SCONJ
ap-1797	167	8	they	they	PRON
ap-1797	167	9	are	be	AUX
ap-1797	167	10	almost	almost	ADV
ap-1797	167	11	identical	identical	ADJ
ap-1797	167	12	with	with	ADP
ap-1797	167	13	the	the	DET
ap-1797	167	14	numerically	numerically	ADV
ap-1797	167	15	exact	exact	ADJ
ap-1797	167	16	values	value	NOUN
ap-1797	167	17	.	.	PUNCT
ap-1797	168	1	the	the	DET
ap-1797	168	2	square	square	ADJ
ap-1797	168	3	moduli	modulus	NOUN
ap-1797	168	4	of	of	ADP
ap-1797	168	5	both	both	DET
ap-1797	168	6	wave	wave	NOUN
ap-1797	168	7	functions	function	NOUN
ap-1797	168	8	are	be	AUX
ap-1797	168	9	symmetric	symmetric	ADJ
ap-1797	168	10	functions	function	NOUN
ap-1797	168	11	of	of	ADP
ap-1797	168	12	x	x	PRON
ap-1797	168	13	,	,	PUNCT
ap-1797	168	14	preserving	preserve	VERB
ap-1797	168	15	the	the	DET
ap-1797	168	16	pt	pt	NOUN
ap-1797	168	17	symmetry	symmetry	NOUN
ap-1797	168	18	of	of	ADP
ap-1797	168	19	the	the	DET
ap-1797	168	20	nonlinear	nonlinear	ADJ
ap-1797	168	21	hamiltonian	hamiltonian	NOUN
ap-1797	168	22	.	.	PUNCT
ap-1797	169	1	contact	contact	NOUN
ap-1797	169	2	interaction	interaction	NOUN
ap-1797	169	3	.	.	PUNCT
ap-1797	170	1	the	the	DET
ap-1797	170	2	remarkable	remarkable	ADJ
ap-1797	170	3	agreement	agreement	NOUN
ap-1797	170	4	of	of	ADP
ap-1797	170	5	both	both	DET
ap-1797	170	6	calculations	calculation	NOUN
ap-1797	170	7	in	in	ADP
ap-1797	170	8	figure	figure	NOUN
ap-1797	170	9	3	3	NUM
ap-1797	170	10	shows	show	NOUN
ap-1797	170	11	,	,	PUNCT
ap-1797	170	12	however	however	ADV
ap-1797	170	13	,	,	PUNCT
ap-1797	170	14	that	that	SCONJ
ap-1797	170	15	it	it	PRON
ap-1797	170	16	still	still	ADV
ap-1797	170	17	approximates	approximate	VERB
ap-1797	170	18	the	the	DET
ap-1797	170	19	nonlinear	nonlinear	ADJ
ap-1797	170	20	case	case	NOUN
ap-1797	170	21	very	very	ADV
ap-1797	170	22	well	well	ADV
ap-1797	170	23	even	even	ADV
ap-1797	170	24	for	for	ADP
ap-1797	170	25	considerable	considerable	ADJ
ap-1797	170	26	nonlinearities	nonlinearitie	NOUN
ap-1797	170	27	g1d	g1d	PROPN
ap-1797	170	28	≈	≈	PROPN
ap-1797	170	29	0.3	0.3	NUM
ap-1797	170	30	.	.	PUNCT
ap-1797	171	1	due	due	ADP
ap-1797	171	2	to	to	ADP
ap-1797	171	3	the	the	DET
ap-1797	171	4	excellent	excellent	ADJ
ap-1797	171	5	quantitative	quantitative	ADJ
ap-1797	171	6	agreement	agreement	NOUN
ap-1797	171	7	between	between	ADP
ap-1797	171	8	the	the	DET
ap-1797	171	9	oneand	oneand	ADJ
ap-1797	171	10	three	three	NUM
ap-1797	171	11	-	-	PUNCT
ap-1797	171	12	dimensional	dimensional	ADJ
ap-1797	171	13	calculations	calculation	NOUN
ap-1797	171	14	we	we	PRON
ap-1797	171	15	will	will	AUX
ap-1797	171	16	only	only	ADV
ap-1797	171	17	consider	consider	VERB
ap-1797	171	18	the	the	DET
ap-1797	171	19	one	one	NUM
ap-1797	171	20	-	-	PUNCT
ap-1797	171	21	dimensional	dimensional	ADJ
ap-1797	171	22	variant	variant	NOUN
ap-1797	171	23	in	in	ADP
ap-1797	171	24	the	the	DET
ap-1797	171	25	following	follow	VERB
ap-1797	171	26	sections	section	NOUN
ap-1797	171	27	.	.	PUNCT
ap-1797	172	1	3.2	3.2	NUM
ap-1797	172	2	.	.	PUNCT
ap-1797	172	3	wave	wave	NOUN
ap-1797	172	4	functions	function	NOUN
ap-1797	172	5	we	we	PRON
ap-1797	172	6	have	have	AUX
ap-1797	172	7	already	already	ADV
ap-1797	172	8	seen	see	VERB
ap-1797	172	9	that	that	SCONJ
ap-1797	172	10	real	real	ADJ
ap-1797	172	11	eigenvalue	eigenvalue	NOUN
ap-1797	172	12	solutions	solution	NOUN
ap-1797	172	13	do	do	AUX
ap-1797	172	14	appear	appear	VERB
ap-1797	172	15	in	in	ADP
ap-1797	172	16	the	the	DET
ap-1797	172	17	nonlinear	nonlinear	ADJ
ap-1797	172	18	gross	gross	ADJ
ap-1797	172	19	-	-	PUNCT
ap-1797	172	20	pitaevskii	pitaevskii	ADJ
ap-1797	172	21	equation	equation	NOUN
ap-1797	172	22	.	.	PUNCT
ap-1797	173	1	but	but	CCONJ
ap-1797	173	2	,	,	PUNCT
ap-1797	173	3	we	we	PRON
ap-1797	173	4	still	still	ADV
ap-1797	173	5	do	do	AUX
ap-1797	173	6	not	not	PART
ap-1797	173	7	know	know	VERB
ap-1797	173	8	whether	whether	SCONJ
ap-1797	173	9	we	we	PRON
ap-1797	173	10	have	have	AUX
ap-1797	173	11	found	find	VERB
ap-1797	173	12	truly	truly	ADV
ap-1797	173	13	pt	pt	ADJ
ap-1797	173	14	symmetric	symmetric	ADJ
ap-1797	173	15	solutions	solution	NOUN
ap-1797	173	16	.	.	PUNCT
ap-1797	174	1	as	as	SCONJ
ap-1797	174	2	explained	explain	VERB
ap-1797	174	3	in	in	ADP
ap-1797	174	4	the	the	DET
ap-1797	174	5	introduction	introduction	NOUN
ap-1797	174	6	,	,	PUNCT
ap-1797	174	7	the	the	DET
ap-1797	174	8	hamiltonian	hamiltonian	NOUN
ap-1797	174	9	is	be	AUX
ap-1797	174	10	only	only	ADV
ap-1797	174	11	pt	pt	X
ap-1797	174	12	symmetric	symmetric	NOUN
ap-1797	174	13	if	if	SCONJ
ap-1797	174	14	the	the	DET
ap-1797	174	15	square	square	ADJ
ap-1797	174	16	modulus	modulus	NOUN
ap-1797	174	17	of	of	ADP
ap-1797	174	18	the	the	DET
ap-1797	174	19	eigenstate	eigenstate	NOUN
ap-1797	174	20	is	be	AUX
ap-1797	174	21	a	a	DET
ap-1797	174	22	symmetric	symmetric	ADJ
ap-1797	174	23	function	function	NOUN
ap-1797	174	24	of	of	ADP
ap-1797	174	25	x.	x.	NOUN
ap-1797	174	26	this	this	DET
ap-1797	174	27	question	question	NOUN
ap-1797	174	28	will	will	AUX
ap-1797	174	29	be	be	AUX
ap-1797	174	30	answered	answer	VERB
ap-1797	174	31	in	in	ADP
ap-1797	174	32	this	this	DET
ap-1797	174	33	section	section	NOUN
ap-1797	174	34	.	.	PUNCT
ap-1797	175	1	figure	figure	NOUN
ap-1797	175	2	4	4	NUM
ap-1797	175	3	shows	show	VERB
ap-1797	175	4	the	the	DET
ap-1797	175	5	wave	wave	NOUN
ap-1797	175	6	functions	function	NOUN
ap-1797	175	7	belonging	belong	VERB
ap-1797	175	8	to	to	ADP
ap-1797	175	9	the	the	DET
ap-1797	175	10	real	real	ADJ
ap-1797	175	11	eigenvalues	eigenvalue	NOUN
ap-1797	175	12	for	for	ADP
ap-1797	175	13	g	g	NOUN
ap-1797	175	14	=	=	SYM
ap-1797	175	15	0.2	0.2	NUM
ap-1797	175	16	and	and	CCONJ
ap-1797	175	17	γ	γ	X
ap-1797	175	18	=	=	SYM
ap-1797	175	19	0.03	0.03	NUM
ap-1797	175	20	.	.	PUNCT
ap-1797	176	1	obviously	obviously	ADV
ap-1797	176	2	,	,	PUNCT
ap-1797	176	3	the	the	DET
ap-1797	176	4	square	square	ADJ
ap-1797	176	5	modulus	modulus	NOUN
ap-1797	176	6	of	of	ADP
ap-1797	176	7	both	both	DET
ap-1797	176	8	wave	wave	NOUN
ap-1797	176	9	functions	function	NOUN
ap-1797	176	10	is	be	AUX
ap-1797	176	11	a	a	DET
ap-1797	176	12	symmetric	symmetric	ADJ
ap-1797	176	13	function	function	NOUN
ap-1797	176	14	of	of	ADP
ap-1797	176	15	x.	x.	NOUN
ap-1797	176	16	this	this	PRON
ap-1797	176	17	preserves	preserve	VERB
ap-1797	176	18	the	the	DET
ap-1797	176	19	hamiltonian	hamiltonian	NOUN
ap-1797	176	20	’s	’s	PART
ap-1797	176	21	pt	pt	PROPN
ap-1797	176	22	symmetry	symmetry	NOUN
ap-1797	176	23	,	,	PUNCT
ap-1797	176	24	it	it	PRON
ap-1797	176	25	is	be	AUX
ap-1797	176	26	not	not	PART
ap-1797	176	27	destroyed	destroy	VERB
ap-1797	176	28	by	by	ADP
ap-1797	176	29	the	the	DET
ap-1797	176	30	nonlinearity	nonlinearity	NOUN
ap-1797	176	31	.	.	PUNCT
ap-1797	177	1	or	or	CCONJ
ap-1797	177	2	in	in	ADP
ap-1797	177	3	other	other	ADJ
ap-1797	177	4	words	word	NOUN
ap-1797	177	5	,	,	PUNCT
ap-1797	177	6	the	the	DET
ap-1797	177	7	nonlinear	nonlinear	ADJ
ap-1797	177	8	hamiltonian	hamiltonian	NOUN
ap-1797	177	9	picks	pick	VERB
ap-1797	177	10	as	as	ADP
ap-1797	177	11	eigenstates	eigenstate	NOUN
ap-1797	177	12	wave	wave	NOUN
ap-1797	177	13	functions	function	NOUN
ap-1797	177	14	which	which	PRON
ap-1797	177	15	render	render	VERB
ap-1797	177	16	itself	itself	PRON
ap-1797	177	17	pt	pt	X
ap-1797	177	18	symmetric	symmetric	NOUN
ap-1797	177	19	.	.	PUNCT
ap-1797	178	1	the	the	DET
ap-1797	178	2	situation	situation	NOUN
ap-1797	178	3	is	be	AUX
ap-1797	178	4	,	,	PUNCT
ap-1797	178	5	however	however	ADV
ap-1797	178	6	,	,	PUNCT
ap-1797	178	7	completely	completely	ADV
ap-1797	178	8	different	different	ADJ
ap-1797	178	9	for	for	ADP
ap-1797	178	10	the	the	DET
ap-1797	178	11	wave	wave	NOUN
ap-1797	178	12	functions	function	NOUN
ap-1797	178	13	of	of	ADP
ap-1797	178	14	the	the	DET
ap-1797	178	15	states	state	NOUN
ap-1797	178	16	with	with	ADP
ap-1797	178	17	complex	complex	ADJ
ap-1797	178	18	eigenvalues	eigenvalue	NOUN
ap-1797	178	19	.	.	PUNCT
ap-1797	179	1	in	in	ADP
ap-1797	179	2	linear	linear	PROPN
ap-1797	179	3	pt	pt	INTJ
ap-1797	179	4	symmetric	symmetric	ADJ
ap-1797	179	5	models	model	NOUN
ap-1797	179	6	the	the	DET
ap-1797	179	7	complex	complex	ADJ
ap-1797	179	8	eigenvalue	eigenvalue	ADJ
ap-1797	179	9	solutions	solution	NOUN
ap-1797	179	10	belong	belong	VERB
ap-1797	179	11	to	to	ADP
ap-1797	179	12	the	the	DET
ap-1797	179	13	pt	pt	PROPN
ap-1797	179	14	broken	break	VERB
ap-1797	179	15	case	case	NOUN
ap-1797	179	16	,	,	PUNCT
ap-1797	179	17	in	in	ADP
ap-1797	179	18	which	which	PRON
ap-1797	179	19	the	the	DET
ap-1797	179	20	wave	wave	NOUN
ap-1797	179	21	functions	function	NOUN
ap-1797	179	22	do	do	AUX
ap-1797	179	23	not	not	PART
ap-1797	179	24	reflect	reflect	VERB
ap-1797	179	25	the	the	DET
ap-1797	179	26	pt	pt	NOUN
ap-1797	179	27	−0.2	−0.2	PROPN
ap-1797	179	28	−0.1	−0.1	PROPN
ap-1797	179	29	0	0	NUM
ap-1797	180	1	0.1	0.1	NUM
ap-1797	180	2	0.2	0.2	NUM
ap-1797	180	3	0.3	0.3	NUM
ap-1797	180	4	0.4	0.4	NUM
ap-1797	180	5	0.5	0.5	NUM
ap-1797	180	6	0.6	0.6	NUM
ap-1797	180	7	−6	−6	NOUN
ap-1797	180	8	−4	−4	X
ap-1797	181	1	−2	−2	NOUN
ap-1797	181	2	0	0	NUM
ap-1797	181	3	2	2	NUM
ap-1797	181	4	4	4	NUM
ap-1797	181	5	6	6	NUM
ap-1797	181	6	φ	φ	NUM
ap-1797	181	7	x	x	SYM
ap-1797	181	8	(	(	PUNCT
ap-1797	181	9	a	a	NOUN
ap-1797	181	10	)	)	PUNCT
ap-1797	181	11	−0.2	−0.2	PROPN
ap-1797	182	1	−0.1	−0.1	PROPN
ap-1797	182	2	0	0	NUM
ap-1797	183	1	0.1	0.1	NUM
ap-1797	183	2	0.2	0.2	NUM
ap-1797	183	3	0.3	0.3	NUM
ap-1797	183	4	0.4	0.4	NUM
ap-1797	183	5	0.5	0.5	NUM
ap-1797	183	6	0.6	0.6	NUM
ap-1797	183	7	−6	−6	NOUN
ap-1797	183	8	−4	−4	X
ap-1797	184	1	−2	−2	NOUN
ap-1797	184	2	0	0	NUM
ap-1797	184	3	2	2	NUM
ap-1797	184	4	4	4	NUM
ap-1797	184	5	6	6	NUM
ap-1797	184	6	φ	φ	NUM
ap-1797	184	7	x	x	SYM
ap-1797	184	8	(	(	PUNCT
ap-1797	184	9	b	b	NOUN
ap-1797	184	10	)	)	PUNCT
ap-1797	184	11	reφ	reφ	NOUN
ap-1797	184	12	imφ	imφ	PROPN
ap-1797	184	13	|φ|2	|φ|2	PROPN
ap-1797	184	14	figure	figure	NOUN
ap-1797	184	15	5	5	NUM
ap-1797	184	16	.	.	NOUN
ap-1797	184	17	wave	wave	NOUN
ap-1797	184	18	functions	function	NOUN
ap-1797	184	19	of	of	ADP
ap-1797	184	20	the	the	DET
ap-1797	184	21	complex	complex	ADJ
ap-1797	184	22	eigenvalue	eigenvalue	ADJ
ap-1797	184	23	solutions	solution	NOUN
ap-1797	184	24	with	with	ADP
ap-1797	184	25	negative	negative	ADJ
ap-1797	184	26	(	(	PUNCT
ap-1797	184	27	a	a	NOUN
ap-1797	184	28	)	)	PUNCT
ap-1797	184	29	and	and	CCONJ
ap-1797	184	30	positive	positive	ADJ
ap-1797	184	31	(	(	PUNCT
ap-1797	184	32	b	b	NOUN
ap-1797	184	33	)	)	PUNCT
ap-1797	184	34	imaginary	imaginary	ADJ
ap-1797	184	35	part	part	NOUN
ap-1797	184	36	in	in	ADP
ap-1797	184	37	the	the	DET
ap-1797	184	38	case	case	NOUN
ap-1797	184	39	g	g	NOUN
ap-1797	184	40	=	=	NOUN
ap-1797	184	41	0.2	0.2	NUM
ap-1797	184	42	and	and	CCONJ
ap-1797	184	43	γ	γ	X
ap-1797	184	44	=	=	SYM
ap-1797	184	45	0.03	0.03	NUM
ap-1797	184	46	.	.	PUNCT
ap-1797	185	1	again	again	ADV
ap-1797	185	2	only	only	ADV
ap-1797	185	3	the	the	DET
ap-1797	185	4	gaussian	gaussian	ADJ
ap-1797	185	5	wave	wave	NOUN
ap-1797	185	6	functions	function	NOUN
ap-1797	185	7	are	be	AUX
ap-1797	185	8	shown	show	VERB
ap-1797	185	9	.	.	PUNCT
ap-1797	186	1	the	the	DET
ap-1797	186	2	square	square	ADJ
ap-1797	186	3	moduli	modulus	NOUN
ap-1797	186	4	are	be	AUX
ap-1797	186	5	not	not	PART
ap-1797	186	6	symmetric	symmetric	ADJ
ap-1797	186	7	functions	function	NOUN
ap-1797	186	8	of	of	ADP
ap-1797	186	9	x	x	PUNCT
ap-1797	186	10	and	and	CCONJ
ap-1797	186	11	destroy	destroy	VERB
ap-1797	186	12	the	the	DET
ap-1797	186	13	hamiltonian	hamiltonian	NOUN
ap-1797	186	14	’s	’s	PART
ap-1797	186	15	pt	pt	PROPN
ap-1797	186	16	symmetry	symmetry	NOUN
ap-1797	186	17	.	.	PUNCT
ap-1797	187	1	symmetry	symmetry	NOUN
ap-1797	187	2	of	of	ADP
ap-1797	187	3	the	the	DET
ap-1797	187	4	hamiltonian	hamiltonian	NOUN
ap-1797	187	5	.	.	PUNCT
ap-1797	188	1	this	this	PRON
ap-1797	188	2	is	be	AUX
ap-1797	188	3	also	also	ADV
ap-1797	188	4	the	the	DET
ap-1797	188	5	case	case	NOUN
ap-1797	188	6	for	for	ADP
ap-1797	188	7	the	the	DET
ap-1797	188	8	solutions	solution	NOUN
ap-1797	188	9	of	of	ADP
ap-1797	188	10	the	the	DET
ap-1797	188	11	gross	gross	ADJ
ap-1797	188	12	-	-	PUNCT
ap-1797	188	13	pitaevskii	pitaevskii	ADJ
ap-1797	188	14	equation	equation	NOUN
ap-1797	188	15	as	as	SCONJ
ap-1797	188	16	can	can	AUX
ap-1797	188	17	be	be	AUX
ap-1797	188	18	seen	see	VERB
ap-1797	188	19	in	in	ADP
ap-1797	188	20	figure	figure	NOUN
ap-1797	188	21	5	5	NUM
ap-1797	188	22	.	.	PUNCT
ap-1797	189	1	the	the	DET
ap-1797	189	2	wave	wave	NOUN
ap-1797	189	3	functions	function	NOUN
ap-1797	189	4	of	of	ADP
ap-1797	189	5	the	the	DET
ap-1797	189	6	solutions	solution	NOUN
ap-1797	189	7	with	with	ADP
ap-1797	189	8	complex	complex	ADJ
ap-1797	189	9	eigenvalues	eigenvalue	NOUN
ap-1797	189	10	are	be	AUX
ap-1797	189	11	not	not	PART
ap-1797	189	12	pt	pt	X
ap-1797	189	13	symmetric	symmetric	NOUN
ap-1797	189	14	.	.	PUNCT
ap-1797	190	1	their	their	PRON
ap-1797	190	2	square	square	ADJ
ap-1797	190	3	moduli	modulus	NOUN
ap-1797	190	4	are	be	AUX
ap-1797	190	5	not	not	PART
ap-1797	190	6	symmetric	symmetric	ADJ
ap-1797	190	7	functions	function	NOUN
ap-1797	190	8	of	of	ADP
ap-1797	190	9	x	x	NOUN
ap-1797	190	10	,	,	PUNCT
ap-1797	190	11	and	and	CCONJ
ap-1797	190	12	thus	thus	ADV
ap-1797	190	13	even	even	ADV
ap-1797	190	14	the	the	DET
ap-1797	190	15	pt	pt	NOUN
ap-1797	190	16	symmetry	symmetry	NOUN
ap-1797	190	17	of	of	ADP
ap-1797	190	18	the	the	DET
ap-1797	190	19	hamiltonian	hamiltonian	NOUN
ap-1797	190	20	is	be	AUX
ap-1797	190	21	destroyed	destroy	VERB
ap-1797	190	22	,	,	PUNCT
ap-1797	190	23	a	a	DET
ap-1797	190	24	circumstance	circumstance	NOUN
ap-1797	190	25	which	which	PRON
ap-1797	190	26	is	be	AUX
ap-1797	190	27	not	not	PART
ap-1797	190	28	possible	possible	ADJ
ap-1797	190	29	in	in	ADP
ap-1797	190	30	a	a	DET
ap-1797	190	31	linear	linear	ADJ
ap-1797	190	32	quantum	quantum	NOUN
ap-1797	190	33	system	system	NOUN
ap-1797	190	34	.	.	PUNCT
ap-1797	191	1	the	the	DET
ap-1797	191	2	wave	wave	NOUN
ap-1797	191	3	function	function	NOUN
ap-1797	191	4	belonging	belong	VERB
ap-1797	191	5	to	to	ADP
ap-1797	191	6	the	the	DET
ap-1797	191	7	eigenvalue	eigenvalue	NOUN
ap-1797	191	8	with	with	ADP
ap-1797	191	9	negative	negative	ADJ
ap-1797	191	10	imaginary	imaginary	ADJ
ap-1797	191	11	part	part	NOUN
ap-1797	191	12	has	have	VERB
ap-1797	191	13	a	a	DET
ap-1797	191	14	higher	high	ADJ
ap-1797	191	15	amplitude	amplitude	NOUN
ap-1797	191	16	in	in	ADP
ap-1797	191	17	the	the	DET
ap-1797	191	18	left	left	ADJ
ap-1797	191	19	well	well	NOUN
ap-1797	191	20	with	with	ADP
ap-1797	191	21	loss	loss	NOUN
ap-1797	191	22	,	,	PUNCT
ap-1797	191	23	whereas	whereas	SCONJ
ap-1797	191	24	the	the	DET
ap-1797	191	25	probability	probability	NOUN
ap-1797	191	26	amplitude	amplitude	NOUN
ap-1797	191	27	of	of	ADP
ap-1797	191	28	the	the	DET
ap-1797	191	29	state	state	NOUN
ap-1797	191	30	with	with	ADP
ap-1797	191	31	positive	positive	ADJ
ap-1797	191	32	imaginary	imaginary	ADJ
ap-1797	191	33	part	part	NOUN
ap-1797	191	34	of	of	ADP
ap-1797	191	35	the	the	DET
ap-1797	191	36	energy	energy	NOUN
ap-1797	191	37	is	be	AUX
ap-1797	191	38	shifted	shift	VERB
ap-1797	191	39	more	more	ADJ
ap-1797	191	40	to	to	ADP
ap-1797	191	41	the	the	DET
ap-1797	191	42	right	right	ADJ
ap-1797	191	43	well	well	NOUN
ap-1797	191	44	with	with	ADP
ap-1797	191	45	gain	gain	NOUN
ap-1797	191	46	.	.	PUNCT
ap-1797	192	1	a	a	DET
ap-1797	192	2	pt	pt	INTJ
ap-1797	192	3	symmetric	symmetric	ADJ
ap-1797	192	4	bose	bose	PROPN
ap-1797	192	5	-	-	PUNCT
ap-1797	192	6	einstein	einstein	NOUN
ap-1797	192	7	condensate	condensate	NOUN
ap-1797	192	8	will	will	AUX
ap-1797	192	9	only	only	ADV
ap-1797	192	10	be	be	AUX
ap-1797	192	11	observable	observable	ADJ
ap-1797	192	12	if	if	SCONJ
ap-1797	192	13	the	the	DET
ap-1797	192	14	eigenstates	eigenstate	NOUN
ap-1797	192	15	are	be	AUX
ap-1797	192	16	stable	stable	ADJ
ap-1797	192	17	with	with	ADP
ap-1797	192	18	respect	respect	NOUN
ap-1797	192	19	to	to	ADP
ap-1797	192	20	quantum	quantum	ADJ
ap-1797	192	21	fluctuations	fluctuation	NOUN
ap-1797	192	22	.	.	PUNCT
ap-1797	193	1	we	we	PRON
ap-1797	193	2	performed	perform	VERB
ap-1797	193	3	a	a	DET
ap-1797	193	4	linear	linear	ADJ
ap-1797	193	5	stability	stability	NOUN
ap-1797	193	6	analysis	analysis	NOUN
ap-1797	193	7	to	to	PART
ap-1797	193	8	check	check	VERB
ap-1797	193	9	the	the	DET
ap-1797	193	10	behavior	behavior	NOUN
ap-1797	193	11	of	of	ADP
ap-1797	193	12	the	the	DET
ap-1797	193	13	eigenstates	eigenstate	NOUN
ap-1797	193	14	with	with	ADP
ap-1797	193	15	real	real	ADJ
ap-1797	193	16	eigenvalues	eigenvalue	NOUN
ap-1797	193	17	.	.	PUNCT
ap-1797	194	1	a	a	DET
ap-1797	194	2	linearization	linearization	NOUN
ap-1797	194	3	of	of	ADP
ap-1797	194	4	the	the	DET
ap-1797	194	5	equations	equation	NOUN
ap-1797	194	6	of	of	ADP
ap-1797	194	7	motion	motion	NOUN
ap-1797	194	8	(	(	PUNCT
ap-1797	194	9	11a)–(11f	11a)–(11f	NUM
ap-1797	194	10	)	)	PUNCT
ap-1797	194	11	of	of	ADP
ap-1797	194	12	the	the	DET
ap-1797	194	13	gaussian	gaussian	ADJ
ap-1797	194	14	parameters	parameter	NOUN
ap-1797	194	15	around	around	ADP
ap-1797	194	16	the	the	DET
ap-1797	194	17	stationary	stationary	ADJ
ap-1797	194	18	states	state	NOUN
ap-1797	194	19	and	and	CCONJ
ap-1797	194	20	the	the	DET
ap-1797	194	21	solution	solution	NOUN
ap-1797	194	22	of	of	ADP
ap-1797	194	23	the	the	DET
ap-1797	194	24	bogoliubov	bogoliubov	PROPN
ap-1797	194	25	-	-	PUNCT
ap-1797	194	26	de	de	ADJ
ap-1797	194	27	gennes	genne	NOUN
ap-1797	194	28	equations	equation	NOUN
ap-1797	194	29	for	for	ADP
ap-1797	194	30	the	the	DET
ap-1797	194	31	numerically	numerically	ADV
ap-1797	194	32	exact	exact	ADJ
ap-1797	194	33	wave	wave	NOUN
ap-1797	194	34	functions	function	NOUN
ap-1797	194	35	has	have	AUX
ap-1797	194	36	been	be	AUX
ap-1797	194	37	done	do	VERB
ap-1797	194	38	[	[	X
ap-1797	194	39	28	28	NUM
ap-1797	194	40	]	]	PUNCT
ap-1797	194	41	.	.	PUNCT
ap-1797	195	1	we	we	PRON
ap-1797	195	2	found	find	VERB
ap-1797	195	3	that	that	SCONJ
ap-1797	195	4	the	the	DET
ap-1797	195	5	excited	excited	ADJ
ap-1797	195	6	state	state	NOUN
ap-1797	195	7	is	be	AUX
ap-1797	195	8	stable	stable	ADJ
ap-1797	195	9	for	for	ADP
ap-1797	195	10	all	all	DET
ap-1797	195	11	combinations	combination	NOUN
ap-1797	195	12	of	of	ADP
ap-1797	195	13	g	g	PROPN
ap-1797	195	14	and	and	CCONJ
ap-1797	195	15	γ	γ	NOUN
ap-1797	195	16	as	as	ADV
ap-1797	195	17	long	long	ADV
ap-1797	195	18	as	as	SCONJ
ap-1797	195	19	it	it	PRON
ap-1797	195	20	exists	exist	VERB
ap-1797	195	21	.	.	PUNCT
ap-1797	196	1	the	the	DET
ap-1797	196	2	ground	ground	NOUN
ap-1797	196	3	state	state	NOUN
ap-1797	196	4	,	,	PUNCT
ap-1797	196	5	however	however	ADV
ap-1797	196	6	,	,	PUNCT
ap-1797	196	7	becomes	become	VERB
ap-1797	196	8	unstable	unstable	ADJ
ap-1797	196	9	as	as	ADV
ap-1797	196	10	soon	soon	ADV
ap-1797	196	11	as	as	SCONJ
ap-1797	196	12	the	the	DET
ap-1797	196	13	pt	pt	PROPN
ap-1797	196	14	broken	break	VERB
ap-1797	196	15	branches	branch	NOUN
ap-1797	196	16	with	with	ADP
ap-1797	196	17	complex	complex	ADJ
ap-1797	196	18	eigenvalues	eigenvalue	NOUN
ap-1797	196	19	emerge	emerge	VERB
ap-1797	196	20	in	in	ADP
ap-1797	196	21	the	the	DET
ap-1797	196	22	energy	energy	NOUN
ap-1797	196	23	diagram	diagram	NOUN
ap-1797	196	24	of	of	ADP
ap-1797	196	25	figure	figure	NOUN
ap-1797	196	26	2	2	NUM
ap-1797	196	27	.	.	NOUN
ap-1797	196	28	263	263	NUM
ap-1797	196	29	holger	holger	NOUN
ap-1797	196	30	cartarius	cartarius	NOUN
ap-1797	196	31	et	et	PROPN
ap-1797	196	32	al	al	PROPN
ap-1797	196	33	.	.	PROPN
ap-1797	197	1	acta	acta	PROPN
ap-1797	197	2	polytechnica	polytechnica	PROPN
ap-1797	197	3	0	0	NUM
ap-1797	197	4	60	60	NUM
ap-1797	197	5	120	120	NUM
ap-1797	197	6	180	180	NUM
ap-1797	197	7	240	240	NUM
ap-1797	197	8	300	300	NUM
ap-1797	197	9	t	t	NOUN
ap-1797	197	10	−4	−4	X
ap-1797	198	1	−2	−2	NOUN
ap-1797	198	2	0	0	NUM
ap-1797	198	3	2	2	NUM
ap-1797	198	4	4	4	NUM
ap-1797	198	5	x	x	SYM
ap-1797	198	6	0	0	NUM
ap-1797	198	7	0.1	0.1	NUM
ap-1797	198	8	0.2	0.2	NUM
ap-1797	198	9	0.3	0.3	NUM
ap-1797	198	10	0.4	0.4	NUM
ap-1797	198	11	0.5	0.5	NUM
ap-1797	198	12	0.6	0.6	NUM
ap-1797	198	13	(	(	PUNCT
ap-1797	198	14	a	a	NOUN
ap-1797	198	15	)	)	PUNCT
ap-1797	198	16	0	0	NUM
ap-1797	198	17	60	60	NUM
ap-1797	198	18	120	120	NUM
ap-1797	198	19	180	180	NUM
ap-1797	198	20	240	240	NUM
ap-1797	198	21	300	300	NUM
ap-1797	198	22	t	t	NOUN
ap-1797	198	23	−4	−4	X
ap-1797	198	24	−2	−2	NOUN
ap-1797	198	25	0	0	NUM
ap-1797	198	26	2	2	NUM
ap-1797	198	27	4	4	NUM
ap-1797	198	28	x	x	SYM
ap-1797	198	29	0	0	NUM
ap-1797	198	30	0.1	0.1	NUM
ap-1797	198	31	0.2	0.2	NUM
ap-1797	198	32	0.3	0.3	NUM
ap-1797	198	33	0.4	0.4	NUM
ap-1797	198	34	(	(	PUNCT
ap-1797	198	35	b	b	NOUN
ap-1797	198	36	)	)	PUNCT
ap-1797	198	37	figure	figure	NOUN
ap-1797	198	38	6	6	NUM
ap-1797	198	39	.	.	PUNCT
ap-1797	199	1	evolution	evolution	NOUN
ap-1797	199	2	of	of	ADP
ap-1797	199	3	the	the	DET
ap-1797	199	4	wave	wave	NOUN
ap-1797	199	5	packet	packet	NOUN
ap-1797	199	6	(	(	PUNCT
ap-1797	199	7	14	14	NUM
ap-1797	199	8	)	)	PUNCT
ap-1797	199	9	in	in	ADP
ap-1797	199	10	the	the	DET
ap-1797	199	11	pt	pt	PROPN
ap-1797	199	12	symmetric	symmetric	ADJ
ap-1797	199	13	double	double	ADJ
ap-1797	199	14	well	well	ADV
ap-1797	199	15	for	for	ADP
ap-1797	199	16	nonvanishing	nonvanishe	VERB
ap-1797	199	17	nonlinearity	nonlinearity	NOUN
ap-1797	199	18	g	g	NOUN
ap-1797	199	19	=	=	NOUN
ap-1797	199	20	0.2	0.2	NUM
ap-1797	199	21	,	,	PUNCT
ap-1797	199	22	ϕ	ϕ	NOUN
ap-1797	199	23	=	=	SYM
ap-1797	199	24	π/2	π/2	NUM
ap-1797	199	25	,	,	PUNCT
ap-1797	199	26	and	and	CCONJ
ap-1797	199	27	the	the	DET
ap-1797	199	28	gain	gain	NOUN
ap-1797	199	29	-	-	PUNCT
ap-1797	199	30	loss	loss	NOUN
ap-1797	199	31	contributions	contribution	NOUN
ap-1797	199	32	γ	γ	X
ap-1797	199	33	=	=	SYM
ap-1797	199	34	0	0	PUNCT
ap-1797	199	35	(	(	PUNCT
ap-1797	199	36	a	a	NOUN
ap-1797	199	37	)	)	PUNCT
ap-1797	199	38	and	and	CCONJ
ap-1797	199	39	γ	γ	X
ap-1797	199	40	=	=	SYM
ap-1797	199	41	0.02	0.02	NUM
ap-1797	199	42	(	(	PUNCT
ap-1797	199	43	b	b	NOUN
ap-1797	199	44	)	)	PUNCT
ap-1797	199	45	.	.	PUNCT
ap-1797	200	1	3.3	3.3	NUM
ap-1797	200	2	.	.	PUNCT
ap-1797	201	1	temporal	temporal	ADJ
ap-1797	201	2	evolution	evolution	NOUN
ap-1797	201	3	and	and	CCONJ
ap-1797	201	4	the	the	DET
ap-1797	201	5	significance	significance	NOUN
ap-1797	201	6	of	of	ADP
ap-1797	201	7	“	"	PUNCT
ap-1797	201	8	stationary	stationary	ADJ
ap-1797	201	9	”	"	PUNCT
ap-1797	201	10	solutions	solution	NOUN
ap-1797	201	11	with	with	ADP
ap-1797	201	12	complex	complex	ADJ
ap-1797	201	13	eigenvalues	eigenvalue	NOUN
ap-1797	201	14	we	we	PRON
ap-1797	201	15	first	first	ADV
ap-1797	201	16	want	want	VERB
ap-1797	201	17	to	to	PART
ap-1797	201	18	investigate	investigate	VERB
ap-1797	201	19	the	the	DET
ap-1797	201	20	temporal	temporal	ADJ
ap-1797	201	21	evolution	evolution	NOUN
ap-1797	201	22	of	of	ADP
ap-1797	201	23	condensate	condensate	NOUN
ap-1797	201	24	wave	wave	NOUN
ap-1797	201	25	functions	function	NOUN
ap-1797	201	26	close	close	ADJ
ap-1797	201	27	to	to	ADP
ap-1797	201	28	the	the	DET
ap-1797	201	29	stationary	stationary	ADJ
ap-1797	201	30	real	real	ADJ
ap-1797	201	31	eigenvalue	eigenvalue	NOUN
ap-1797	201	32	solutions	solution	NOUN
ap-1797	201	33	for	for	ADP
ap-1797	201	34	values	value	NOUN
ap-1797	201	35	of	of	ADP
ap-1797	201	36	γ	γ	NOUN
ap-1797	201	37	below	below	ADP
ap-1797	201	38	the	the	DET
ap-1797	201	39	appearance	appearance	NOUN
ap-1797	201	40	of	of	ADP
ap-1797	201	41	the	the	DET
ap-1797	201	42	pt	pt	NOUN
ap-1797	201	43	broken	break	VERB
ap-1797	201	44	states	state	NOUN
ap-1797	201	45	.	.	PUNCT
ap-1797	202	1	two	two	NUM
ap-1797	202	2	examples	example	NOUN
ap-1797	202	3	of	of	ADP
ap-1797	202	4	numerically	numerically	ADV
ap-1797	202	5	exact	exact	ADJ
ap-1797	202	6	propagations	propagation	NOUN
ap-1797	202	7	using	use	VERB
ap-1797	202	8	the	the	DET
ap-1797	202	9	split	split	ADJ
ap-1797	202	10	operator	operator	NOUN
ap-1797	202	11	method	method	NOUN
ap-1797	202	12	are	be	AUX
ap-1797	202	13	given	give	VERB
ap-1797	202	14	in	in	ADP
ap-1797	202	15	figure	figure	NOUN
ap-1797	202	16	6	6	NUM
ap-1797	202	17	for	for	ADP
ap-1797	202	18	the	the	DET
ap-1797	202	19	initial	initial	ADJ
ap-1797	202	20	wave	wave	NOUN
ap-1797	202	21	packet	packet	NOUN
ap-1797	202	22	ψ(x	ψ(x	PROPN
ap-1797	202	23	,	,	PUNCT
ap-1797	202	24	t	t	NOUN
ap-1797	202	25	=	=	SYM
ap-1797	202	26	0	0	NUM
ap-1797	202	27	)	)	PUNCT
ap-1797	202	28	=	=	SYM
ap-1797	202	29	1√	1√	NUM
ap-1797	202	30	2	2	NUM
ap-1797	202	31	(	(	PUNCT
ap-1797	202	32	φgs(x	φgs(x	PROPN
ap-1797	202	33	)	)	PUNCT
ap-1797	202	34	+	+	CCONJ
ap-1797	202	35	eiϕφes(x	eiϕφes(x	PROPN
ap-1797	202	36	)	)	PUNCT
ap-1797	202	37	)	)	PUNCT
ap-1797	203	1	(	(	PUNCT
ap-1797	203	2	14	14	NUM
ap-1797	203	3	)	)	PUNCT
ap-1797	203	4	with	with	ADP
ap-1797	203	5	the	the	DET
ap-1797	203	6	ground	ground	NOUN
ap-1797	203	7	state	state	NOUN
ap-1797	203	8	φgs(x	φgs(x	PROPN
ap-1797	203	9	)	)	PUNCT
ap-1797	203	10	and	and	CCONJ
ap-1797	203	11	the	the	DET
ap-1797	203	12	excited	excited	ADJ
ap-1797	203	13	state	state	NOUN
ap-1797	203	14	φes(x	φes(x	PROPN
ap-1797	203	15	)	)	PUNCT
ap-1797	203	16	.	.	PUNCT
ap-1797	204	1	in	in	ADP
ap-1797	204	2	this	this	DET
ap-1797	204	3	case	case	NOUN
ap-1797	204	4	one	one	NUM
ap-1797	204	5	expects	expect	VERB
ap-1797	204	6	for	for	ADP
ap-1797	204	7	linear	linear	NOUN
ap-1797	204	8	systems	system	NOUN
ap-1797	204	9	the	the	DET
ap-1797	204	10	behavior	behavior	NOUN
ap-1797	204	11	that	that	PRON
ap-1797	204	12	an	an	DET
ap-1797	204	13	oscillation	oscillation	NOUN
ap-1797	204	14	of	of	ADP
ap-1797	204	15	the	the	DET
ap-1797	204	16	probability	probability	NOUN
ap-1797	204	17	amplitude	amplitude	NOUN
ap-1797	204	18	between	between	ADP
ap-1797	204	19	the	the	DET
ap-1797	204	20	two	two	NUM
ap-1797	204	21	wells	well	NOUN
ap-1797	204	22	sets	set	NOUN
ap-1797	204	23	in	in	ADP
ap-1797	204	24	.	.	PUNCT
ap-1797	205	1	the	the	DET
ap-1797	205	2	frequency	frequency	NOUN
ap-1797	205	3	decreases	decrease	VERB
ap-1797	205	4	with	with	ADP
ap-1797	205	5	increasing	increase	VERB
ap-1797	205	6	γ	γ	NOUN
ap-1797	205	7	until	until	SCONJ
ap-1797	205	8	the	the	DET
ap-1797	205	9	oscillation	oscillation	NOUN
ap-1797	205	10	stops	stop	VERB
ap-1797	205	11	at	at	ADP
ap-1797	205	12	γ	γ	X
ap-1797	205	13	=	=	PRON
ap-1797	205	14	γep	γep	PROPN
ap-1797	205	15	[	[	X
ap-1797	205	16	11	11	NUM
ap-1797	205	17	]	]	PUNCT
ap-1797	205	18	.	.	PUNCT
ap-1797	206	1	this	this	DET
ap-1797	206	2	behavior	behavior	NOUN
ap-1797	206	3	is	be	AUX
ap-1797	206	4	reproduced	reproduce	VERB
ap-1797	206	5	in	in	ADP
ap-1797	206	6	figure	figure	NOUN
ap-1797	206	7	6	6	NUM
ap-1797	206	8	,	,	PUNCT
ap-1797	206	9	i.e.	i.e.	X
ap-1797	206	10	the	the	DET
ap-1797	206	11	qualitative	qualitative	ADJ
ap-1797	206	12	pattern	pattern	NOUN
ap-1797	206	13	of	of	ADP
ap-1797	206	14	the	the	DET
ap-1797	206	15	motion	motion	NOUN
ap-1797	206	16	is	be	AUX
ap-1797	206	17	conserved	conserve	VERB
ap-1797	206	18	in	in	ADP
ap-1797	206	19	the	the	DET
ap-1797	206	20	nonlinear	nonlinear	ADJ
ap-1797	206	21	gross	gross	ADJ
ap-1797	206	22	-	-	PUNCT
ap-1797	206	23	pitaevskii	pitaevskii	ADJ
ap-1797	206	24	equation	equation	NOUN
ap-1797	206	25	(	(	PUNCT
ap-1797	206	26	1	1	NUM
ap-1797	206	27	)	)	PUNCT
ap-1797	206	28	.	.	PUNCT
ap-1797	207	1	a	a	DET
ap-1797	207	2	quantitative	quantitative	ADJ
ap-1797	207	3	analysis	analysis	NOUN
ap-1797	207	4	shows	show	VERB
ap-1797	207	5	that	that	SCONJ
ap-1797	207	6	the	the	DET
ap-1797	207	7	nonlinearity	nonlinearity	NOUN
ap-1797	207	8	leads	lead	VERB
ap-1797	207	9	to	to	ADP
ap-1797	207	10	slightly	slightly	ADV
ap-1797	207	11	higher	high	ADJ
ap-1797	207	12	oscillation	oscillation	NOUN
ap-1797	207	13	frequencies	frequency	NOUN
ap-1797	207	14	.	.	PUNCT
ap-1797	208	1	however	however	ADV
ap-1797	208	2	,	,	PUNCT
ap-1797	208	3	with	with	ADP
ap-1797	208	4	the	the	DET
ap-1797	208	5	emergence	emergence	NOUN
ap-1797	208	6	of	of	ADP
ap-1797	208	7	the	the	DET
ap-1797	208	8	additional	additional	ADJ
ap-1797	208	9	pt	pt	INTJ
ap-1797	208	10	broken	break	VERB
ap-1797	208	11	states	state	NOUN
ap-1797	208	12	we	we	PRON
ap-1797	208	13	observe	observe	VERB
ap-1797	208	14	a	a	DET
ap-1797	208	15	qualitative	qualitative	ADJ
ap-1797	208	16	change	change	NOUN
ap-1797	208	17	between	between	ADP
ap-1797	208	18	the	the	DET
ap-1797	208	19	linear	linear	ADJ
ap-1797	208	20	and	and	CCONJ
ap-1797	208	21	nonlinear	nonlinear	ADJ
ap-1797	208	22	systems	system	NOUN
ap-1797	208	23	.	.	PUNCT
ap-1797	209	1	as	as	SCONJ
ap-1797	209	2	was	be	AUX
ap-1797	209	3	mentioned	mention	VERB
ap-1797	209	4	above	above	ADV
ap-1797	209	5	,	,	PUNCT
ap-1797	209	6	the	the	DET
ap-1797	209	7	ground	ground	NOUN
ap-1797	209	8	state	state	NOUN
ap-1797	209	9	becomes	become	VERB
ap-1797	209	10	unstable	unstable	ADJ
ap-1797	209	11	in	in	ADP
ap-1797	209	12	this	this	DET
ap-1797	209	13	regime	regime	NOUN
ap-1797	209	14	.	.	PUNCT
ap-1797	210	1	the	the	DET
ap-1797	210	2	relevance	relevance	NOUN
ap-1797	210	3	of	of	ADP
ap-1797	210	4	this	this	DET
ap-1797	210	5	unstable	unstable	ADJ
ap-1797	210	6	character	character	NOUN
ap-1797	210	7	can	can	AUX
ap-1797	210	8	be	be	AUX
ap-1797	210	9	seen	see	VERB
ap-1797	210	10	in	in	ADP
ap-1797	210	11	figure	figure	NOUN
ap-1797	210	12	7a	7a	NUM
ap-1797	210	13	,	,	PUNCT
ap-1797	210	14	where	where	SCONJ
ap-1797	210	15	the	the	DET
ap-1797	210	16	initial	initial	ADJ
ap-1797	210	17	wave	wave	NOUN
ap-1797	210	18	packet	packet	NOUN
ap-1797	210	19	(	(	PUNCT
ap-1797	210	20	14	14	NUM
ap-1797	210	21	)	)	PUNCT
ap-1797	210	22	is	be	AUX
ap-1797	210	23	evolved	evolve	VERB
ap-1797	210	24	for	for	ADP
ap-1797	210	25	g	g	NOUN
ap-1797	210	26	=	=	SYM
ap-1797	210	27	0.2	0.2	NUM
ap-1797	210	28	,	,	PUNCT
ap-1797	210	29	γ	γ	X
ap-1797	210	30	=	=	NOUN
ap-1797	210	31	0.03	0.03	NUM
ap-1797	210	32	,	,	PUNCT
ap-1797	210	33	and	and	CCONJ
ap-1797	210	34	the	the	DET
ap-1797	210	35	phase	phase	NOUN
ap-1797	210	36	ϕ	ϕ	X
ap-1797	210	37	=	=	SYM
ap-1797	210	38	π	π	X
ap-1797	210	39	.	.	PUNCT
ap-1797	210	40	already	already	ADV
ap-1797	210	41	during	during	ADP
ap-1797	210	42	the	the	DET
ap-1797	210	43	first	first	ADJ
ap-1797	210	44	oscillation	oscillation	NOUN
ap-1797	210	45	a	a	DET
ap-1797	210	46	complete	complete	ADJ
ap-1797	210	47	deformation	deformation	NOUN
ap-1797	210	48	of	of	ADP
ap-1797	210	49	the	the	DET
ap-1797	210	50	typical	typical	ADJ
ap-1797	210	51	pattern	pattern	NOUN
ap-1797	210	52	is	be	AUX
ap-1797	210	53	observed	observe	VERB
ap-1797	210	54	.	.	PUNCT
ap-1797	211	1	then	then	ADV
ap-1797	211	2	the	the	DET
ap-1797	211	3	oscillation	oscillation	NOUN
ap-1797	211	4	stops	stop	VERB
ap-1797	211	5	and	and	CCONJ
ap-1797	211	6	changes	change	NOUN
ap-1797	211	7	into	into	ADP
ap-1797	211	8	an	an	DET
ap-1797	211	9	unrestricted	unrestricted	ADJ
ap-1797	211	10	growth	growth	NOUN
ap-1797	211	11	of	of	ADP
ap-1797	211	12	the	the	DET
ap-1797	211	13	probability	probability	NOUN
ap-1797	211	14	amplitude	amplitude	NOUN
ap-1797	211	15	in	in	ADP
ap-1797	211	16	the	the	DET
ap-1797	211	17	right	right	ADJ
ap-1797	211	18	well	well	INTJ
ap-1797	211	19	,	,	PUNCT
ap-1797	211	20	0	0	NUM
ap-1797	211	21	60	60	NUM
ap-1797	211	22	120	120	NUM
ap-1797	211	23	t	t	NOUN
ap-1797	211	24	−4	−4	X
ap-1797	212	1	−2	−2	NOUN
ap-1797	212	2	0	0	NUM
ap-1797	212	3	2	2	NUM
ap-1797	212	4	4	4	NUM
ap-1797	212	5	x	x	SYM
ap-1797	212	6	0	0	NUM
ap-1797	212	7	0.5	0.5	NUM
ap-1797	212	8	(	(	PUNCT
ap-1797	212	9	a	a	NOUN
ap-1797	212	10	)	)	PUNCT
ap-1797	212	11	0	0	NUM
ap-1797	212	12	60	60	NUM
ap-1797	212	13	120	120	NUM
ap-1797	212	14	180	180	NUM
ap-1797	212	15	240	240	NUM
ap-1797	212	16	300	300	NUM
ap-1797	212	17	t	t	NOUN
ap-1797	212	18	−4	−4	X
ap-1797	212	19	−2	−2	NOUN
ap-1797	212	20	0	0	NUM
ap-1797	212	21	2	2	NUM
ap-1797	212	22	4	4	NUM
ap-1797	212	23	x	x	SYM
ap-1797	212	24	0	0	NUM
ap-1797	212	25	0.1	0.1	NUM
ap-1797	212	26	0.2	0.2	NUM
ap-1797	212	27	0.3	0.3	NUM
ap-1797	212	28	(	(	PUNCT
ap-1797	212	29	b	b	NOUN
ap-1797	212	30	)	)	PUNCT
ap-1797	212	31	figure	figure	NOUN
ap-1797	212	32	7	7	NUM
ap-1797	212	33	.	.	PUNCT
ap-1797	212	34	evolution	evolution	NOUN
ap-1797	212	35	of	of	ADP
ap-1797	212	36	the	the	DET
ap-1797	212	37	wave	wave	NOUN
ap-1797	212	38	packet	packet	NOUN
ap-1797	212	39	(	(	PUNCT
ap-1797	212	40	14	14	NUM
ap-1797	212	41	)	)	PUNCT
ap-1797	212	42	in	in	ADP
ap-1797	212	43	the	the	DET
ap-1797	212	44	pt	pt	PROPN
ap-1797	212	45	symmetric	symmetric	ADJ
ap-1797	212	46	double	double	ADJ
ap-1797	212	47	well	well	ADV
ap-1797	212	48	for	for	ADP
ap-1797	212	49	nonvanishing	nonvanishe	VERB
ap-1797	212	50	nonlinearity	nonlinearity	NOUN
ap-1797	212	51	g	g	NOUN
ap-1797	212	52	=	=	NOUN
ap-1797	212	53	0.2	0.2	NUM
ap-1797	212	54	and	and	CCONJ
ap-1797	212	55	the	the	DET
ap-1797	212	56	gain	gain	NOUN
ap-1797	212	57	-	-	PUNCT
ap-1797	212	58	loss	loss	NOUN
ap-1797	212	59	contributions	contribution	NOUN
ap-1797	212	60	γ	γ	X
ap-1797	212	61	=	=	SYM
ap-1797	212	62	0.03	0.03	NUM
ap-1797	212	63	with	with	ADP
ap-1797	212	64	phase	phase	NOUN
ap-1797	212	65	ϕ	ϕ	X
ap-1797	212	66	=	=	SYM
ap-1797	212	67	π	π	X
ap-1797	212	68	(	(	PUNCT
ap-1797	212	69	a	a	NOUN
ap-1797	212	70	)	)	PUNCT
ap-1797	212	71	and	and	CCONJ
ap-1797	212	72	γ	γ	X
ap-1797	212	73	=	=	SYM
ap-1797	212	74	0.04	0.04	NUM
ap-1797	212	75	with	with	ADP
ap-1797	212	76	ϕ	ϕ	NOUN
ap-1797	212	77	=	=	SYM
ap-1797	212	78	π/2	π/2	NUM
ap-1797	212	79	(	(	PUNCT
ap-1797	212	80	b	b	NOUN
ap-1797	212	81	)	)	PUNCT
ap-1797	212	82	.	.	PUNCT
ap-1797	213	1	the	the	DET
ap-1797	213	2	wave	wave	NOUN
ap-1797	213	3	function	function	NOUN
ap-1797	213	4	“	"	PUNCT
ap-1797	213	5	explodes	explode	NOUN
ap-1797	213	6	”	"	PUNCT
ap-1797	213	7	.	.	PUNCT
ap-1797	214	1	this	this	DET
ap-1797	214	2	behavior	behavior	NOUN
ap-1797	214	3	is	be	AUX
ap-1797	214	4	not	not	PART
ap-1797	214	5	surprising	surprising	ADJ
ap-1797	214	6	.	.	PUNCT
ap-1797	215	1	one	one	NUM
ap-1797	215	2	of	of	ADP
ap-1797	215	3	the	the	DET
ap-1797	215	4	superimposed	superimpose	VERB
ap-1797	215	5	states	state	NOUN
ap-1797	215	6	in	in	ADP
ap-1797	215	7	(	(	PUNCT
ap-1797	215	8	14	14	NUM
ap-1797	215	9	)	)	PUNCT
ap-1797	215	10	is	be	AUX
ap-1797	215	11	unstable	unstable	ADJ
ap-1797	215	12	and	and	CCONJ
ap-1797	215	13	the	the	DET
ap-1797	215	14	two	two	NUM
ap-1797	215	15	pt	pt	NOUN
ap-1797	215	16	broken	break	VERB
ap-1797	215	17	solutions	solution	NOUN
ap-1797	215	18	with	with	ADP
ap-1797	215	19	complex	complex	ADJ
ap-1797	215	20	eigenvalues	eigenvalue	NOUN
ap-1797	215	21	exist	exist	VERB
ap-1797	215	22	.	.	PUNCT
ap-1797	216	1	one	one	PRON
ap-1797	216	2	can	can	AUX
ap-1797	216	3	expect	expect	VERB
ap-1797	216	4	that	that	SCONJ
ap-1797	216	5	,	,	PUNCT
ap-1797	216	6	in	in	ADP
ap-1797	216	7	the	the	DET
ap-1797	216	8	nonlinear	nonlinear	ADJ
ap-1797	216	9	system	system	NOUN
ap-1797	216	10	,	,	PUNCT
ap-1797	216	11	there	there	PRON
ap-1797	216	12	is	be	VERB
ap-1797	216	13	a	a	DET
ap-1797	216	14	considerable	considerable	ADJ
ap-1797	216	15	overlap	overlap	NOUN
ap-1797	216	16	of	of	ADP
ap-1797	216	17	the	the	DET
ap-1797	216	18	time	time	NOUN
ap-1797	216	19	evolved	evolve	VERB
ap-1797	216	20	wave	wave	NOUN
ap-1797	216	21	function	function	NOUN
ap-1797	216	22	(	(	PUNCT
ap-1797	216	23	14	14	NUM
ap-1797	216	24	)	)	PUNCT
ap-1797	216	25	with	with	ADP
ap-1797	216	26	the	the	DET
ap-1797	216	27	pt	pt	PROPN
ap-1797	216	28	broken	break	VERB
ap-1797	216	29	eigenstates	eigenstate	NOUN
ap-1797	216	30	,	,	PUNCT
ap-1797	216	31	cf	cf	INTJ
ap-1797	216	32	.	.	PUNCT
ap-1797	217	1	also	also	ADV
ap-1797	217	2	figures	figure	VERB
ap-1797	217	3	4	4	NUM
ap-1797	217	4	and	and	CCONJ
ap-1797	217	5	5	5	NUM
ap-1797	217	6	.	.	PUNCT
ap-1797	218	1	then	then	ADV
ap-1797	218	2	,	,	PUNCT
ap-1797	218	3	the	the	DET
ap-1797	218	4	eigenstate	eigenstate	NOUN
ap-1797	218	5	with	with	ADP
ap-1797	218	6	positive	positive	ADJ
ap-1797	218	7	imaginary	imaginary	ADJ
ap-1797	218	8	part	part	NOUN
ap-1797	218	9	of	of	ADP
ap-1797	218	10	the	the	DET
ap-1797	218	11	energy	energy	NOUN
ap-1797	218	12	will	will	AUX
ap-1797	218	13	always	always	ADV
ap-1797	218	14	dominate	dominate	VERB
ap-1797	218	15	for	for	ADP
ap-1797	218	16	long	long	ADJ
ap-1797	218	17	times	time	NOUN
ap-1797	218	18	since	since	SCONJ
ap-1797	218	19	it	it	PRON
ap-1797	218	20	increases	increase	VERB
ap-1797	218	21	,	,	PUNCT
ap-1797	218	22	and	and	CCONJ
ap-1797	218	23	determines	determine	VERB
ap-1797	218	24	the	the	DET
ap-1797	218	25	further	further	ADJ
ap-1797	218	26	evolution	evolution	NOUN
ap-1797	218	27	.	.	PUNCT
ap-1797	219	1	in	in	ADP
ap-1797	219	2	a	a	DET
ap-1797	219	3	realistic	realistic	ADJ
ap-1797	219	4	situation	situation	NOUN
ap-1797	219	5	an	an	DET
ap-1797	219	6	infinite	infinite	ADJ
ap-1797	219	7	growth	growth	NOUN
ap-1797	219	8	of	of	ADP
ap-1797	219	9	the	the	DET
ap-1797	219	10	probability	probability	NOUN
ap-1797	219	11	amplitude	amplitude	NOUN
ap-1797	219	12	will	will	AUX
ap-1797	219	13	not	not	PART
ap-1797	219	14	appear	appear	VERB
ap-1797	219	15	.	.	PUNCT
ap-1797	220	1	it	it	PRON
ap-1797	220	2	has	have	VERB
ap-1797	220	3	its	its	PRON
ap-1797	220	4	origin	origin	NOUN
ap-1797	220	5	in	in	ADP
ap-1797	220	6	the	the	DET
ap-1797	220	7	pt	pt	ADJ
ap-1797	220	8	symmetric	symmetric	ADJ
ap-1797	220	9	potential	potential	NOUN
ap-1797	220	10	(	(	PUNCT
ap-1797	220	11	4	4	NUM
ap-1797	220	12	)	)	PUNCT
ap-1797	220	13	and	and	CCONJ
ap-1797	220	14	requires	require	VERB
ap-1797	220	15	an	an	DET
ap-1797	220	16	infinite	infinite	ADJ
ap-1797	220	17	reservoir	reservoir	NOUN
ap-1797	220	18	of	of	ADP
ap-1797	220	19	atoms	atom	NOUN
ap-1797	220	20	.	.	PUNCT
ap-1797	221	1	at	at	ADP
ap-1797	221	2	some	some	DET
ap-1797	221	3	point	point	NOUN
ap-1797	221	4	in	in	ADP
ap-1797	221	5	time	time	NOUN
ap-1797	221	6	this	this	DET
ap-1797	221	7	description	description	NOUN
ap-1797	221	8	will	will	AUX
ap-1797	221	9	break	break	VERB
ap-1797	221	10	down	down	ADP
ap-1797	221	11	.	.	PUNCT
ap-1797	222	1	the	the	DET
ap-1797	222	2	instability	instability	NOUN
ap-1797	222	3	does	do	AUX
ap-1797	222	4	not	not	PART
ap-1797	222	5	necessarily	necessarily	ADV
ap-1797	222	6	lead	lead	VERB
ap-1797	222	7	immediately	immediately	ADV
ap-1797	222	8	to	to	ADP
ap-1797	222	9	a	a	DET
ap-1797	222	10	destruction	destruction	NOUN
ap-1797	222	11	of	of	ADP
ap-1797	222	12	the	the	DET
ap-1797	222	13	original	original	ADJ
ap-1797	222	14	oscillating	oscillate	VERB
ap-1797	222	15	behavior	behavior	NOUN
ap-1797	222	16	,	,	PUNCT
ap-1797	222	17	as	as	SCONJ
ap-1797	222	18	is	be	AUX
ap-1797	222	19	shown	show	VERB
ap-1797	222	20	for	for	ADP
ap-1797	222	21	the	the	DET
ap-1797	222	22	example	example	NOUN
ap-1797	222	23	with	with	ADP
ap-1797	222	24	g	g	PROPN
ap-1797	222	25	=	=	PROPN
ap-1797	222	26	0.2	0.2	NUM
ap-1797	222	27	and	and	CCONJ
ap-1797	222	28	γ	γ	X
ap-1797	222	29	=	=	SYM
ap-1797	222	30	0.04	0.04	NUM
ap-1797	222	31	in	in	ADP
ap-1797	222	32	figure	figure	NOUN
ap-1797	222	33	7b	7b	NOUN
ap-1797	222	34	,	,	PUNCT
ap-1797	222	35	i.e.	i.e.	X
ap-1797	222	36	very	very	ADV
ap-1797	222	37	close	close	ADJ
ap-1797	222	38	to	to	ADP
ap-1797	222	39	γep	γep	PRON
ap-1797	222	40	.	.	PUNCT
ap-1797	223	1	even	even	ADV
ap-1797	223	2	for	for	ADP
ap-1797	223	3	a	a	DET
ap-1797	223	4	gain	gain	NOUN
ap-1797	223	5	-	-	PUNCT
ap-1797	223	6	loss	loss	NOUN
ap-1797	223	7	influence	influence	NOUN
ap-1797	223	8	larger	large	ADJ
ap-1797	223	9	than	than	ADP
ap-1797	223	10	that	that	PRON
ap-1797	223	11	chosen	choose	VERB
ap-1797	223	12	for	for	ADP
ap-1797	223	13	figure	figure	NOUN
ap-1797	223	14	7a	7a	NOUN
ap-1797	223	15	it	it	PRON
ap-1797	223	16	was	be	AUX
ap-1797	223	17	possible	possible	ADJ
ap-1797	223	18	to	to	PART
ap-1797	223	19	find	find	VERB
ap-1797	223	20	a	a	DET
ap-1797	223	21	stable	stable	ADJ
ap-1797	223	22	oscillation	oscillation	NOUN
ap-1797	223	23	for	for	ADP
ap-1797	223	24	the	the	DET
ap-1797	223	25	phase	phase	NOUN
ap-1797	223	26	ϕ	ϕ	NOUN
ap-1797	223	27	=	=	NOUN
ap-1797	223	28	π/2	π/2	NUM
ap-1797	223	29	.	.	PUNCT
ap-1797	224	1	the	the	DET
ap-1797	224	2	behavior	behavior	NOUN
ap-1797	224	3	known	know	VERB
ap-1797	224	4	from	from	ADP
ap-1797	224	5	linear	linear	PROPN
ap-1797	224	6	systems	system	NOUN
ap-1797	224	7	re	re	NOUN
ap-1797	225	1	-	-	NOUN
ap-1797	226	1	emerges	emerge	NOUN
ap-1797	226	2	.	.	PUNCT
ap-1797	227	1	the	the	DET
ap-1797	227	2	probability	probability	NOUN
ap-1797	227	3	amplitude	amplitude	NOUN
ap-1797	227	4	almost	almost	ADV
ap-1797	227	5	pulsates	pulsate	VERB
ap-1797	227	6	in	in	ADP
ap-1797	227	7	both	both	DET
ap-1797	227	8	wells	well	NOUN
ap-1797	227	9	with	with	ADP
ap-1797	227	10	a	a	DET
ap-1797	227	11	low	low	ADJ
ap-1797	227	12	frequency	frequency	NOUN
ap-1797	227	13	.	.	PUNCT
ap-1797	228	1	from	from	ADP
ap-1797	228	2	the	the	DET
ap-1797	228	3	dynamical	dynamical	ADJ
ap-1797	228	4	point	point	NOUN
ap-1797	228	5	of	of	ADP
ap-1797	228	6	view	view	NOUN
ap-1797	228	7	the	the	DET
ap-1797	228	8	solutions	solution	NOUN
ap-1797	228	9	of	of	ADP
ap-1797	228	10	the	the	DET
ap-1797	228	11	time	time	NOUN
ap-1797	228	12	-	-	PUNCT
ap-1797	228	13	independent	independent	ADJ
ap-1797	228	14	gross	gross	ADJ
ap-1797	228	15	-	-	PUNCT
ap-1797	228	16	pitaevskii	pitaevskii	ADJ
ap-1797	228	17	equation	equation	NOUN
ap-1797	228	18	(	(	PUNCT
ap-1797	228	19	6	6	NUM
ap-1797	228	20	)	)	PUNCT
ap-1797	228	21	with	with	ADP
ap-1797	228	22	complex	complex	ADJ
ap-1797	228	23	eigenvalues	eigenvalue	NOUN
ap-1797	228	24	have	have	VERB
ap-1797	228	25	to	to	PART
ap-1797	228	26	be	be	AUX
ap-1797	228	27	considered	consider	VERB
ap-1797	228	28	with	with	ADP
ap-1797	228	29	some	some	DET
ap-1797	228	30	care	care	NOUN
ap-1797	228	31	.	.	PUNCT
ap-1797	229	1	strictly	strictly	ADV
ap-1797	229	2	speaking	speak	VERB
ap-1797	229	3	,	,	PUNCT
ap-1797	229	4	they	they	PRON
ap-1797	229	5	lose	lose	VERB
ap-1797	229	6	their	their	PRON
ap-1797	229	7	physical	physical	ADJ
ap-1797	229	8	relevance	relevance	NOUN
ap-1797	229	9	.	.	PUNCT
ap-1797	230	1	due	due	ADP
ap-1797	230	2	to	to	ADP
ap-1797	230	3	the	the	DET
ap-1797	230	4	decay	decay	NOUN
ap-1797	230	5	or	or	CCONJ
ap-1797	230	6	growth	growth	NOUN
ap-1797	230	7	of	of	ADP
ap-1797	230	8	the	the	DET
ap-1797	230	9	probability	probability	NOUN
ap-1797	230	10	amplitude	amplitude	NOUN
ap-1797	230	11	mentioned	mention	VERB
ap-1797	230	12	above	above	ADP
ap-1797	230	13	the	the	DET
ap-1797	230	14	nonlinear	nonlinear	ADJ
ap-1797	230	15	term	term	NOUN
ap-1797	230	16	−g|ψ|2	−g|ψ|2	NOUN
ap-1797	230	17	in	in	ADP
ap-1797	230	18	the	the	DET
ap-1797	230	19	hamiltonian	hamiltonian	NOUN
ap-1797	230	20	becomes	become	VERB
ap-1797	230	21	explicitly	explicitly	ADV
ap-1797	230	22	time	time	NOUN
ap-1797	230	23	dependent	dependent	ADJ
ap-1797	230	24	.	.	PUNCT
ap-1797	231	1	thus	thus	ADV
ap-1797	231	2	,	,	PUNCT
ap-1797	231	3	the	the	DET
ap-1797	231	4	states	state	NOUN
ap-1797	231	5	are	be	AUX
ap-1797	231	6	not	not	PART
ap-1797	231	7	true	true	ADJ
ap-1797	231	8	stationary	stationary	ADJ
ap-1797	231	9	solutions	solution	NOUN
ap-1797	231	10	of	of	ADP
ap-1797	231	11	the	the	DET
ap-1797	231	12	time	time	NOUN
ap-1797	231	13	-	-	PUNCT
ap-1797	231	14	dependent	dependent	ADJ
ap-1797	231	15	gross	gross	ADJ
ap-1797	231	16	-	-	PUNCT
ap-1797	231	17	pitaevskii	pitaevskii	ADJ
ap-1797	231	18	equation	equation	NOUN
ap-1797	231	19	(	(	PUNCT
ap-1797	231	20	1	1	NUM
ap-1797	231	21	)	)	PUNCT
ap-1797	231	22	.	.	PUNCT
ap-1797	232	1	they	they	PRON
ap-1797	232	2	are	be	AUX
ap-1797	232	3	,	,	PUNCT
ap-1797	232	4	however	however	ADV
ap-1797	232	5	,	,	PUNCT
ap-1797	232	6	still	still	ADV
ap-1797	232	7	useful	useful	ADJ
ap-1797	232	8	to	to	PART
ap-1797	232	9	indicate	indicate	VERB
ap-1797	232	10	the	the	DET
ap-1797	232	11	264	264	NUM
ap-1797	232	12	vol	vol	NOUN
ap-1797	232	13	.	.	PUNCT
ap-1797	233	1	53	53	NUM
ap-1797	233	2	no	no	NOUN
ap-1797	233	3	.	.	PUNCT
ap-1797	234	1	3/2013	3/2013	PROPN
ap-1797	234	2	stationary	stationary	ADJ
ap-1797	234	3	and	and	CCONJ
ap-1797	234	4	dynamical	dynamical	ADJ
ap-1797	234	5	solutions	solution	NOUN
ap-1797	234	6	of	of	ADP
ap-1797	234	7	the	the	DET
ap-1797	234	8	gross	gross	ADJ
ap-1797	234	9	-	-	PUNCT
ap-1797	234	10	pitaevskii	pitaevskii	ADJ
ap-1797	234	11	equation	equation	NOUN
ap-1797	234	12	0	0	NUM
ap-1797	234	13	1	1	NUM
ap-1797	234	14	2	2	NUM
ap-1797	234	15	3	3	NUM
ap-1797	234	16	4	4	NUM
ap-1797	234	17	5	5	NUM
ap-1797	234	18	6	6	NUM
ap-1797	234	19	7	7	NUM
ap-1797	234	20	8	8	NUM
ap-1797	234	21	9	9	NUM
ap-1797	234	22	10	10	NUM
ap-1797	234	23	0	0	NUM
ap-1797	234	24	10	10	NUM
ap-1797	234	25	20	20	NUM
ap-1797	234	26	30	30	NUM
ap-1797	234	27	40	40	NUM
ap-1797	234	28	50	50	NUM
ap-1797	234	29	n	n	PRON
ap-1797	234	30	2	2	NUM
ap-1797	234	31	t	t	NOUN
ap-1797	234	32	actual	actual	ADJ
ap-1797	234	33	time	time	NOUN
ap-1797	234	34	developement	developement	NOUN
ap-1797	234	35	exp(−2	exp(−2	NUM
ap-1797	234	36	imµt	imµt	ADJ
ap-1797	234	37	)	)	PUNCT
ap-1797	234	38	figure	figure	NOUN
ap-1797	234	39	8	8	NUM
ap-1797	234	40	.	.	PUNCT
ap-1797	235	1	temporal	temporal	ADJ
ap-1797	235	2	evolution	evolution	NOUN
ap-1797	235	3	of	of	ADP
ap-1797	235	4	the	the	DET
ap-1797	235	5	norm	norm	NOUN
ap-1797	235	6	of	of	ADP
ap-1797	235	7	an	an	DET
ap-1797	235	8	initial	initial	ADJ
ap-1797	235	9	complex	complex	ADJ
ap-1797	235	10	eigenvalue	eigenvalue	ADJ
ap-1797	235	11	state	state	NOUN
ap-1797	235	12	with	with	ADP
ap-1797	235	13	imµ	imµ	PROPN
ap-1797	235	14	>	>	X
ap-1797	235	15	0	0	X
ap-1797	235	16	.	.	PUNCT
ap-1797	236	1	the	the	DET
ap-1797	236	2	parameters	parameter	NOUN
ap-1797	236	3	are	be	AUX
ap-1797	236	4	g	g	NOUN
ap-1797	236	5	=	=	NUM
ap-1797	236	6	0.2	0.2	NUM
ap-1797	236	7	and	and	CCONJ
ap-1797	236	8	γ	γ	X
ap-1797	236	9	=	=	SYM
ap-1797	236	10	0.03	0.03	NUM
ap-1797	236	11	.	.	PUNCT
ap-1797	237	1	temporal	temporal	ADJ
ap-1797	237	2	evolution	evolution	NOUN
ap-1797	237	3	of	of	ADP
ap-1797	237	4	the	the	DET
ap-1797	237	5	condensate	condensate	NOUN
ap-1797	237	6	.	.	PUNCT
ap-1797	238	1	for	for	ADP
ap-1797	238	2	example	example	NOUN
ap-1797	238	3	,	,	PUNCT
ap-1797	238	4	it	it	PRON
ap-1797	238	5	was	be	AUX
ap-1797	238	6	possible	possible	ADJ
ap-1797	238	7	above	above	ADV
ap-1797	238	8	to	to	PART
ap-1797	238	9	explain	explain	VERB
ap-1797	238	10	the	the	DET
ap-1797	238	11	explosion	explosion	NOUN
ap-1797	238	12	of	of	ADP
ap-1797	238	13	the	the	DET
ap-1797	238	14	condensate	condensate	NOUN
ap-1797	238	15	wave	wave	NOUN
ap-1797	238	16	function	function	NOUN
ap-1797	238	17	in	in	ADP
ap-1797	238	18	figure	figure	NOUN
ap-1797	238	19	7a	7a	NUM
ap-1797	238	20	by	by	ADP
ap-1797	238	21	the	the	DET
ap-1797	238	22	presence	presence	NOUN
ap-1797	238	23	of	of	ADP
ap-1797	238	24	the	the	DET
ap-1797	238	25	growing	grow	VERB
ap-1797	238	26	pt	pt	NOUN
ap-1797	238	27	broken	break	VERB
ap-1797	238	28	state	state	NOUN
ap-1797	238	29	.	.	PUNCT
ap-1797	239	1	furthermore	furthermore	ADV
ap-1797	239	2	,	,	PUNCT
ap-1797	239	3	it	it	PRON
ap-1797	239	4	is	be	AUX
ap-1797	239	5	possible	possible	ADJ
ap-1797	239	6	to	to	PART
ap-1797	239	7	show	show	VERB
ap-1797	239	8	that	that	SCONJ
ap-1797	239	9	the	the	DET
ap-1797	239	10	complex	complex	ADJ
ap-1797	239	11	eigenvalue	eigenvalue	ADJ
ap-1797	239	12	solutions	solution	NOUN
ap-1797	239	13	can	can	AUX
ap-1797	239	14	still	still	ADV
ap-1797	239	15	indicate	indicate	VERB
ap-1797	239	16	the	the	DET
ap-1797	239	17	actual	actual	ADJ
ap-1797	239	18	temporal	temporal	ADJ
ap-1797	239	19	evolution	evolution	NOUN
ap-1797	239	20	of	of	ADP
ap-1797	239	21	an	an	DET
ap-1797	239	22	initial	initial	ADJ
ap-1797	239	23	wave	wave	NOUN
ap-1797	239	24	packet	packet	NOUN
ap-1797	239	25	.	.	PUNCT
ap-1797	240	1	in	in	ADP
ap-1797	240	2	particular	particular	ADJ
ap-1797	240	3	,	,	PUNCT
ap-1797	240	4	for	for	ADP
ap-1797	240	5	small	small	ADJ
ap-1797	240	6	times	time	NOUN
ap-1797	240	7	the	the	DET
ap-1797	240	8	prediction	prediction	NOUN
ap-1797	240	9	from	from	ADP
ap-1797	240	10	the	the	DET
ap-1797	240	11	“	"	PUNCT
ap-1797	240	12	stationary	stationary	ADJ
ap-1797	240	13	”	"	PUNCT
ap-1797	240	14	complex	complex	ADJ
ap-1797	240	15	eigenvalue	eigenvalue	NOUN
ap-1797	240	16	solutions	solution	NOUN
ap-1797	240	17	for	for	ADP
ap-1797	240	18	the	the	DET
ap-1797	240	19	norm	norm	NOUN
ap-1797	240	20	n2	n2	NOUN
ap-1797	240	21	=	=	SYM
ap-1797	240	22	∫	∫	PROPN
ap-1797	240	23	|ψ|2	|ψ|2	PROPN
ap-1797	240	24	dx	dx	PROPN
ap-1797	240	25	describes	describe	VERB
ap-1797	240	26	very	very	ADV
ap-1797	240	27	well	well	ADV
ap-1797	240	28	the	the	DET
ap-1797	240	29	true	true	ADJ
ap-1797	240	30	onset	onset	NOUN
ap-1797	240	31	of	of	ADP
ap-1797	240	32	the	the	DET
ap-1797	240	33	growth	growth	NOUN
ap-1797	240	34	,	,	PUNCT
ap-1797	240	35	as	as	SCONJ
ap-1797	240	36	can	can	AUX
ap-1797	240	37	be	be	AUX
ap-1797	240	38	seen	see	VERB
ap-1797	240	39	for	for	ADP
ap-1797	240	40	an	an	DET
ap-1797	240	41	initial	initial	ADJ
ap-1797	240	42	state	state	NOUN
ap-1797	240	43	with	with	ADP
ap-1797	240	44	imµ	imµ	PROPN
ap-1797	240	45	>	>	X
ap-1797	240	46	0	0	PUNCT
ap-1797	241	1	in	in	ADP
ap-1797	241	2	figure	figure	NOUN
ap-1797	241	3	8	8	NUM
ap-1797	241	4	.	.	PUNCT
ap-1797	241	5	to	to	PART
ap-1797	241	6	investigate	investigate	VERB
ap-1797	241	7	the	the	DET
ap-1797	241	8	correspondence	correspondence	NOUN
ap-1797	241	9	of	of	ADP
ap-1797	241	10	the	the	DET
ap-1797	241	11	complex	complex	ADJ
ap-1797	241	12	eigenvalue	eigenvalue	ADJ
ap-1797	241	13	solutions	solution	NOUN
ap-1797	241	14	with	with	ADP
ap-1797	241	15	the	the	DET
ap-1797	241	16	exact	exact	ADJ
ap-1797	241	17	time	time	NOUN
ap-1797	241	18	integration	integration	NOUN
ap-1797	241	19	for	for	ADP
ap-1797	241	20	longer	long	ADJ
ap-1797	241	21	times	time	NOUN
ap-1797	241	22	we	we	PRON
ap-1797	241	23	introduce	introduce	VERB
ap-1797	241	24	the	the	DET
ap-1797	241	25	difference	difference	NOUN
ap-1797	241	26	d	d	NOUN
ap-1797	241	27	=	=	SYM
ap-1797	241	28	1	1	NUM
ap-1797	241	29	n	n	NOUN
ap-1797	241	30	(	(	PUNCT
ap-1797	241	31	√∫	√∫	ADJ
ap-1797	241	32	right	right	INTJ
ap-1797	241	33	well	well	INTJ
ap-1797	241	34	|ψ|	|ψ|	PROPN
ap-1797	241	35	2	2	NUM
ap-1797	241	36	dx	dx	NOUN
ap-1797	241	37	−	−	PROPN
ap-1797	241	38	√∫	√∫	NOUN
ap-1797	241	39	left	leave	VERB
ap-1797	241	40	well	well	INTJ
ap-1797	241	41	|ψ|	|ψ|	PROPN
ap-1797	241	42	2	2	NUM
ap-1797	241	43	dx	dx	PROPN
ap-1797	241	44	)	)	PUNCT
ap-1797	241	45	,	,	PUNCT
ap-1797	241	46	(	(	PUNCT
ap-1797	241	47	15	15	NUM
ap-1797	241	48	)	)	PUNCT
ap-1797	241	49	of	of	ADP
ap-1797	241	50	the	the	DET
ap-1797	241	51	wave	wave	NOUN
ap-1797	241	52	function	function	NOUN
ap-1797	241	53	’s	’s	PART
ap-1797	241	54	norm	norm	NOUN
ap-1797	241	55	in	in	ADP
ap-1797	241	56	the	the	DET
ap-1797	241	57	right	right	NOUN
ap-1797	241	58	and	and	CCONJ
ap-1797	241	59	left	leave	VERB
ap-1797	241	60	wells	well	NOUN
ap-1797	241	61	.	.	PUNCT
ap-1797	242	1	it	it	PRON
ap-1797	242	2	tells	tell	VERB
ap-1797	242	3	us	we	PRON
ap-1797	242	4	how	how	SCONJ
ap-1797	242	5	the	the	DET
ap-1797	242	6	probability	probability	NOUN
ap-1797	242	7	density	density	NOUN
ap-1797	242	8	is	be	AUX
ap-1797	242	9	distributed	distribute	VERB
ap-1797	242	10	in	in	ADP
ap-1797	242	11	both	both	DET
ap-1797	242	12	wells	well	NOUN
ap-1797	242	13	.	.	PUNCT
ap-1797	243	1	a	a	DET
ap-1797	243	2	positive	positive	ADJ
ap-1797	243	3	value	value	NOUN
ap-1797	243	4	signalizes	signalize	VERB
ap-1797	243	5	a	a	DET
ap-1797	243	6	higher	high	ADJ
ap-1797	243	7	probability	probability	NOUN
ap-1797	243	8	density	density	NOUN
ap-1797	243	9	in	in	ADP
ap-1797	243	10	the	the	DET
ap-1797	243	11	right	right	ADJ
ap-1797	243	12	well	well	NOUN
ap-1797	243	13	with	with	ADP
ap-1797	243	14	gain	gain	NOUN
ap-1797	243	15	,	,	PUNCT
ap-1797	243	16	whereas	whereas	SCONJ
ap-1797	243	17	a	a	DET
ap-1797	243	18	negative	negative	ADJ
ap-1797	243	19	value	value	NOUN
ap-1797	243	20	indicates	indicate	VERB
ap-1797	243	21	a	a	DET
ap-1797	243	22	concentration	concentration	NOUN
ap-1797	243	23	of	of	ADP
ap-1797	243	24	the	the	DET
ap-1797	243	25	condensate	condensate	NOUN
ap-1797	243	26	’s	’s	PART
ap-1797	243	27	probability	probability	NOUN
ap-1797	243	28	density	density	NOUN
ap-1797	243	29	in	in	ADP
ap-1797	243	30	the	the	DET
ap-1797	243	31	left	left	ADJ
ap-1797	243	32	well	well	NOUN
ap-1797	243	33	with	with	ADP
ap-1797	243	34	loss	loss	NOUN
ap-1797	243	35	.	.	PUNCT
ap-1797	244	1	in	in	ADP
ap-1797	244	2	figure	figure	NOUN
ap-1797	244	3	9	9	NUM
ap-1797	244	4	we	we	PRON
ap-1797	244	5	compare	compare	VERB
ap-1797	244	6	the	the	DET
ap-1797	244	7	norm	norm	NOUN
ap-1797	244	8	difference	difference	NOUN
ap-1797	244	9	d	d	PROPN
ap-1797	244	10	of	of	ADP
ap-1797	244	11	the	the	DET
ap-1797	244	12	correct	correct	ADJ
ap-1797	244	13	temporal	temporal	ADJ
ap-1797	244	14	evolution	evolution	NOUN
ap-1797	244	15	with	with	ADP
ap-1797	244	16	that	that	PRON
ap-1797	244	17	of	of	ADP
ap-1797	244	18	the	the	DET
ap-1797	244	19	complex	complex	ADJ
ap-1797	244	20	eigenvalue	eigenvalue	NOUN
ap-1797	244	21	solution	solution	NOUN
ap-1797	244	22	with	with	ADP
ap-1797	244	23	positive	positive	ADJ
ap-1797	244	24	imaginary	imaginary	ADJ
ap-1797	244	25	part	part	NOUN
ap-1797	244	26	,	,	PUNCT
ap-1797	244	27	i.e.	i.e.	X
ap-1797	244	28	the	the	DET
ap-1797	244	29	growing	grow	VERB
ap-1797	244	30	state	state	NOUN
ap-1797	244	31	for	for	ADP
ap-1797	244	32	the	the	DET
ap-1797	244	33	same	same	ADJ
ap-1797	244	34	parameters	parameter	NOUN
ap-1797	244	35	.	.	PUNCT
ap-1797	245	1	since	since	SCONJ
ap-1797	245	2	the	the	DET
ap-1797	245	3	norm	norm	NOUN
ap-1797	245	4	of	of	ADP
ap-1797	245	5	the	the	DET
ap-1797	245	6	time	time	NOUN
ap-1797	245	7	evolved	evolve	VERB
ap-1797	245	8	wave	wave	NOUN
ap-1797	245	9	changes	change	NOUN
ap-1797	245	10	due	due	ADJ
ap-1797	245	11	to	to	ADP
ap-1797	245	12	the	the	DET
ap-1797	245	13	gain	gain	NOUN
ap-1797	245	14	-	-	PUNCT
ap-1797	245	15	loss	loss	NOUN
ap-1797	245	16	part	part	NOUN
ap-1797	245	17	of	of	ADP
ap-1797	245	18	the	the	DET
ap-1797	245	19	potential	potential	NOUN
ap-1797	245	20	we	we	PRON
ap-1797	245	21	have	have	VERB
ap-1797	245	22	to	to	PART
ap-1797	245	23	adapt	adapt	VERB
ap-1797	245	24	the	the	DET
ap-1797	245	25	effective	effective	ADJ
ap-1797	245	26	g	g	NOUN
ap-1797	245	27	in	in	ADP
ap-1797	245	28	the	the	DET
ap-1797	245	29	stationary	stationary	ADJ
ap-1797	245	30	gross	gross	ADJ
ap-1797	245	31	-	-	PUNCT
ap-1797	245	32	pitaevskii	pitaevskii	ADJ
ap-1797	245	33	equation	equation	NOUN
ap-1797	245	34	(	(	PUNCT
ap-1797	245	35	6	6	NUM
ap-1797	245	36	)	)	PUNCT
ap-1797	245	37	,	,	PUNCT
ap-1797	245	38	g	g	PROPN
ap-1797	245	39	→	→	SYM
ap-1797	245	40	gn2	gn2	NOUN
ap-1797	245	41	,	,	PUNCT
ap-1797	245	42	(	(	PUNCT
ap-1797	245	43	16	16	NUM
ap-1797	245	44	)	)	PUNCT
ap-1797	245	45	such	such	ADJ
ap-1797	245	46	that	that	SCONJ
ap-1797	245	47	the	the	DET
ap-1797	245	48	two	two	NUM
ap-1797	245	49	norm	norm	NOUN
ap-1797	245	50	differences	difference	NOUN
ap-1797	245	51	are	be	AUX
ap-1797	245	52	comparable	comparable	ADJ
ap-1797	245	53	.	.	PUNCT
ap-1797	246	1	in	in	ADP
ap-1797	246	2	figure	figure	NOUN
ap-1797	246	3	9a	9a	NOUN
ap-1797	246	4	we	we	PRON
ap-1797	246	5	plot	plot	VERB
ap-1797	246	6	d	d	NOUN
ap-1797	246	7	for	for	ADP
ap-1797	246	8	the	the	DET
ap-1797	246	9	situation	situation	NOUN
ap-1797	246	10	depicted	depict	VERB
ap-1797	246	11	in	in	ADP
ap-1797	246	12	figure	figure	NOUN
ap-1797	246	13	7	7	NUM
ap-1797	246	14	.	.	PUNCT
ap-1797	246	15	with	with	ADP
ap-1797	246	16	increasing	increase	VERB
ap-1797	246	17	time	time	NOUN
ap-1797	246	18	the	the	DET
ap-1797	246	19	state	state	NOUN
ap-1797	246	20	first	first	ADJ
ap-1797	246	21	decays	decay	NOUN
ap-1797	246	22	and	and	CCONJ
ap-1797	246	23	the	the	DET
ap-1797	246	24	norm	norm	NOUN
ap-1797	246	25	drops	drop	VERB
ap-1797	246	26	.	.	PUNCT
ap-1797	247	1	at	at	ADP
ap-1797	247	2	low	low	ADJ
ap-1797	247	3	values	value	NOUN
ap-1797	247	4	of	of	ADP
ap-1797	247	5	the	the	DET
ap-1797	247	6	norm	norm	NOUN
ap-1797	247	7	the	the	DET
ap-1797	247	8	effective	effective	ADJ
ap-1797	247	9	g	g	NOUN
ap-1797	247	10	(	(	PUNCT
ap-1797	247	11	16	16	NUM
ap-1797	247	12	)	)	PUNCT
ap-1797	247	13	assumes	assume	VERB
ap-1797	247	14	values	value	NOUN
ap-1797	247	15	at	at	ADP
ap-1797	247	16	which	which	PRON
ap-1797	247	17	only	only	ADV
ap-1797	247	18	the	the	DET
ap-1797	247	19	true	true	ADJ
ap-1797	247	20	stationary	stationary	ADJ
ap-1797	247	21	states	state	NOUN
ap-1797	247	22	with	with	ADP
ap-1797	247	23	real	real	ADJ
ap-1797	247	24	eigenvalues	eigenvalue	NOUN
ap-1797	247	25	and	and	CCONJ
ap-1797	247	26	d	d	NOUN
ap-1797	247	27	=	=	SYM
ap-1797	247	28	0	0	NUM
ap-1797	247	29	exist	exist	VERB
ap-1797	247	30	.	.	PUNCT
ap-1797	248	1	the	the	DET
ap-1797	248	2	latter	latter	ADJ
ap-1797	248	3	property	property	NOUN
ap-1797	248	4	can	can	AUX
ap-1797	248	5	be	be	AUX
ap-1797	248	6	seen	see	VERB
ap-1797	248	7	in	in	ADP
ap-1797	248	8	the	the	DET
ap-1797	248	9	figure	figure	NOUN
ap-1797	248	10	.	.	PUNCT
ap-1797	249	1	however	however	ADV
ap-1797	249	2	,	,	PUNCT
ap-1797	249	3	at	at	ADP
ap-1797	249	4	t	t	PROPN
ap-1797	249	5	≈	≈	PROPN
ap-1797	249	6	12	12	NUM
ap-1797	249	7	the	the	DET
ap-1797	249	8	overlap	overlap	NOUN
ap-1797	249	9	with	with	ADP
ap-1797	249	10	the	the	DET
ap-1797	249	11	growing	grow	VERB
ap-1797	249	12	−0.8	−0.8	CCONJ
ap-1797	249	13	−0.6	−0.6	PROPN
ap-1797	249	14	−0.4	−0.4	PUNCT
ap-1797	249	15	−0.2	−0.2	PROPN
ap-1797	249	16	0.0	0.0	NUM
ap-1797	250	1	0.2	0.2	NUM
ap-1797	250	2	0.4	0.4	NUM
ap-1797	250	3	0.6	0.6	NUM
ap-1797	250	4	0.8	0.8	NUM
ap-1797	250	5	1.0	1.0	NUM
ap-1797	250	6	0	0	NUM
ap-1797	250	7	20	20	NUM
ap-1797	250	8	40	40	NUM
ap-1797	250	9	60	60	NUM
ap-1797	250	10	80	80	NUM
ap-1797	250	11	100	100	NUM
ap-1797	250	12	120	120	NUM
ap-1797	250	13	140	140	NUM
ap-1797	250	14	160	160	NUM
ap-1797	250	15	d	d	NOUN
ap-1797	250	16	t	t	PROPN
ap-1797	250	17	(	(	PUNCT
ap-1797	250	18	a	a	NOUN
ap-1797	250	19	)	)	PUNCT
ap-1797	250	20	0.3	0.3	NUM
ap-1797	250	21	0.4	0.4	NUM
ap-1797	250	22	0.5	0.5	NUM
ap-1797	250	23	0.6	0.6	NUM
ap-1797	250	24	0.7	0.7	NUM
ap-1797	250	25	0.8	0.8	NUM
ap-1797	250	26	0.9	0.9	NUM
ap-1797	250	27	1.0	1.0	NUM
ap-1797	250	28	0	0	NUM
ap-1797	250	29	10	10	NUM
ap-1797	250	30	20	20	NUM
ap-1797	250	31	30	30	NUM
ap-1797	250	32	40	40	NUM
ap-1797	250	33	50	50	NUM
ap-1797	250	34	60	60	NUM
ap-1797	250	35	70	70	NUM
ap-1797	250	36	80	80	NUM
ap-1797	250	37	d	d	NOUN
ap-1797	250	38	t	t	PROPN
ap-1797	250	39	(	(	PUNCT
ap-1797	250	40	b	b	NOUN
ap-1797	250	41	)	)	PUNCT
ap-1797	250	42	actual	actual	ADJ
ap-1797	250	43	time	time	NOUN
ap-1797	250	44	developement	developement	NOUN
ap-1797	250	45	adapted	adapt	VERB
ap-1797	250	46	broken	break	VERB
ap-1797	250	47	eigenstate	eigenstate	NOUN
ap-1797	250	48	figure	figure	NOUN
ap-1797	250	49	9	9	NUM
ap-1797	250	50	.	.	PUNCT
ap-1797	250	51	comparison	comparison	NOUN
ap-1797	250	52	of	of	ADP
ap-1797	250	53	the	the	DET
ap-1797	250	54	norm	norm	NOUN
ap-1797	250	55	difference	difference	NOUN
ap-1797	250	56	d	d	PROPN
ap-1797	250	57	of	of	ADP
ap-1797	250	58	the	the	DET
ap-1797	250	59	correct	correct	ADJ
ap-1797	250	60	temporal	temporal	ADJ
ap-1797	250	61	evolution	evolution	NOUN
ap-1797	250	62	with	with	ADP
ap-1797	250	63	that	that	PRON
ap-1797	250	64	of	of	ADP
ap-1797	250	65	complex	complex	ADJ
ap-1797	250	66	eigenvalue	eigenvalue	ADJ
ap-1797	250	67	solutions	solution	NOUN
ap-1797	250	68	.	.	PUNCT
ap-1797	251	1	in	in	ADP
ap-1797	251	2	(	(	PUNCT
ap-1797	251	3	a	a	X
ap-1797	251	4	)	)	PUNCT
ap-1797	251	5	the	the	DET
ap-1797	251	6	same	same	ADJ
ap-1797	251	7	situation	situation	NOUN
ap-1797	251	8	as	as	SCONJ
ap-1797	251	9	in	in	ADP
ap-1797	251	10	figure	figure	NOUN
ap-1797	251	11	7	7	NUM
ap-1797	251	12	is	be	AUX
ap-1797	251	13	depicted	depict	VERB
ap-1797	251	14	,	,	PUNCT
ap-1797	251	15	whereas	whereas	SCONJ
ap-1797	251	16	(	(	PUNCT
ap-1797	251	17	b	b	X
ap-1797	251	18	)	)	PUNCT
ap-1797	251	19	shows	show	VERB
ap-1797	251	20	the	the	DET
ap-1797	251	21	evolution	evolution	NOUN
ap-1797	251	22	of	of	ADP
ap-1797	251	23	the	the	DET
ap-1797	251	24	complex	complex	ADJ
ap-1797	251	25	eigenvalue	eigenvalue	ADJ
ap-1797	251	26	state	state	NOUN
ap-1797	251	27	with	with	ADP
ap-1797	251	28	positive	positive	ADJ
ap-1797	251	29	imaginary	imaginary	ADJ
ap-1797	251	30	part	part	NOUN
ap-1797	251	31	.	.	PUNCT
ap-1797	252	1	in	in	ADP
ap-1797	252	2	both	both	DET
ap-1797	252	3	cases	case	NOUN
ap-1797	252	4	the	the	DET
ap-1797	252	5	norm	norm	NOUN
ap-1797	252	6	difference	difference	NOUN
ap-1797	252	7	follows	follow	VERB
ap-1797	252	8	the	the	DET
ap-1797	252	9	growing	grow	VERB
ap-1797	252	10	complex	complex	ADJ
ap-1797	252	11	eigenvalue	eigenvalue	ADJ
ap-1797	252	12	state	state	NOUN
ap-1797	252	13	for	for	ADP
ap-1797	252	14	long	long	ADJ
ap-1797	252	15	times	time	NOUN
ap-1797	252	16	.	.	PUNCT
ap-1797	253	1	γ	γ	PROPN
ap-1797	253	2	was	be	AUX
ap-1797	253	3	chosen	choose	VERB
ap-1797	253	4	to	to	PART
ap-1797	253	5	be	be	AUX
ap-1797	253	6	0.03	0.03	NUM
ap-1797	253	7	and	and	CCONJ
ap-1797	253	8	the	the	DET
ap-1797	253	9	initial	initial	ADJ
ap-1797	253	10	g	g	NOUN
ap-1797	253	11	was	be	AUX
ap-1797	253	12	0.2	0.2	NUM
ap-1797	253	13	.	.	PUNCT
ap-1797	254	1	eigenstate	eigenstate	NOUN
ap-1797	254	2	wins	win	NOUN
ap-1797	254	3	and	and	CCONJ
ap-1797	254	4	the	the	DET
ap-1797	254	5	norm	norm	NOUN
ap-1797	254	6	starts	start	VERB
ap-1797	254	7	to	to	PART
ap-1797	254	8	grow	grow	VERB
ap-1797	254	9	.	.	PUNCT
ap-1797	255	1	after	after	ADP
ap-1797	255	2	some	some	DET
ap-1797	255	3	oscillations	oscillation	NOUN
ap-1797	255	4	of	of	ADP
ap-1797	255	5	d	d	PROPN
ap-1797	255	6	,	,	PUNCT
ap-1797	255	7	one	one	PRON
ap-1797	255	8	observes	observe	VERB
ap-1797	255	9	for	for	ADP
ap-1797	255	10	times	time	NOUN
ap-1797	255	11	t	t	PROPN
ap-1797	255	12	>	>	X
ap-1797	255	13	120	120	NUM
ap-1797	255	14	that	that	SCONJ
ap-1797	255	15	the	the	DET
ap-1797	255	16	norm	norm	NOUN
ap-1797	255	17	differences	difference	NOUN
ap-1797	255	18	of	of	ADP
ap-1797	255	19	the	the	DET
ap-1797	255	20	two	two	NUM
ap-1797	255	21	calculations	calculation	NOUN
ap-1797	255	22	agree	agree	VERB
ap-1797	255	23	more	more	ADV
ap-1797	255	24	and	and	CCONJ
ap-1797	255	25	more	more	ADJ
ap-1797	255	26	.	.	PUNCT
ap-1797	256	1	this	this	PRON
ap-1797	256	2	indicates	indicate	VERB
ap-1797	256	3	that	that	SCONJ
ap-1797	256	4	the	the	DET
ap-1797	256	5	wave	wave	NOUN
ap-1797	256	6	function	function	NOUN
ap-1797	256	7	initially	initially	ADV
ap-1797	256	8	prepared	prepare	VERB
ap-1797	256	9	in	in	ADP
ap-1797	256	10	a	a	DET
ap-1797	256	11	superposition	superposition	NOUN
ap-1797	256	12	of	of	ADP
ap-1797	256	13	two	two	NUM
ap-1797	256	14	eigenstates	eigenstate	NOUN
ap-1797	256	15	evolves	evolve	NOUN
ap-1797	256	16	into	into	ADP
ap-1797	256	17	the	the	DET
ap-1797	256	18	shape	shape	NOUN
ap-1797	256	19	of	of	ADP
ap-1797	256	20	the	the	DET
ap-1797	256	21	growing	grow	VERB
ap-1797	256	22	eigenstate	eigenstate	NOUN
ap-1797	256	23	for	for	ADP
ap-1797	256	24	long	long	ADJ
ap-1797	256	25	times	time	NOUN
ap-1797	256	26	.	.	PUNCT
ap-1797	257	1	that	that	PRON
ap-1797	257	2	is	be	AUX
ap-1797	257	3	,	,	PUNCT
ap-1797	257	4	the	the	DET
ap-1797	257	5	complex	complex	ADJ
ap-1797	257	6	eigenvalue	eigenvalue	ADJ
ap-1797	257	7	solution	solution	NOUN
ap-1797	257	8	with	with	ADP
ap-1797	257	9	positive	positive	ADJ
ap-1797	257	10	imaginary	imaginary	ADJ
ap-1797	257	11	part	part	NOUN
ap-1797	257	12	still	still	ADV
ap-1797	257	13	has	have	VERB
ap-1797	257	14	a	a	DET
ap-1797	257	15	meaning	meaning	NOUN
ap-1797	257	16	for	for	ADP
ap-1797	257	17	long	long	ADJ
ap-1797	257	18	times	time	NOUN
ap-1797	257	19	although	although	SCONJ
ap-1797	257	20	it	it	PRON
ap-1797	257	21	is	be	AUX
ap-1797	257	22	not	not	PART
ap-1797	257	23	a	a	DET
ap-1797	257	24	true	true	ADJ
ap-1797	257	25	stationary	stationary	ADJ
ap-1797	257	26	solution	solution	NOUN
ap-1797	257	27	of	of	ADP
ap-1797	257	28	the	the	DET
ap-1797	257	29	time	time	NOUN
ap-1797	257	30	-	-	PUNCT
ap-1797	257	31	dependent	dependent	ADJ
ap-1797	257	32	gross	gross	ADJ
ap-1797	257	33	-	-	PUNCT
ap-1797	257	34	pitaevskii	pitaevskii	ADJ
ap-1797	257	35	equation	equation	NOUN
ap-1797	257	36	(	(	PUNCT
ap-1797	257	37	1	1	NUM
ap-1797	257	38	)	)	PUNCT
ap-1797	257	39	.	.	PUNCT
ap-1797	258	1	a	a	DET
ap-1797	258	2	similar	similar	ADJ
ap-1797	258	3	behavior	behavior	NOUN
ap-1797	258	4	can	can	AUX
ap-1797	258	5	be	be	AUX
ap-1797	258	6	observed	observe	VERB
ap-1797	258	7	in	in	ADP
ap-1797	258	8	figure	figure	NOUN
ap-1797	258	9	9b	9b	NOUN
ap-1797	258	10	,	,	PUNCT
ap-1797	258	11	where	where	SCONJ
ap-1797	258	12	the	the	DET
ap-1797	258	13	initial	initial	ADJ
ap-1797	258	14	state	state	NOUN
ap-1797	258	15	was	be	AUX
ap-1797	258	16	the	the	DET
ap-1797	258	17	growing	grow	VERB
ap-1797	258	18	complex	complex	ADJ
ap-1797	258	19	eigenvalue	eigenvalue	NOUN
ap-1797	258	20	solution	solution	NOUN
ap-1797	258	21	of	of	ADP
ap-1797	258	22	(	(	PUNCT
ap-1797	258	23	6	6	NUM
ap-1797	258	24	)	)	PUNCT
ap-1797	258	25	.	.	PUNCT
ap-1797	259	1	since	since	SCONJ
ap-1797	259	2	we	we	PRON
ap-1797	259	3	start	start	VERB
ap-1797	259	4	with	with	ADP
ap-1797	259	5	the	the	DET
ap-1797	259	6	increasing	increase	VERB
ap-1797	259	7	norm	norm	NOUN
ap-1797	259	8	solution	solution	NOUN
ap-1797	259	9	the	the	DET
ap-1797	259	10	agreement	agreement	NOUN
ap-1797	259	11	between	between	ADP
ap-1797	259	12	both	both	DET
ap-1797	259	13	calculations	calculation	NOUN
ap-1797	259	14	sets	set	NOUN
ap-1797	259	15	in	in	ADP
ap-1797	259	16	earlier	early	ADJ
ap-1797	259	17	.	.	PUNCT
ap-1797	260	1	4	4	X
ap-1797	260	2	.	.	X
ap-1797	260	3	conclusion	conclusion	NOUN
ap-1797	260	4	the	the	DET
ap-1797	260	5	work	work	NOUN
ap-1797	260	6	presented	present	VERB
ap-1797	260	7	in	in	ADP
ap-1797	260	8	this	this	DET
ap-1797	260	9	article	article	NOUN
ap-1797	260	10	shows	show	VERB
ap-1797	260	11	that	that	SCONJ
ap-1797	260	12	pt	pt	PRON
ap-1797	260	13	symmetric	symmetric	ADJ
ap-1797	260	14	eigenfunctions	eigenfunction	NOUN
ap-1797	260	15	exist	exist	VERB
ap-1797	260	16	in	in	ADP
ap-1797	260	17	nonlinear	nonlinear	ADJ
ap-1797	260	18	quantum	quantum	ADJ
ap-1797	260	19	systems	system	NOUN
ap-1797	260	20	,	,	PUNCT
ap-1797	260	21	in	in	ADP
ap-1797	260	22	particular	particular	ADJ
ap-1797	260	23	,	,	PUNCT
ap-1797	260	24	in	in	ADP
ap-1797	260	25	bose	bose	NOUN
ap-1797	260	26	-	-	PUNCT
ap-1797	260	27	einstein	einstein	NOUN
ap-1797	260	28	condensates	condensate	NOUN
ap-1797	260	29	described	describe	VERB
ap-1797	260	30	by	by	ADP
ap-1797	260	31	the	the	DET
ap-1797	260	32	gross	gross	ADJ
ap-1797	260	33	-	-	PUNCT
ap-1797	260	34	pitaevskii	pitaevskii	ADJ
ap-1797	260	35	equation	equation	NOUN
ap-1797	260	36	.	.	PUNCT
ap-1797	261	1	the	the	DET
ap-1797	261	2	solutions	solution	NOUN
ap-1797	261	3	render	render	VERB
ap-1797	261	4	the	the	DET
ap-1797	261	5	hamiltonian	hamiltonian	NOUN
ap-1797	261	6	itself	itself	PRON
ap-1797	261	7	pt	pt	X
ap-1797	261	8	symmetric	symmetric	NOUN
ap-1797	261	9	.	.	PUNCT
ap-1797	262	1	a	a	DET
ap-1797	262	2	comparison	comparison	NOUN
ap-1797	262	3	of	of	ADP
ap-1797	262	4	numerically	numerically	ADV
ap-1797	262	5	exact	exact	ADJ
ap-1797	262	6	calculations	calculation	NOUN
ap-1797	262	7	and	and	CCONJ
ap-1797	262	8	a	a	DET
ap-1797	262	9	gaussian	gaussian	ADJ
ap-1797	262	10	approximation	approximation	NOUN
ap-1797	262	11	demonstrated	demonstrate	VERB
ap-1797	262	12	that	that	SCONJ
ap-1797	262	13	the	the	DET
ap-1797	262	14	gaussian	gaussian	NOUN
ap-1797	262	15	ansatz	ansatz	ADV
ap-1797	262	16	provides	provide	VERB
ap-1797	262	17	quantitatively	quantitatively	ADV
ap-1797	262	18	well	well	ADV
ap-1797	262	19	converged	converge	VERB
ap-1797	262	20	numerical	numerical	ADJ
ap-1797	262	21	results	result	NOUN
ap-1797	262	22	.	.	PUNCT
ap-1797	263	1	a	a	DET
ap-1797	263	2	fully	fully	ADV
ap-1797	263	3	three	three	NUM
ap-1797	263	4	-	-	PUNCT
ap-1797	263	5	dimensional	dimensional	ADJ
ap-1797	263	6	calculation	calculation	NOUN
ap-1797	263	7	of	of	ADP
ap-1797	263	8	the	the	DET
ap-1797	263	9	condensate	condensate	NOUN
ap-1797	263	10	is	be	AUX
ap-1797	263	11	possible	possible	ADJ
ap-1797	263	12	,	,	PUNCT
ap-1797	263	13	but	but	CCONJ
ap-1797	263	14	is	be	AUX
ap-1797	263	15	not	not	PART
ap-1797	263	16	necessary	necessary	ADJ
ap-1797	263	17	to	to	PART
ap-1797	263	18	describe	describe	VERB
ap-1797	263	19	the	the	DET
ap-1797	263	20	effects	effect	NOUN
ap-1797	263	21	appearing	appear	VERB
ap-1797	263	22	due	due	ADP
ap-1797	263	23	to	to	ADP
ap-1797	263	24	the	the	DET
ap-1797	263	25	non	non	ADJ
ap-1797	263	26	-	-	ADJ
ap-1797	263	27	hermitian	hermitian	ADJ
ap-1797	263	28	265	265	NUM
ap-1797	263	29	holger	holger	NOUN
ap-1797	263	30	cartarius	cartarius	NOUN
ap-1797	263	31	et	et	PROPN
ap-1797	263	32	al	al	PROPN
ap-1797	263	33	.	.	PROPN
ap-1797	263	34	acta	acta	PROPN
ap-1797	263	35	polytechnica	polytechnica	PROPN
ap-1797	263	36	gain	gain	NOUN
ap-1797	263	37	-	-	PUNCT
ap-1797	263	38	loss	loss	NOUN
ap-1797	263	39	potential	potential	NOUN
ap-1797	263	40	.	.	PUNCT
ap-1797	264	1	it	it	PRON
ap-1797	264	2	is	be	AUX
ap-1797	264	3	even	even	ADV
ap-1797	264	4	possible	possible	ADJ
ap-1797	264	5	to	to	PART
ap-1797	264	6	extract	extract	VERB
ap-1797	264	7	quantitative	quantitative	ADJ
ap-1797	264	8	values	value	NOUN
ap-1797	264	9	from	from	ADP
ap-1797	264	10	a	a	DET
ap-1797	264	11	one	one	NUM
ap-1797	264	12	-	-	PUNCT
ap-1797	264	13	dimensional	dimensional	ADJ
ap-1797	264	14	description	description	NOUN
ap-1797	264	15	of	of	ADP
ap-1797	264	16	the	the	DET
ap-1797	264	17	condensate	condensate	NOUN
ap-1797	264	18	containing	contain	VERB
ap-1797	264	19	only	only	ADV
ap-1797	264	20	the	the	DET
ap-1797	264	21	relevant	relevant	ADJ
ap-1797	264	22	direction	direction	NOUN
ap-1797	264	23	,	,	PUNCT
ap-1797	264	24	in	in	ADP
ap-1797	264	25	which	which	PRON
ap-1797	264	26	the	the	DET
ap-1797	264	27	pt	pt	ADJ
ap-1797	264	28	symmetric	symmetric	ADJ
ap-1797	264	29	potential	potential	ADJ
ap-1797	264	30	acts	act	NOUN
ap-1797	264	31	.	.	PUNCT
ap-1797	265	1	solutions	solution	NOUN
ap-1797	265	2	of	of	ADP
ap-1797	265	3	the	the	DET
ap-1797	265	4	time	time	NOUN
ap-1797	265	5	-	-	PUNCT
ap-1797	265	6	independent	independent	ADJ
ap-1797	265	7	gross	gross	ADJ
ap-1797	265	8	-	-	PUNCT
ap-1797	265	9	pitaevskii	pitaevskii	ADJ
ap-1797	265	10	equation	equation	NOUN
ap-1797	265	11	with	with	ADP
ap-1797	265	12	complex	complex	ADJ
ap-1797	265	13	energy	energy	NOUN
ap-1797	265	14	eigenvalues	eigenvalue	NOUN
ap-1797	265	15	are	be	AUX
ap-1797	265	16	found	find	VERB
ap-1797	265	17	as	as	ADV
ap-1797	265	18	well	well	ADV
ap-1797	265	19	,	,	PUNCT
ap-1797	265	20	and	and	CCONJ
ap-1797	265	21	belong	belong	VERB
ap-1797	265	22	to	to	ADP
ap-1797	265	23	eigenstates	eigenstate	NOUN
ap-1797	265	24	with	with	ADP
ap-1797	265	25	broken	broken	ADJ
ap-1797	265	26	pt	pt	NOUN
ap-1797	265	27	symmetry	symmetry	NOUN
ap-1797	265	28	,	,	PUNCT
ap-1797	265	29	destroying	destroy	VERB
ap-1797	265	30	the	the	DET
ap-1797	265	31	hamiltonian	hamiltonian	NOUN
ap-1797	265	32	’s	’s	PART
ap-1797	265	33	symmetry	symmetry	NOUN
ap-1797	265	34	.	.	PUNCT
ap-1797	266	1	they	they	PRON
ap-1797	266	2	have	have	VERB
ap-1797	266	3	no	no	DET
ap-1797	266	4	direct	direct	ADJ
ap-1797	266	5	physical	physical	ADJ
ap-1797	266	6	meaning	meaning	NOUN
ap-1797	266	7	,	,	PUNCT
ap-1797	266	8	since	since	SCONJ
ap-1797	266	9	they	they	PRON
ap-1797	266	10	are	be	AUX
ap-1797	266	11	not	not	PART
ap-1797	266	12	true	true	ADJ
ap-1797	266	13	stationary	stationary	ADJ
ap-1797	266	14	states	state	NOUN
ap-1797	266	15	of	of	ADP
ap-1797	266	16	the	the	DET
ap-1797	266	17	time	time	NOUN
ap-1797	266	18	-	-	PUNCT
ap-1797	266	19	dependent	dependent	ADJ
ap-1797	266	20	gross	gross	ADJ
ap-1797	266	21	-	-	PUNCT
ap-1797	266	22	pitaevskii	pitaevskii	ADJ
ap-1797	266	23	equation	equation	NOUN
ap-1797	266	24	due	due	ADP
ap-1797	266	25	to	to	ADP
ap-1797	266	26	their	their	PRON
ap-1797	266	27	complex	complex	ADJ
ap-1797	266	28	energy	energy	NOUN
ap-1797	266	29	eigenvalues	eigenvalue	NOUN
ap-1797	266	30	indicating	indicate	VERB
ap-1797	266	31	a	a	DET
ap-1797	266	32	growth	growth	NOUN
ap-1797	266	33	or	or	CCONJ
ap-1797	266	34	decay	decay	NOUN
ap-1797	266	35	of	of	ADP
ap-1797	266	36	the	the	DET
ap-1797	266	37	probability	probability	NOUN
ap-1797	266	38	amplitude	amplitude	NOUN
ap-1797	266	39	.	.	PUNCT
ap-1797	267	1	however	however	ADV
ap-1797	267	2	,	,	PUNCT
ap-1797	267	3	one	one	PRON
ap-1797	267	4	can	can	AUX
ap-1797	267	5	observe	observe	VERB
ap-1797	267	6	that	that	SCONJ
ap-1797	267	7	they	they	PRON
ap-1797	267	8	influence	influence	VERB
ap-1797	267	9	the	the	DET
ap-1797	267	10	ground	ground	NOUN
ap-1797	267	11	state	state	NOUN
ap-1797	267	12	.	.	PUNCT
ap-1797	268	1	for	for	ADP
ap-1797	268	2	nonvanishing	nonvanishe	VERB
ap-1797	268	3	nonlinearity	nonlinearity	NOUN
ap-1797	268	4	g	g	ADP
ap-1797	268	5	the	the	DET
ap-1797	268	6	complex	complex	ADJ
ap-1797	268	7	eigenvalue	eigenvalue	ADJ
ap-1797	268	8	solutions	solution	NOUN
ap-1797	268	9	bifurcate	bifurcate	NOUN
ap-1797	268	10	from	from	ADP
ap-1797	268	11	the	the	DET
ap-1797	268	12	ground	ground	NOUN
ap-1797	268	13	state	state	NOUN
ap-1797	268	14	when	when	SCONJ
ap-1797	268	15	a	a	DET
ap-1797	268	16	critical	critical	ADJ
ap-1797	268	17	value	value	NOUN
ap-1797	268	18	of	of	ADP
ap-1797	268	19	the	the	DET
ap-1797	268	20	gain	gain	NOUN
ap-1797	268	21	-	-	PUNCT
ap-1797	268	22	loss	loss	NOUN
ap-1797	268	23	parameter	parameter	NOUN
ap-1797	268	24	γ	γ	NOUN
ap-1797	268	25	is	be	AUX
ap-1797	268	26	exceeded	exceed	VERB
ap-1797	268	27	.	.	PUNCT
ap-1797	269	1	at	at	ADP
ap-1797	269	2	this	this	DET
ap-1797	269	3	point	point	NOUN
ap-1797	269	4	the	the	DET
ap-1797	269	5	ground	ground	NOUN
ap-1797	269	6	state	state	NOUN
ap-1797	269	7	becomes	become	VERB
ap-1797	269	8	unstable	unstable	ADJ
ap-1797	269	9	,	,	PUNCT
ap-1797	269	10	whereas	whereas	SCONJ
ap-1797	269	11	the	the	DET
ap-1797	269	12	excited	excited	ADJ
ap-1797	269	13	real	real	ADJ
ap-1797	269	14	eigenvalue	eigenvalue	NOUN
ap-1797	269	15	solution	solution	NOUN
ap-1797	269	16	is	be	AUX
ap-1797	269	17	not	not	PART
ap-1797	269	18	affected	affect	VERB
ap-1797	269	19	by	by	ADP
ap-1797	269	20	the	the	DET
ap-1797	269	21	appearance	appearance	NOUN
ap-1797	269	22	of	of	ADP
ap-1797	269	23	the	the	DET
ap-1797	269	24	new	new	ADJ
ap-1797	269	25	states	state	NOUN
ap-1797	269	26	and	and	CCONJ
ap-1797	269	27	stays	stay	VERB
ap-1797	269	28	stable	stable	ADJ
ap-1797	269	29	as	as	ADV
ap-1797	269	30	long	long	ADV
ap-1797	269	31	as	as	SCONJ
ap-1797	269	32	it	it	PRON
ap-1797	269	33	exists	exist	VERB
ap-1797	269	34	.	.	PUNCT
ap-1797	270	1	the	the	DET
ap-1797	270	2	time	time	NOUN
ap-1797	270	3	evolution	evolution	NOUN
ap-1797	270	4	of	of	ADP
ap-1797	270	5	the	the	DET
ap-1797	270	6	condensate	condensate	NOUN
ap-1797	270	7	showed	show	VERB
ap-1797	270	8	that	that	SCONJ
ap-1797	270	9	the	the	DET
ap-1797	270	10	eigensolutions	eigensolution	NOUN
ap-1797	270	11	of	of	ADP
ap-1797	270	12	the	the	DET
ap-1797	270	13	time	time	NOUN
ap-1797	270	14	-	-	PUNCT
ap-1797	270	15	independent	independent	ADJ
ap-1797	270	16	grosspitaevskii	grosspitaevskii	ADJ
ap-1797	270	17	equation	equation	NOUN
ap-1797	270	18	with	with	ADP
ap-1797	270	19	complex	complex	ADJ
ap-1797	270	20	eigenvalues	eigenvalue	NOUN
ap-1797	270	21	may	may	AUX
ap-1797	270	22	help	help	VERB
ap-1797	270	23	to	to	PART
ap-1797	270	24	estimate	estimate	VERB
ap-1797	270	25	the	the	DET
ap-1797	270	26	true	true	ADJ
ap-1797	270	27	temporal	temporal	ADJ
ap-1797	270	28	behavior	behavior	NOUN
ap-1797	270	29	of	of	ADP
ap-1797	270	30	a	a	DET
ap-1797	270	31	condensate	condensate	NOUN
ap-1797	270	32	wave	wave	NOUN
ap-1797	270	33	function	function	NOUN
ap-1797	270	34	.	.	PUNCT
ap-1797	271	1	for	for	ADP
ap-1797	271	2	small	small	ADJ
ap-1797	271	3	times	time	NOUN
ap-1797	271	4	,	,	PUNCT
ap-1797	271	5	the	the	DET
ap-1797	271	6	imaginary	imaginary	ADJ
ap-1797	271	7	part	part	NOUN
ap-1797	271	8	of	of	ADP
ap-1797	271	9	the	the	DET
ap-1797	271	10	energy	energy	NOUN
ap-1797	271	11	correctly	correctly	ADV
ap-1797	271	12	describes	describe	VERB
ap-1797	271	13	the	the	DET
ap-1797	271	14	onset	onset	NOUN
ap-1797	271	15	of	of	ADP
ap-1797	271	16	the	the	DET
ap-1797	271	17	wave	wave	NOUN
ap-1797	271	18	function	function	NOUN
ap-1797	271	19	’s	’s	PART
ap-1797	271	20	growth	growth	NOUN
ap-1797	271	21	or	or	CCONJ
ap-1797	271	22	decay	decay	NOUN
ap-1797	271	23	.	.	PUNCT
ap-1797	272	1	for	for	ADP
ap-1797	272	2	large	large	ADJ
ap-1797	272	3	times	time	NOUN
ap-1797	272	4	,	,	PUNCT
ap-1797	272	5	all	all	DET
ap-1797	272	6	initial	initial	ADJ
ap-1797	272	7	wave	wave	NOUN
ap-1797	272	8	functions	function	NOUN
ap-1797	272	9	tend	tend	VERB
ap-1797	272	10	to	to	ADP
ap-1797	272	11	the	the	DET
ap-1797	272	12	state	state	NOUN
ap-1797	272	13	with	with	ADP
ap-1797	272	14	positive	positive	ADJ
ap-1797	272	15	imaginary	imaginary	ADJ
ap-1797	272	16	part	part	NOUN
ap-1797	272	17	of	of	ADP
ap-1797	272	18	the	the	DET
ap-1797	272	19	energy	energy	NOUN
ap-1797	272	20	,	,	PUNCT
ap-1797	272	21	which	which	PRON
ap-1797	272	22	is	be	AUX
ap-1797	272	23	located	locate	VERB
ap-1797	272	24	predominantly	predominantly	ADV
ap-1797	272	25	in	in	ADP
ap-1797	272	26	the	the	DET
ap-1797	272	27	well	well	NOUN
ap-1797	272	28	with	with	ADP
ap-1797	272	29	gain	gain	NOUN
ap-1797	272	30	.	.	PUNCT
ap-1797	273	1	certainly	certainly	ADV
ap-1797	273	2	,	,	PUNCT
ap-1797	273	3	there	there	PRON
ap-1797	273	4	is	be	VERB
ap-1797	273	5	a	a	DET
ap-1797	273	6	number	number	NOUN
ap-1797	273	7	of	of	ADP
ap-1797	273	8	questions	question	NOUN
ap-1797	273	9	which	which	PRON
ap-1797	273	10	still	still	ADV
ap-1797	273	11	have	have	VERB
ap-1797	273	12	to	to	PART
ap-1797	273	13	be	be	AUX
ap-1797	273	14	answered	answer	VERB
ap-1797	273	15	.	.	PUNCT
ap-1797	274	1	a	a	DET
ap-1797	274	2	better	well	ADJ
ap-1797	274	3	understanding	understanding	NOUN
ap-1797	274	4	of	of	ADP
ap-1797	274	5	the	the	DET
ap-1797	274	6	nonlinearity	nonlinearity	NOUN
ap-1797	274	7	’s	’s	PART
ap-1797	274	8	influence	influence	NOUN
ap-1797	274	9	on	on	ADP
ap-1797	274	10	the	the	DET
ap-1797	274	11	solutions	solution	NOUN
ap-1797	274	12	is	be	AUX
ap-1797	274	13	important	important	ADJ
ap-1797	274	14	.	.	PUNCT
ap-1797	275	1	analytically	analytically	ADV
ap-1797	275	2	solvable	solvable	ADJ
ap-1797	275	3	matrix	matrix	NOUN
ap-1797	275	4	models	model	NOUN
ap-1797	275	5	might	might	AUX
ap-1797	275	6	help	help	VERB
ap-1797	275	7	to	to	PART
ap-1797	275	8	get	get	VERB
ap-1797	275	9	a	a	DET
ap-1797	275	10	better	well	ADJ
ap-1797	275	11	insight	insight	NOUN
ap-1797	275	12	.	.	PUNCT
ap-1797	276	1	furthermore	furthermore	ADV
ap-1797	276	2	,	,	PUNCT
ap-1797	276	3	the	the	DET
ap-1797	276	4	relation	relation	NOUN
ap-1797	276	5	of	of	ADP
ap-1797	276	6	the	the	DET
ap-1797	276	7	threeand	threeand	NOUN
ap-1797	276	8	one	one	NUM
ap-1797	276	9	-	-	PUNCT
ap-1797	276	10	dimensional	dimensional	ADJ
ap-1797	276	11	results	result	NOUN
ap-1797	276	12	should	should	AUX
ap-1797	276	13	be	be	AUX
ap-1797	276	14	investigated	investigate	VERB
ap-1797	276	15	for	for	ADP
ap-1797	276	16	higher	high	ADJ
ap-1797	276	17	values	value	NOUN
ap-1797	276	18	of	of	ADP
ap-1797	276	19	the	the	DET
ap-1797	276	20	nonlinearity	nonlinearity	NOUN
ap-1797	276	21	g.	g.	NOUN
ap-1797	276	22	a	a	DET
ap-1797	276	23	full	full	ADJ
ap-1797	276	24	analytical	analytical	ADJ
ap-1797	276	25	continuation	continuation	NOUN
ap-1797	276	26	of	of	ADP
ap-1797	276	27	the	the	DET
ap-1797	276	28	non	non	ADJ
ap-1797	276	29	-	-	ADJ
ap-1797	276	30	analytical	analytical	ADJ
ap-1797	276	31	gross	gross	ADJ
ap-1797	276	32	-	-	PUNCT
ap-1797	276	33	pitaevskii	pitaevskii	ADJ
ap-1797	276	34	equation	equation	NOUN
ap-1797	276	35	should	should	AUX
ap-1797	276	36	help	help	VERB
ap-1797	276	37	to	to	PART
ap-1797	276	38	understand	understand	VERB
ap-1797	276	39	the	the	DET
ap-1797	276	40	change	change	NOUN
ap-1797	276	41	in	in	ADP
ap-1797	276	42	the	the	DET
ap-1797	276	43	number	number	NOUN
ap-1797	276	44	of	of	ADP
ap-1797	276	45	solutions	solution	NOUN
ap-1797	276	46	observed	observe	VERB
ap-1797	276	47	in	in	ADP
ap-1797	276	48	the	the	DET
ap-1797	276	49	eigenvalue	eigenvalue	PROPN
ap-1797	276	50	diagrams	diagram	NOUN
ap-1797	276	51	.	.	PUNCT
ap-1797	277	1	in	in	ADP
ap-1797	277	2	a	a	DET
ap-1797	277	3	proper	proper	ADJ
ap-1797	277	4	extension	extension	NOUN
ap-1797	277	5	,	,	PUNCT
ap-1797	277	6	the	the	DET
ap-1797	277	7	critical	critical	ADJ
ap-1797	277	8	values	value	NOUN
ap-1797	277	9	of	of	ADP
ap-1797	277	10	γ	γ	NOUN
ap-1797	277	11	at	at	ADP
ap-1797	277	12	which	which	PRON
ap-1797	277	13	solutions	solution	NOUN
ap-1797	277	14	appear	appear	VERB
ap-1797	277	15	or	or	CCONJ
ap-1797	277	16	vanish	vanish	VERB
ap-1797	277	17	should	should	AUX
ap-1797	277	18	turn	turn	VERB
ap-1797	277	19	out	out	ADP
ap-1797	277	20	to	to	PART
ap-1797	277	21	be	be	AUX
ap-1797	277	22	bifurcation	bifurcation	NOUN
ap-1797	277	23	points	point	NOUN
ap-1797	277	24	.	.	PUNCT
ap-1797	278	1	it	it	PRON
ap-1797	278	2	would	would	AUX
ap-1797	278	3	be	be	AUX
ap-1797	278	4	desirable	desirable	ADJ
ap-1797	278	5	to	to	PART
ap-1797	278	6	understand	understand	VERB
ap-1797	278	7	how	how	SCONJ
ap-1797	278	8	a	a	DET
ap-1797	278	9	coherent	coherent	ADJ
ap-1797	278	10	inor	inor	NOUN
ap-1797	278	11	outcoupling	outcoupling	NOUN
ap-1797	278	12	of	of	ADP
ap-1797	278	13	atoms	atom	NOUN
ap-1797	278	14	can	can	AUX
ap-1797	278	15	be	be	AUX
ap-1797	278	16	understood	understand	VERB
ap-1797	278	17	on	on	ADP
ap-1797	278	18	a	a	DET
ap-1797	278	19	microscopic	microscopic	ADJ
ap-1797	278	20	level	level	NOUN
ap-1797	278	21	.	.	PUNCT
ap-1797	279	1	this	this	PRON
ap-1797	279	2	will	will	AUX
ap-1797	279	3	be	be	AUX
ap-1797	279	4	important	important	ADJ
ap-1797	279	5	for	for	ADP
ap-1797	279	6	a	a	DET
ap-1797	279	7	realistic	realistic	ADJ
ap-1797	279	8	description	description	NOUN
ap-1797	279	9	of	of	ADP
ap-1797	279	10	experimental	experimental	ADJ
ap-1797	279	11	situations	situation	NOUN
ap-1797	279	12	.	.	PUNCT
ap-1797	280	1	it	it	PRON
ap-1797	280	2	is	be	AUX
ap-1797	280	3	also	also	ADV
ap-1797	280	4	possible	possible	ADJ
ap-1797	280	5	to	to	PART
ap-1797	280	6	extend	extend	VERB
ap-1797	280	7	the	the	DET
ap-1797	280	8	model	model	NOUN
ap-1797	280	9	such	such	ADJ
ap-1797	280	10	that	that	SCONJ
ap-1797	280	11	it	it	PRON
ap-1797	280	12	can	can	AUX
ap-1797	280	13	be	be	AUX
ap-1797	280	14	understood	understand	VERB
ap-1797	280	15	as	as	ADP
ap-1797	280	16	an	an	DET
ap-1797	280	17	embedding	embedding	NOUN
ap-1797	280	18	in	in	ADP
ap-1797	280	19	a	a	DET
ap-1797	280	20	chain	chain	NOUN
ap-1797	280	21	of	of	ADP
ap-1797	280	22	potential	potential	ADJ
ap-1797	280	23	wells	well	NOUN
ap-1797	280	24	.	.	PUNCT
ap-1797	281	1	here	here	ADV
ap-1797	281	2	the	the	DET
ap-1797	281	3	gain	gain	NOUN
ap-1797	281	4	-	-	PUNCT
ap-1797	281	5	loss	loss	NOUN
ap-1797	281	6	contributions	contribution	NOUN
ap-1797	281	7	can	can	AUX
ap-1797	281	8	result	result	VERB
ap-1797	281	9	from	from	ADP
ap-1797	281	10	an	an	DET
ap-1797	281	11	effective	effective	ADJ
ap-1797	281	12	description	description	NOUN
ap-1797	281	13	of	of	ADP
ap-1797	281	14	a	a	DET
ap-1797	281	15	transport	transport	NOUN
ap-1797	281	16	effect	effect	NOUN
ap-1797	281	17	when	when	SCONJ
ap-1797	281	18	only	only	ADV
ap-1797	281	19	two	two	NUM
ap-1797	281	20	wells	well	NOUN
ap-1797	281	21	somewhere	somewhere	ADV
ap-1797	281	22	in	in	ADP
ap-1797	281	23	the	the	DET
ap-1797	281	24	middle	middle	NOUN
ap-1797	281	25	of	of	ADP
ap-1797	281	26	the	the	DET
ap-1797	281	27	chain	chain	NOUN
ap-1797	281	28	are	be	AUX
ap-1797	281	29	taken	take	VERB
ap-1797	281	30	into	into	ADP
ap-1797	281	31	account	account	NOUN
ap-1797	281	32	.	.	PUNCT
ap-1797	282	1	furthermore	furthermore	ADV
ap-1797	282	2	,	,	PUNCT
ap-1797	282	3	it	it	PRON
ap-1797	282	4	would	would	AUX
ap-1797	282	5	be	be	AUX
ap-1797	282	6	interesting	interesting	ADJ
ap-1797	282	7	to	to	PART
ap-1797	282	8	see	see	VERB
ap-1797	282	9	how	how	SCONJ
ap-1797	282	10	a	a	DET
ap-1797	282	11	gain	gain	NOUN
ap-1797	282	12	-	-	PUNCT
ap-1797	282	13	loss	loss	NOUN
ap-1797	282	14	potential	potential	NOUN
ap-1797	282	15	interacts	interact	VERB
ap-1797	282	16	with	with	ADP
ap-1797	282	17	long	long	ADJ
ap-1797	282	18	-	-	PUNCT
ap-1797	282	19	range	range	NOUN
ap-1797	282	20	inter	inter	ADJ
ap-1797	282	21	-	-	ADJ
ap-1797	282	22	atomic	atomic	ADJ
ap-1797	282	23	interactions	interaction	NOUN
ap-1797	282	24	such	such	ADJ
ap-1797	282	25	as	as	ADP
ap-1797	282	26	the	the	DET
ap-1797	282	27	dipole	dipole	NOUN
ap-1797	282	28	-	-	PUNCT
ap-1797	282	29	dipole	dipole	NOUN
ap-1797	282	30	interaction	interaction	NOUN
ap-1797	282	31	leading	lead	VERB
ap-1797	282	32	often	often	ADV
ap-1797	282	33	to	to	ADP
ap-1797	282	34	qualitatively	qualitatively	ADV
ap-1797	282	35	new	new	ADJ
ap-1797	282	36	effects	effect	NOUN
ap-1797	282	37	[	[	X
ap-1797	282	38	30	30	NUM
ap-1797	282	39	]	]	PUNCT
ap-1797	282	40	.	.	PUNCT
ap-1797	283	1	references	reference	NOUN
ap-1797	283	2	[	[	X
ap-1797	283	3	1	1	NUM
ap-1797	283	4	]	]	X
ap-1797	283	5	gross	gross	ADJ
ap-1797	283	6	,	,	PUNCT
ap-1797	283	7	e.	e.	PROPN
ap-1797	283	8	p.	p.	PROPN
ap-1797	283	9	structure	structure	NOUN
ap-1797	283	10	of	of	ADP
ap-1797	283	11	a	a	DET
ap-1797	283	12	quantized	quantize	VERB
ap-1797	283	13	vortex	vortex	NOUN
ap-1797	283	14	in	in	ADP
ap-1797	283	15	boson	boson	NOUN
ap-1797	283	16	systems	system	NOUN
ap-1797	283	17	.	.	PUNCT
ap-1797	284	1	nuovo	nuovo	PROPN
ap-1797	284	2	cimento	cimento	PROPN
ap-1797	284	3	20	20	NUM
ap-1797	284	4	,	,	PUNCT
ap-1797	284	5	454	454	NUM
ap-1797	284	6	(	(	PUNCT
ap-1797	284	7	1961	1961	NUM
ap-1797	284	8	)	)	PUNCT
ap-1797	284	9	.	.	PUNCT
ap-1797	285	1	[	[	X
ap-1797	285	2	2	2	NUM
ap-1797	285	3	]	]	X
ap-1797	285	4	pitaevskii	pitaevskii	PROPN
ap-1797	285	5	,	,	PUNCT
ap-1797	285	6	l.	l.	PROPN
ap-1797	285	7	p.	p.	PROPN
ap-1797	285	8	vortex	vortex	NOUN
ap-1797	285	9	lines	line	NOUN
ap-1797	285	10	in	in	ADP
ap-1797	285	11	an	an	DET
ap-1797	285	12	imperfect	imperfect	ADJ
ap-1797	285	13	bose	bose	NOUN
ap-1797	285	14	gas	gas	NOUN
ap-1797	285	15	.	.	PUNCT
ap-1797	286	1	sov	sov	NOUN
ap-1797	286	2	.	.	PUNCT
ap-1797	287	1	phys	phy	NOUN
ap-1797	287	2	.	.	PUNCT
ap-1797	288	1	jetp	jetp	PROPN
ap-1797	288	2	13	13	NUM
ap-1797	288	3	,	,	PUNCT
ap-1797	288	4	451	451	NUM
ap-1797	288	5	(	(	PUNCT
ap-1797	288	6	1961	1961	NUM
ap-1797	288	7	)	)	PUNCT
ap-1797	288	8	.	.	PUNCT
ap-1797	289	1	[	[	X
ap-1797	289	2	3	3	NUM
ap-1797	289	3	]	]	X
ap-1797	289	4	bender	bender	NOUN
ap-1797	289	5	,	,	PUNCT
ap-1797	289	6	c.	c.	PROPN
ap-1797	289	7	m.	m.	NOUN
ap-1797	289	8	and	and	CCONJ
ap-1797	289	9	boettcher	boettcher	PROPN
ap-1797	289	10	,	,	PUNCT
ap-1797	289	11	s.	s.	PROPN
ap-1797	289	12	real	real	PROPN
ap-1797	289	13	spectra	spectra	PROPN
ap-1797	289	14	in	in	ADP
ap-1797	289	15	non	non	ADJ
ap-1797	289	16	-	-	ADJ
ap-1797	289	17	hermitian	hermitian	ADJ
ap-1797	289	18	hamiltonians	hamiltonian	NOUN
ap-1797	289	19	having	have	VERB
ap-1797	289	20	pt	pt	PRON
ap-1797	289	21	symmetry	symmetry	NOUN
ap-1797	289	22	.	.	PUNCT
ap-1797	290	1	phys	phy	NOUN
ap-1797	290	2	.	.	PUNCT
ap-1797	291	1	rev	rev	PROPN
ap-1797	291	2	.	.	PROPN
ap-1797	291	3	lett	lett	PROPN
ap-1797	291	4	.	.	PROPN
ap-1797	291	5	80	80	NUM
ap-1797	291	6	,	,	PUNCT
ap-1797	291	7	5243	5243	NUM
ap-1797	291	8	(	(	PUNCT
ap-1797	291	9	1998	1998	NUM
ap-1797	291	10	)	)	PUNCT
ap-1797	291	11	.	.	PUNCT
ap-1797	292	1	[	[	X
ap-1797	292	2	4	4	NUM
ap-1797	292	3	]	]	X
ap-1797	292	4	guo	guo	PROPN
ap-1797	292	5	,	,	PUNCT
ap-1797	292	6	a.	a.	PROPN
ap-1797	292	7	,	,	PUNCT
ap-1797	292	8	et	et	PROPN
ap-1797	292	9	al	al	PROPN
ap-1797	292	10	.	.	PROPN
ap-1797	293	1	observation	observation	NOUN
ap-1797	293	2	of	of	ADP
ap-1797	293	3	pt	pt	PROPN
ap-1797	293	4	-symmetry	-symmetry	NOUN
ap-1797	293	5	breaking	break	VERB
ap-1797	293	6	in	in	ADP
ap-1797	293	7	complex	complex	ADJ
ap-1797	293	8	optical	optical	ADJ
ap-1797	293	9	potentials	potential	NOUN
ap-1797	293	10	.	.	PUNCT
ap-1797	294	1	phys	phy	NOUN
ap-1797	294	2	.	.	PUNCT
ap-1797	295	1	rev	rev	PROPN
ap-1797	295	2	.	.	PROPN
ap-1797	295	3	lett	lett	PROPN
ap-1797	295	4	.	.	PROPN
ap-1797	295	5	103	103	NUM
ap-1797	295	6	,	,	PUNCT
ap-1797	295	7	093902	093902	NUM
ap-1797	295	8	(	(	PUNCT
ap-1797	295	9	2009	2009	NUM
ap-1797	295	10	)	)	PUNCT
ap-1797	295	11	.	.	PUNCT
ap-1797	296	1	[	[	X
ap-1797	296	2	5	5	NUM
ap-1797	296	3	]	]	PUNCT
ap-1797	296	4	rüter	rüter	NOUN
ap-1797	296	5	,	,	PUNCT
ap-1797	296	6	c.	c.	PROPN
ap-1797	296	7	e.	e.	PROPN
ap-1797	296	8	,	,	PUNCT
ap-1797	296	9	et	et	PROPN
ap-1797	296	10	al	al	PROPN
ap-1797	296	11	.	.	PUNCT
ap-1797	296	12	observation	observation	NOUN
ap-1797	296	13	of	of	ADP
ap-1797	296	14	parity	parity	NOUN
ap-1797	296	15	-	-	PUNCT
ap-1797	296	16	time	time	NOUN
ap-1797	296	17	symmetry	symmetry	NOUN
ap-1797	296	18	in	in	ADP
ap-1797	296	19	optics	optic	NOUN
ap-1797	296	20	.	.	PUNCT
ap-1797	297	1	nat	nat	NOUN
ap-1797	297	2	.	.	PUNCT
ap-1797	298	1	phys	phy	NOUN
ap-1797	298	2	.	.	PUNCT
ap-1797	299	1	6	6	NUM
ap-1797	299	2	,	,	PUNCT
ap-1797	299	3	192	192	NUM
ap-1797	299	4	(	(	PUNCT
ap-1797	299	5	2010	2010	NUM
ap-1797	299	6	)	)	PUNCT
ap-1797	299	7	.	.	PUNCT
ap-1797	300	1	[	[	X
ap-1797	300	2	6	6	NUM
ap-1797	300	3	]	]	X
ap-1797	300	4	makris	makris	X
ap-1797	300	5	,	,	PUNCT
ap-1797	300	6	k.	k.	PROPN
ap-1797	300	7	g.	g.	PROPN
ap-1797	300	8	,	,	PUNCT
ap-1797	300	9	et	et	PROPN
ap-1797	300	10	al	al	PROPN
ap-1797	300	11	.	.	PROPN
ap-1797	300	12	beam	beam	PROPN
ap-1797	300	13	dynamics	dynamic	NOUN
ap-1797	300	14	in	in	ADP
ap-1797	300	15	pt	pt	PROPN
ap-1797	300	16	symmetric	symmetric	ADJ
ap-1797	300	17	optical	optical	ADJ
ap-1797	300	18	lattices	lattice	NOUN
ap-1797	300	19	.	.	PUNCT
ap-1797	301	1	phys	phy	NOUN
ap-1797	301	2	.	.	PUNCT
ap-1797	302	1	rev	rev	PROPN
ap-1797	302	2	.	.	PROPN
ap-1797	302	3	lett	lett	PROPN
ap-1797	302	4	.	.	PROPN
ap-1797	303	1	100	100	NUM
ap-1797	303	2	,	,	PUNCT
ap-1797	303	3	103904	103904	NUM
ap-1797	303	4	(	(	PUNCT
ap-1797	303	5	2008	2008	NUM
ap-1797	303	6	)	)	PUNCT
ap-1797	303	7	.	.	PUNCT
ap-1797	304	1	[	[	X
ap-1797	304	2	7	7	NUM
ap-1797	304	3	]	]	X
ap-1797	304	4	makris	makris	X
ap-1797	304	5	,	,	PUNCT
ap-1797	304	6	k.	k.	PROPN
ap-1797	304	7	g.	g.	PROPN
ap-1797	304	8	,	,	PUNCT
ap-1797	304	9	et	et	PROPN
ap-1797	305	1	al	al	PROPN
ap-1797	305	2	.	.	PROPN
ap-1797	305	3	pt	pt	PROPN
ap-1797	305	4	-symmetric	-symmetric	ADJ
ap-1797	305	5	optical	optical	ADJ
ap-1797	305	6	lattices	lattice	NOUN
ap-1797	305	7	.	.	PUNCT
ap-1797	306	1	phys	phy	NOUN
ap-1797	306	2	.	.	PUNCT
ap-1797	307	1	rev	rev	PROPN
ap-1797	307	2	.	.	PUNCT
ap-1797	308	1	a	a	DET
ap-1797	308	2	81	81	NUM
ap-1797	308	3	,	,	PUNCT
ap-1797	308	4	063807	063807	NUM
ap-1797	308	5	(	(	PUNCT
ap-1797	308	6	2010	2010	NUM
ap-1797	308	7	)	)	PUNCT
ap-1797	308	8	.	.	PUNCT
ap-1797	309	1	[	[	X
ap-1797	309	2	8	8	NUM
ap-1797	309	3	]	]	X
ap-1797	309	4	ruschhaupt	ruschhaupt	ADJ
ap-1797	309	5	,	,	PUNCT
ap-1797	309	6	a.	a.	PROPN
ap-1797	309	7	,	,	PUNCT
ap-1797	309	8	et	et	PROPN
ap-1797	309	9	al	al	PROPN
ap-1797	309	10	.	.	PROPN
ap-1797	310	1	physical	physical	ADJ
ap-1797	310	2	realization	realization	NOUN
ap-1797	310	3	of	of	ADP
ap-1797	310	4	pt	pt	NOUN
ap-1797	310	5	-symmetric	-symmetric	ADJ
ap-1797	310	6	potential	potential	ADJ
ap-1797	310	7	scattering	scattering	NOUN
ap-1797	310	8	in	in	ADP
ap-1797	310	9	a	a	DET
ap-1797	310	10	planar	planar	ADJ
ap-1797	310	11	slab	slab	NOUN
ap-1797	310	12	waveguide	waveguide	NOUN
ap-1797	310	13	.	.	PUNCT
ap-1797	311	1	j.	j.	PROPN
ap-1797	311	2	phys	phys	PROPN
ap-1797	311	3	.	.	PUNCT
ap-1797	312	1	a	a	DET
ap-1797	312	2	38	38	NUM
ap-1797	312	3	,	,	PUNCT
ap-1797	312	4	l171	l171	PROPN
ap-1797	312	5	(	(	PUNCT
ap-1797	312	6	2005	2005	NUM
ap-1797	312	7	)	)	PUNCT
ap-1797	312	8	.	.	PUNCT
ap-1797	313	1	[	[	X
ap-1797	313	2	9	9	NUM
ap-1797	313	3	]	]	X
ap-1797	313	4	el	el	PROPN
ap-1797	313	5	-	-	PUNCT
ap-1797	313	6	ganainy	ganainy	PROPN
ap-1797	313	7	,	,	PUNCT
ap-1797	313	8	r.	r.	PROPN
ap-1797	313	9	,	,	PUNCT
ap-1797	313	10	et	et	PROPN
ap-1797	313	11	al	al	PROPN
ap-1797	313	12	.	.	PROPN
ap-1797	313	13	theory	theory	NOUN
ap-1797	313	14	of	of	ADP
ap-1797	313	15	coupled	couple	VERB
ap-1797	313	16	optical	optical	ADJ
ap-1797	313	17	pt	pt	ADJ
ap-1797	313	18	-	-	PUNCT
ap-1797	313	19	symmetric	symmetric	ADJ
ap-1797	313	20	structures	structure	NOUN
ap-1797	313	21	.	.	PUNCT
ap-1797	314	1	opt	opt	PROPN
ap-1797	314	2	.	.	PUNCT
ap-1797	315	1	lett	lett	PROPN
ap-1797	315	2	.	.	PUNCT
ap-1797	316	1	32	32	NUM
ap-1797	316	2	,	,	PUNCT
ap-1797	316	3	2632	2632	NUM
ap-1797	316	4	(	(	PUNCT
ap-1797	316	5	2007	2007	NUM
ap-1797	316	6	)	)	PUNCT
ap-1797	316	7	.	.	PUNCT
ap-1797	317	1	[	[	X
ap-1797	317	2	10	10	NUM
ap-1797	317	3	]	]	X
ap-1797	317	4	musslimani	musslimani	X
ap-1797	317	5	,	,	PUNCT
ap-1797	317	6	z.	z.	PROPN
ap-1797	317	7	,	,	PUNCT
ap-1797	317	8	et	et	PROPN
ap-1797	317	9	al	al	PROPN
ap-1797	317	10	.	.	PROPN
ap-1797	317	11	optical	optical	ADJ
ap-1797	317	12	solitons	soliton	NOUN
ap-1797	317	13	in	in	ADP
ap-1797	317	14	pt	pt	PRON
ap-1797	317	15	periodic	periodic	ADJ
ap-1797	317	16	potentials	potential	NOUN
ap-1797	317	17	.	.	PUNCT
ap-1797	318	1	phys	phy	NOUN
ap-1797	318	2	.	.	PUNCT
ap-1797	319	1	rev	rev	PROPN
ap-1797	319	2	.	.	PROPN
ap-1797	319	3	lett	lett	PROPN
ap-1797	319	4	.	.	PROPN
ap-1797	320	1	100	100	NUM
ap-1797	320	2	,	,	PUNCT
ap-1797	320	3	30402	30402	NUM
ap-1797	320	4	(	(	PUNCT
ap-1797	320	5	2008	2008	NUM
ap-1797	320	6	)	)	PUNCT
ap-1797	320	7	.	.	PUNCT
ap-1797	321	1	[	[	X
ap-1797	321	2	11	11	NUM
ap-1797	321	3	]	]	X
ap-1797	321	4	klaiman	klaiman	NOUN
ap-1797	321	5	,	,	PUNCT
ap-1797	321	6	s.	s.	PROPN
ap-1797	321	7	,	,	PUNCT
ap-1797	321	8	et	et	PROPN
ap-1797	321	9	al	al	PROPN
ap-1797	321	10	.	.	PUNCT
ap-1797	321	11	visualization	visualization	NOUN
ap-1797	321	12	of	of	ADP
ap-1797	321	13	branch	branch	NOUN
ap-1797	321	14	points	point	NOUN
ap-1797	321	15	in	in	ADP
ap-1797	321	16	pt	pt	ADJ
ap-1797	321	17	-	-	ADJ
ap-1797	321	18	symmetric	symmetric	ADJ
ap-1797	321	19	waveguides	waveguide	NOUN
ap-1797	321	20	.	.	PUNCT
ap-1797	322	1	phys	phy	NOUN
ap-1797	322	2	.	.	PUNCT
ap-1797	323	1	rev	rev	PROPN
ap-1797	323	2	.	.	PROPN
ap-1797	323	3	lett	lett	PROPN
ap-1797	323	4	.	.	PUNCT
ap-1797	324	1	101	101	NUM
ap-1797	324	2	,	,	PUNCT
ap-1797	324	3	080402	080402	NUM
ap-1797	324	4	(	(	PUNCT
ap-1797	324	5	2008	2008	NUM
ap-1797	324	6	)	)	PUNCT
ap-1797	324	7	.	.	PUNCT
ap-1797	325	1	[	[	X
ap-1797	325	2	12	12	NUM
ap-1797	325	3	]	]	PUNCT
ap-1797	325	4	driben	driben	PROPN
ap-1797	325	5	,	,	PUNCT
ap-1797	325	6	r.	r.	PROPN
ap-1797	325	7	and	and	CCONJ
ap-1797	325	8	malomed	malomed	PROPN
ap-1797	325	9	,	,	PUNCT
ap-1797	325	10	b.	b.	PROPN
ap-1797	325	11	a.	a.	NOUN
ap-1797	325	12	stability	stability	NOUN
ap-1797	325	13	of	of	ADP
ap-1797	325	14	solitons	soliton	NOUN
ap-1797	325	15	in	in	ADP
ap-1797	325	16	parity	parity	NOUN
ap-1797	325	17	-	-	PUNCT
ap-1797	325	18	time	time	NOUN
ap-1797	325	19	-	-	PUNCT
ap-1797	325	20	symmetric	symmetric	ADJ
ap-1797	325	21	couplers	coupler	NOUN
ap-1797	325	22	.	.	PUNCT
ap-1797	326	1	opt	opt	PROPN
ap-1797	326	2	.	.	PUNCT
ap-1797	327	1	lett	lett	PROPN
ap-1797	327	2	.	.	PROPN
ap-1797	328	1	36	36	NUM
ap-1797	328	2	,	,	PUNCT
ap-1797	328	3	4323	4323	NUM
ap-1797	328	4	(	(	PUNCT
ap-1797	328	5	2011	2011	NUM
ap-1797	328	6	)	)	PUNCT
ap-1797	328	7	.	.	PUNCT
ap-1797	329	1	[	[	X
ap-1797	329	2	13	13	NUM
ap-1797	329	3	]	]	SYM
ap-1797	329	4	graefe	graefe	NOUN
ap-1797	329	5	,	,	PUNCT
ap-1797	329	6	e.	e.	PROPN
ap-1797	329	7	m.	m.	PROPN
ap-1797	329	8	,	,	PUNCT
ap-1797	329	9	et	et	PROPN
ap-1797	329	10	al	al	PROPN
ap-1797	329	11	.	.	PUNCT
ap-1797	330	1	a	a	DET
ap-1797	330	2	non	non	ADJ
ap-1797	330	3	-	-	ADJ
ap-1797	330	4	hermitian	hermitian	ADJ
ap-1797	330	5	pt	pt	PROPN
ap-1797	330	6	symmetric	symmetric	PROPN
ap-1797	330	7	bose	bose	PROPN
ap-1797	330	8	-	-	PUNCT
ap-1797	330	9	hubbard	hubbard	NOUN
ap-1797	330	10	model	model	NOUN
ap-1797	330	11	:	:	PUNCT
ap-1797	330	12	eigenvalue	eigenvalue	NOUN
ap-1797	330	13	rings	ring	NOUN
ap-1797	330	14	from	from	ADP
ap-1797	330	15	unfolding	unfold	VERB
ap-1797	330	16	higher	high	ADJ
ap-1797	330	17	-	-	PUNCT
ap-1797	330	18	order	order	NOUN
ap-1797	330	19	exceptional	exceptional	ADJ
ap-1797	330	20	points	point	NOUN
ap-1797	330	21	.	.	PUNCT
ap-1797	331	1	j.	j.	PROPN
ap-1797	331	2	phys	phys	PROPN
ap-1797	331	3	.	.	PUNCT
ap-1797	332	1	a	a	DET
ap-1797	332	2	41	41	NUM
ap-1797	332	3	,	,	PUNCT
ap-1797	332	4	255206	255206	NUM
ap-1797	332	5	(	(	PUNCT
ap-1797	332	6	2008	2008	NUM
ap-1797	332	7	)	)	PUNCT
ap-1797	332	8	.	.	PUNCT
ap-1797	333	1	[	[	X
ap-1797	333	2	14	14	NUM
ap-1797	333	3	]	]	X
ap-1797	333	4	graefe	graefe	NOUN
ap-1797	333	5	,	,	PUNCT
ap-1797	333	6	e.	e.	PROPN
ap-1797	333	7	m.	m.	PROPN
ap-1797	333	8	,	,	PUNCT
ap-1797	333	9	et	et	PROPN
ap-1797	333	10	al	al	PROPN
ap-1797	333	11	.	.	PUNCT
ap-1797	333	12	mean	mean	ADJ
ap-1797	333	13	-	-	PUNCT
ap-1797	333	14	field	field	NOUN
ap-1797	333	15	dynamics	dynamic	NOUN
ap-1797	333	16	of	of	ADP
ap-1797	333	17	a	a	DET
ap-1797	333	18	non	non	ADJ
ap-1797	333	19	-	-	ADJ
ap-1797	333	20	hermitian	hermitian	ADJ
ap-1797	333	21	bose	bose	PROPN
ap-1797	333	22	-	-	PUNCT
ap-1797	333	23	hubbard	hubbard	NOUN
ap-1797	333	24	dimer	dimer	NOUN
ap-1797	333	25	.	.	PUNCT
ap-1797	334	1	phys	phy	NOUN
ap-1797	334	2	.	.	PUNCT
ap-1797	335	1	rev	rev	PROPN
ap-1797	335	2	.	.	PROPN
ap-1797	335	3	lett	lett	PROPN
ap-1797	335	4	.	.	PUNCT
ap-1797	336	1	101	101	NUM
ap-1797	336	2	,	,	PUNCT
ap-1797	336	3	150408	150408	NUM
ap-1797	336	4	(	(	PUNCT
ap-1797	336	5	2008	2008	NUM
ap-1797	336	6	)	)	PUNCT
ap-1797	336	7	.	.	PUNCT
ap-1797	337	1	[	[	X
ap-1797	337	2	15	15	NUM
ap-1797	337	3	]	]	X
ap-1797	337	4	graefe	graefe	NOUN
ap-1797	337	5	,	,	PUNCT
ap-1797	337	6	e.-m	e.-m	PROPN
ap-1797	337	7	.	.	PROPN
ap-1797	337	8	,	,	PUNCT
ap-1797	337	9	et	et	PROPN
ap-1797	337	10	al	al	PROPN
ap-1797	337	11	.	.	PUNCT
ap-1797	337	12	quantum	quantum	ADJ
ap-1797	337	13	-	-	ADJ
ap-1797	337	14	classical	classical	ADJ
ap-1797	337	15	correspondence	correspondence	NOUN
ap-1797	337	16	for	for	ADP
ap-1797	337	17	a	a	DET
ap-1797	337	18	non	non	ADJ
ap-1797	337	19	-	-	ADJ
ap-1797	337	20	hermitian	hermitian	ADJ
ap-1797	337	21	bose	bose	PROPN
ap-1797	337	22	-	-	PUNCT
ap-1797	337	23	hubbard	hubbard	NOUN
ap-1797	337	24	dimer	dimer	NOUN
ap-1797	337	25	.	.	PUNCT
ap-1797	338	1	phys	phy	NOUN
ap-1797	338	2	.	.	PUNCT
ap-1797	339	1	rev	rev	PROPN
ap-1797	339	2	.	.	PUNCT
ap-1797	340	1	a	a	DET
ap-1797	340	2	82	82	NUM
ap-1797	340	3	,	,	PUNCT
ap-1797	340	4	013629	013629	NUM
ap-1797	340	5	(	(	PUNCT
ap-1797	340	6	2010	2010	NUM
ap-1797	340	7	)	)	PUNCT
ap-1797	340	8	.	.	PUNCT
ap-1797	341	1	[	[	X
ap-1797	341	2	16	16	NUM
ap-1797	341	3	]	]	X
ap-1797	341	4	musslimani	musslimani	PROPN
ap-1797	341	5	,	,	PUNCT
ap-1797	341	6	z.	z.	PROPN
ap-1797	341	7	h.	h.	PROPN
ap-1797	341	8	,	,	PUNCT
ap-1797	341	9	et	et	PROPN
ap-1797	341	10	al	al	PROPN
ap-1797	341	11	.	.	PROPN
ap-1797	342	1	analytical	analytical	ADJ
ap-1797	342	2	solutions	solution	NOUN
ap-1797	342	3	to	to	ADP
ap-1797	342	4	a	a	DET
ap-1797	342	5	class	class	NOUN
ap-1797	342	6	of	of	ADP
ap-1797	342	7	nonlinear	nonlinear	ADJ
ap-1797	342	8	schrödinger	schrödinger	ADJ
ap-1797	342	9	equations	equation	NOUN
ap-1797	342	10	with	with	ADP
ap-1797	342	11	pt	pt	X
ap-1797	342	12	-like	-like	PROPN
ap-1797	342	13	potentials	potential	NOUN
ap-1797	342	14	.	.	PUNCT
ap-1797	343	1	j.	j.	PROPN
ap-1797	343	2	phys	phys	PROPN
ap-1797	343	3	.	.	PUNCT
ap-1797	344	1	a	a	DET
ap-1797	344	2	41	41	NUM
ap-1797	344	3	,	,	PUNCT
ap-1797	344	4	244019	244019	NUM
ap-1797	344	5	(	(	PUNCT
ap-1797	344	6	2008	2008	NUM
ap-1797	344	7	)	)	PUNCT
ap-1797	344	8	.	.	PUNCT
ap-1797	345	1	[	[	X
ap-1797	345	2	17	17	NUM
ap-1797	345	3	]	]	X
ap-1797	345	4	ramezani	ramezani	PROPN
ap-1797	345	5	,	,	PUNCT
ap-1797	345	6	h.	h.	PROPN
ap-1797	345	7	,	,	PUNCT
ap-1797	345	8	et	et	PROPN
ap-1797	345	9	al	al	PROPN
ap-1797	345	10	.	.	PUNCT
ap-1797	346	1	unidirectional	unidirectional	PROPN
ap-1797	346	2	nonlinear	nonlinear	ADJ
ap-1797	346	3	pt	pt	NOUN
ap-1797	346	4	-symmetric	-symmetric	ADJ
ap-1797	346	5	optical	optical	ADJ
ap-1797	346	6	structures	structure	NOUN
ap-1797	346	7	.	.	PUNCT
ap-1797	347	1	phys	phy	NOUN
ap-1797	347	2	.	.	PUNCT
ap-1797	348	1	rev	rev	PROPN
ap-1797	348	2	.	.	PUNCT
ap-1797	349	1	a	a	DET
ap-1797	349	2	82	82	NUM
ap-1797	349	3	,	,	PUNCT
ap-1797	349	4	043803	043803	NUM
ap-1797	349	5	(	(	PUNCT
ap-1797	349	6	2010	2010	NUM
ap-1797	349	7	)	)	PUNCT
ap-1797	349	8	.	.	PUNCT
ap-1797	350	1	[	[	X
ap-1797	350	2	18	18	NUM
ap-1797	350	3	]	]	X
ap-1797	350	4	cartarius	cartarius	NOUN
ap-1797	350	5	,	,	PUNCT
ap-1797	350	6	h.	h.	PROPN
ap-1797	350	7	and	and	CCONJ
ap-1797	350	8	wunner	wunner	NOUN
ap-1797	350	9	,	,	PUNCT
ap-1797	350	10	g.	g.	PROPN
ap-1797	350	11	model	model	NOUN
ap-1797	350	12	of	of	ADP
ap-1797	350	13	a	a	DET
ap-1797	350	14	pt	pt	NOUN
ap-1797	350	15	-symmetric	-symmetric	NOUN
ap-1797	350	16	bose	bose	NOUN
ap-1797	350	17	-	-	PUNCT
ap-1797	350	18	einstein	einstein	NOUN
ap-1797	350	19	condensate	condensate	NOUN
ap-1797	350	20	in	in	ADP
ap-1797	350	21	a	a	DET
ap-1797	350	22	δ	δ	NOUN
ap-1797	350	23	-	-	PUNCT
ap-1797	350	24	function	function	NOUN
ap-1797	350	25	double	double	ADJ
ap-1797	350	26	-	-	PUNCT
ap-1797	350	27	well	well	NOUN
ap-1797	350	28	potential	potential	NOUN
ap-1797	350	29	.	.	PUNCT
ap-1797	351	1	phys	phy	NOUN
ap-1797	351	2	.	.	PUNCT
ap-1797	352	1	rev	rev	PROPN
ap-1797	352	2	.	.	PUNCT
ap-1797	353	1	a	a	DET
ap-1797	353	2	86	86	NUM
ap-1797	353	3	,	,	PUNCT
ap-1797	353	4	013612	013612	NUM
ap-1797	353	5	(	(	PUNCT
ap-1797	353	6	2012	2012	NUM
ap-1797	353	7	)	)	PUNCT
ap-1797	353	8	.	.	PUNCT
ap-1797	354	1	[	[	X
ap-1797	354	2	19	19	NUM
ap-1797	354	3	]	]	X
ap-1797	354	4	jakubský	jakubský	NOUN
ap-1797	354	5	,	,	PUNCT
ap-1797	354	6	v.	v.	PROPN
ap-1797	354	7	and	and	CCONJ
ap-1797	354	8	znojil	znojil	NOUN
ap-1797	354	9	,	,	PUNCT
ap-1797	354	10	m.	m.	NOUN
ap-1797	354	11	an	an	DET
ap-1797	354	12	explicitly	explicitly	ADV
ap-1797	354	13	solvable	solvable	ADJ
ap-1797	354	14	model	model	NOUN
ap-1797	354	15	of	of	ADP
ap-1797	354	16	the	the	DET
ap-1797	354	17	spontaneous	spontaneous	ADJ
ap-1797	354	18	pt	pt	ADJ
ap-1797	354	19	-	-	PUNCT
ap-1797	354	20	symmetry	symmetry	NOUN
ap-1797	354	21	breaking	breaking	NOUN
ap-1797	354	22	.	.	PUNCT
ap-1797	355	1	czech	czech	PROPN
ap-1797	355	2	.	.	PUNCT
ap-1797	356	1	j.	j.	PROPN
ap-1797	356	2	phys	phys	PROPN
ap-1797	356	3	.	.	PUNCT
ap-1797	357	1	55	55	NUM
ap-1797	357	2	,	,	PUNCT
ap-1797	357	3	1113	1113	NUM
ap-1797	357	4	(	(	PUNCT
ap-1797	357	5	2005	2005	NUM
ap-1797	357	6	)	)	PUNCT
ap-1797	357	7	.	.	PUNCT
ap-1797	358	1	[	[	X
ap-1797	358	2	20	20	NUM
ap-1797	358	3	]	]	X
ap-1797	358	4	mostafazadeh	mostafazadeh	NOUN
ap-1797	358	5	,	,	PUNCT
ap-1797	358	6	a.	a.	PROPN
ap-1797	358	7	delta	delta	NOUN
ap-1797	358	8	-	-	PUNCT
ap-1797	358	9	function	function	NOUN
ap-1797	358	10	potential	potential	NOUN
ap-1797	358	11	with	with	ADP
ap-1797	358	12	a	a	DET
ap-1797	358	13	complex	complex	ADJ
ap-1797	358	14	coupling	coupling	NOUN
ap-1797	358	15	.	.	PUNCT
ap-1797	359	1	j.	j.	PROPN
ap-1797	359	2	phys	phys	PROPN
ap-1797	359	3	.	.	PUNCT
ap-1797	360	1	a	a	DET
ap-1797	360	2	39	39	NUM
ap-1797	360	3	,	,	PUNCT
ap-1797	360	4	13495	13495	NUM
ap-1797	360	5	(	(	PUNCT
ap-1797	360	6	2006	2006	NUM
ap-1797	360	7	)	)	PUNCT
ap-1797	360	8	.	.	PUNCT
ap-1797	361	1	266	266	NUM
ap-1797	361	2	vol	vol	NOUN
ap-1797	361	3	.	.	PUNCT
ap-1797	362	1	53	53	NUM
ap-1797	362	2	no	no	NOUN
ap-1797	362	3	.	.	PUNCT
ap-1797	363	1	3/2013	3/2013	PROPN
ap-1797	363	2	stationary	stationary	ADJ
ap-1797	363	3	and	and	CCONJ
ap-1797	363	4	dynamical	dynamical	ADJ
ap-1797	363	5	solutions	solution	NOUN
ap-1797	363	6	of	of	ADP
ap-1797	363	7	the	the	DET
ap-1797	363	8	gross	gross	ADJ
ap-1797	363	9	-	-	PUNCT
ap-1797	363	10	pitaevskii	pitaevskii	ADJ
ap-1797	363	11	equation	equation	NOUN
ap-1797	363	12	[	[	X
ap-1797	363	13	21	21	NUM
ap-1797	363	14	]	]	X
ap-1797	363	15	mostafazadeh	mostafazadeh	PROPN
ap-1797	363	16	,	,	PUNCT
ap-1797	363	17	a.	a.	NOUN
ap-1797	363	18	and	and	CCONJ
ap-1797	363	19	mehri	mehri	NOUN
ap-1797	363	20	-	-	PUNCT
ap-1797	363	21	dehnavi	dehnavi	ADJ
ap-1797	363	22	,	,	PUNCT
ap-1797	363	23	h.	h.	PROPN
ap-1797	363	24	spectral	spectral	ADJ
ap-1797	363	25	singularities	singularity	NOUN
ap-1797	363	26	,	,	PUNCT
ap-1797	363	27	biorthonormal	biorthonormal	ADJ
ap-1797	363	28	systems	system	NOUN
ap-1797	363	29	and	and	CCONJ
ap-1797	363	30	a	a	DET
ap-1797	363	31	two	two	NUM
ap-1797	363	32	-	-	PUNCT
ap-1797	363	33	parameter	parameter	NOUN
ap-1797	363	34	family	family	NOUN
ap-1797	363	35	of	of	ADP
ap-1797	363	36	complex	complex	ADJ
ap-1797	363	37	point	point	NOUN
ap-1797	363	38	interactions	interaction	NOUN
ap-1797	363	39	.	.	PUNCT
ap-1797	364	1	j.	j.	PROPN
ap-1797	364	2	phys	phys	PROPN
ap-1797	364	3	.	.	PUNCT
ap-1797	365	1	a	a	DET
ap-1797	365	2	42	42	NUM
ap-1797	365	3	,	,	PUNCT
ap-1797	365	4	125303	125303	NUM
ap-1797	365	5	(	(	PUNCT
ap-1797	365	6	2009	2009	NUM
ap-1797	365	7	)	)	PUNCT
ap-1797	365	8	.	.	PUNCT
ap-1797	366	1	[	[	X
ap-1797	366	2	22	22	NUM
ap-1797	366	3	]	]	X
ap-1797	366	4	mehri	mehri	NOUN
ap-1797	366	5	-	-	PUNCT
ap-1797	366	6	dehnavi	dehnavi	ADJ
ap-1797	366	7	,	,	PUNCT
ap-1797	366	8	h.	h.	PROPN
ap-1797	366	9	,	,	PUNCT
ap-1797	366	10	et	et	PROPN
ap-1797	366	11	al	al	PROPN
ap-1797	366	12	.	.	PUNCT
ap-1797	366	13	application	application	NOUN
ap-1797	366	14	of	of	ADP
ap-1797	366	15	pseudo	pseudo	NOUN
ap-1797	366	16	-	-	ADJ
ap-1797	366	17	hermitian	hermitian	ADJ
ap-1797	366	18	quantum	quantum	ADJ
ap-1797	366	19	mechanics	mechanic	NOUN
ap-1797	366	20	to	to	ADP
ap-1797	366	21	a	a	DET
ap-1797	366	22	complex	complex	ADJ
ap-1797	366	23	scattering	scattering	ADJ
ap-1797	366	24	potential	potential	NOUN
ap-1797	366	25	with	with	ADP
ap-1797	366	26	point	point	NOUN
ap-1797	366	27	interactions	interaction	NOUN
ap-1797	366	28	.	.	PUNCT
ap-1797	367	1	j.	j.	PROPN
ap-1797	367	2	phys	phys	PROPN
ap-1797	367	3	.	.	PUNCT
ap-1797	368	1	a	a	DET
ap-1797	368	2	43	43	NUM
ap-1797	368	3	,	,	PUNCT
ap-1797	368	4	145301	145301	NUM
ap-1797	368	5	(	(	PUNCT
ap-1797	368	6	2010	2010	NUM
ap-1797	368	7	)	)	PUNCT
ap-1797	368	8	.	.	PUNCT
ap-1797	369	1	[	[	X
ap-1797	369	2	23	23	NUM
ap-1797	369	3	]	]	SYM
ap-1797	369	4	jones	jones	PROPN
ap-1797	369	5	,	,	PUNCT
ap-1797	369	6	h.	h.	PROPN
ap-1797	369	7	f.	f.	PROPN
ap-1797	369	8	interface	interface	PROPN
ap-1797	369	9	between	between	ADP
ap-1797	369	10	hermitian	hermitian	PROPN
ap-1797	369	11	and	and	CCONJ
ap-1797	369	12	non	non	ADJ
ap-1797	369	13	-	-	ADJ
ap-1797	369	14	hermitian	hermitian	ADJ
ap-1797	369	15	hamiltonians	hamiltonian	NOUN
ap-1797	369	16	in	in	ADP
ap-1797	369	17	a	a	DET
ap-1797	369	18	model	model	NOUN
ap-1797	369	19	calculation	calculation	NOUN
ap-1797	369	20	.	.	PUNCT
ap-1797	370	1	phys	phy	NOUN
ap-1797	370	2	.	.	PUNCT
ap-1797	371	1	rev	rev	PROPN
ap-1797	371	2	.	.	PUNCT
ap-1797	372	1	d	d	PROPN
ap-1797	372	2	78	78	NUM
ap-1797	372	3	,	,	PUNCT
ap-1797	372	4	065032	065032	NUM
ap-1797	372	5	(	(	PUNCT
ap-1797	372	6	2008	2008	NUM
ap-1797	372	7	)	)	PUNCT
ap-1797	372	8	.	.	PUNCT
ap-1797	373	1	[	[	X
ap-1797	373	2	24	24	NUM
ap-1797	373	3	]	]	PUNCT
ap-1797	373	4	rau	rau	PROPN
ap-1797	373	5	,	,	PUNCT
ap-1797	373	6	s.	s.	PROPN
ap-1797	373	7	,	,	PUNCT
ap-1797	373	8	et	et	PROPN
ap-1797	373	9	al	al	PROPN
ap-1797	373	10	.	.	PUNCT
ap-1797	373	11	pitchfork	pitchfork	NOUN
ap-1797	373	12	bifurcations	bifurcation	NOUN
ap-1797	373	13	in	in	ADP
ap-1797	373	14	blood	blood	NOUN
ap-1797	373	15	-	-	PUNCT
ap-1797	373	16	cell	cell	NOUN
ap-1797	373	17	-	-	PUNCT
ap-1797	373	18	shaped	shape	VERB
ap-1797	373	19	dipolar	dipolar	ADJ
ap-1797	373	20	bose	bose	NOUN
ap-1797	373	21	-	-	PUNCT
ap-1797	373	22	einstein	einstein	NOUN
ap-1797	373	23	condensates	condensate	NOUN
ap-1797	373	24	.	.	PUNCT
ap-1797	374	1	phys	phy	NOUN
ap-1797	374	2	.	.	PUNCT
ap-1797	375	1	rev	rev	PROPN
ap-1797	375	2	.	.	PUNCT
ap-1797	376	1	a	a	DET
ap-1797	376	2	81	81	NUM
ap-1797	376	3	,	,	PUNCT
ap-1797	376	4	031605(r	031605(r	NOUN
ap-1797	376	5	)	)	PUNCT
ap-1797	376	6	(	(	PUNCT
ap-1797	376	7	2010	2010	NUM
ap-1797	376	8	)	)	PUNCT
ap-1797	376	9	.	.	PUNCT
ap-1797	377	1	[	[	X
ap-1797	377	2	25	25	NUM
ap-1797	377	3	]	]	PUNCT
ap-1797	377	4	rau	rau	PROPN
ap-1797	377	5	,	,	PUNCT
ap-1797	377	6	s.	s.	PROPN
ap-1797	377	7	,	,	PUNCT
ap-1797	377	8	et	et	PROPN
ap-1797	377	9	al	al	PROPN
ap-1797	377	10	.	.	PUNCT
ap-1797	377	11	variational	variational	ADJ
ap-1797	377	12	methods	method	NOUN
ap-1797	377	13	with	with	ADP
ap-1797	377	14	coupled	couple	VERB
ap-1797	377	15	gaussian	gaussian	ADJ
ap-1797	377	16	functions	function	NOUN
ap-1797	377	17	for	for	ADP
ap-1797	377	18	bose	bose	NOUN
ap-1797	377	19	-	-	PUNCT
ap-1797	377	20	einstein	einstein	NOUN
ap-1797	377	21	condensates	condensate	NOUN
ap-1797	377	22	with	with	ADP
ap-1797	377	23	long	long	ADJ
ap-1797	377	24	-	-	PUNCT
ap-1797	377	25	range	range	NOUN
ap-1797	377	26	interactions	interaction	NOUN
ap-1797	377	27	.	.	PUNCT
ap-1797	378	1	i.	i.	PROPN
ap-1797	378	2	general	general	PROPN
ap-1797	378	3	concept	concept	PROPN
ap-1797	378	4	.	.	PUNCT
ap-1797	379	1	phys	phy	NOUN
ap-1797	379	2	.	.	PUNCT
ap-1797	380	1	rev	rev	PROPN
ap-1797	380	2	.	.	PUNCT
ap-1797	381	1	a	a	DET
ap-1797	381	2	82	82	NUM
ap-1797	381	3	,	,	PUNCT
ap-1797	381	4	023610	023610	NUM
ap-1797	381	5	(	(	PUNCT
ap-1797	381	6	2010	2010	NUM
ap-1797	381	7	)	)	PUNCT
ap-1797	381	8	.	.	PUNCT
ap-1797	382	1	[	[	X
ap-1797	382	2	26	26	NUM
ap-1797	382	3	]	]	X
ap-1797	382	4	rau	rau	PROPN
ap-1797	382	5	,	,	PUNCT
ap-1797	382	6	s.	s.	PROPN
ap-1797	382	7	,	,	PUNCT
ap-1797	382	8	et	et	PROPN
ap-1797	382	9	al	al	PROPN
ap-1797	382	10	.	.	PUNCT
ap-1797	382	11	variational	variational	ADJ
ap-1797	382	12	methods	method	NOUN
ap-1797	382	13	with	with	ADP
ap-1797	382	14	coupled	couple	VERB
ap-1797	382	15	gaussian	gaussian	ADJ
ap-1797	382	16	functions	function	NOUN
ap-1797	382	17	for	for	ADP
ap-1797	382	18	bose	bose	NOUN
ap-1797	382	19	-	-	PUNCT
ap-1797	382	20	einstein	einstein	NOUN
ap-1797	382	21	condensates	condensate	NOUN
ap-1797	382	22	with	with	ADP
ap-1797	382	23	long	long	ADJ
ap-1797	382	24	-	-	PUNCT
ap-1797	382	25	range	range	NOUN
ap-1797	382	26	interactions	interaction	NOUN
ap-1797	382	27	.	.	PUNCT
ap-1797	383	1	ii	ii	X
ap-1797	383	2	.	.	PUNCT
ap-1797	383	3	applications	application	NOUN
ap-1797	383	4	.	.	PUNCT
ap-1797	384	1	phys	phy	NOUN
ap-1797	384	2	.	.	PUNCT
ap-1797	385	1	rev	rev	PROPN
ap-1797	385	2	.	.	PUNCT
ap-1797	386	1	a	a	DET
ap-1797	386	2	82	82	NUM
ap-1797	386	3	,	,	PUNCT
ap-1797	386	4	023611	023611	NUM
ap-1797	386	5	(	(	PUNCT
ap-1797	386	6	2010	2010	NUM
ap-1797	386	7	)	)	PUNCT
ap-1797	386	8	.	.	PUNCT
ap-1797	387	1	[	[	X
ap-1797	387	2	27	27	NUM
ap-1797	387	3	]	]	SYM
ap-1797	387	4	mclachlan	mclachlan	NOUN
ap-1797	387	5	,	,	PUNCT
ap-1797	387	6	a.	a.	PROPN
ap-1797	387	7	d.	d.	PROPN
ap-1797	387	8	a	a	DET
ap-1797	387	9	variational	variational	ADJ
ap-1797	387	10	solution	solution	NOUN
ap-1797	387	11	of	of	ADP
ap-1797	387	12	the	the	DET
ap-1797	387	13	timedependent	timedependent	NOUN
ap-1797	387	14	schrödinger	schrödinger	ADJ
ap-1797	387	15	equation	equation	NOUN
ap-1797	387	16	.	.	PUNCT
ap-1797	388	1	mol	mol	PROPN
ap-1797	388	2	.	.	PUNCT
ap-1797	389	1	phys	phy	NOUN
ap-1797	389	2	.	.	PUNCT
ap-1797	390	1	8	8	NUM
ap-1797	390	2	,	,	PUNCT
ap-1797	390	3	39	39	NUM
ap-1797	390	4	(	(	PUNCT
ap-1797	390	5	1964	1964	NUM
ap-1797	390	6	)	)	PUNCT
ap-1797	390	7	.	.	PUNCT
ap-1797	391	1	[	[	X
ap-1797	391	2	28	28	NUM
ap-1797	391	3	]	]	X
ap-1797	391	4	dast	dast	X
ap-1797	391	5	,	,	PUNCT
ap-1797	391	6	d.	d.	PROPN
ap-1797	391	7	,	,	PUNCT
ap-1797	391	8	et	et	PROPN
ap-1797	391	9	al	al	PROPN
ap-1797	391	10	.	.	PUNCT
ap-1797	392	1	a	a	DET
ap-1797	392	2	bose	bose	NOUN
ap-1797	392	3	-	-	PUNCT
ap-1797	392	4	einstein	einstein	NOUN
ap-1797	392	5	condensate	condensate	NOUN
ap-1797	392	6	in	in	ADP
ap-1797	392	7	a	a	DET
ap-1797	392	8	pt	pt	NOUN
ap-1797	392	9	symmetric	symmetric	ADJ
ap-1797	392	10	double	double	ADJ
ap-1797	392	11	well	well	ADV
ap-1797	392	12	.	.	PUNCT
ap-1797	393	1	fortschr	fortschr	NOUN
ap-1797	393	2	.	.	PUNCT
ap-1797	394	1	phys	phy	NOUN
ap-1797	394	2	.	.	PUNCT
ap-1797	395	1	61	61	NUM
ap-1797	395	2	,	,	PUNCT
ap-1797	395	3	124	124	NUM
ap-1797	395	4	(	(	PUNCT
ap-1797	395	5	2013	2013	NUM
ap-1797	395	6	)	)	PUNCT
ap-1797	395	7	.	.	PUNCT
ap-1797	396	1	[	[	X
ap-1797	396	2	29	29	NUM
ap-1797	396	3	]	]	X
ap-1797	396	4	press	press	NOUN
ap-1797	396	5	,	,	PUNCT
ap-1797	396	6	w.	w.	PROPN
ap-1797	396	7	h.	h.	PROPN
ap-1797	396	8	,	,	PUNCT
ap-1797	396	9	et	et	PROPN
ap-1797	397	1	al	al	PROPN
ap-1797	397	2	.	.	PROPN
ap-1797	397	3	numerical	numerical	PROPN
ap-1797	397	4	recipes	recipe	NOUN
ap-1797	397	5	in	in	ADP
ap-1797	397	6	fortran	fortran	NOUN
ap-1797	397	7	77	77	NUM
ap-1797	397	8	.	.	PUNCT
ap-1797	398	1	cambridge	cambridge	PROPN
ap-1797	398	2	university	university	PROPN
ap-1797	398	3	press	press	PROPN
ap-1797	398	4	,	,	PUNCT
ap-1797	398	5	new	new	PROPN
ap-1797	398	6	york	york	PROPN
ap-1797	398	7	,	,	PUNCT
ap-1797	398	8	second	second	ADJ
ap-1797	398	9	edition	edition	NOUN
ap-1797	398	10	(	(	PUNCT
ap-1797	398	11	1992	1992	NUM
ap-1797	398	12	)	)	PUNCT
ap-1797	398	13	.	.	PUNCT
ap-1797	399	1	[	[	X
ap-1797	399	2	30	30	NUM
ap-1797	399	3	]	]	X
ap-1797	399	4	lahaye	lahaye	NOUN
ap-1797	399	5	,	,	PUNCT
ap-1797	399	6	t.	t.	PROPN
ap-1797	399	7	,	,	PUNCT
ap-1797	399	8	et	et	PROPN
ap-1797	399	9	al	al	PROPN
ap-1797	399	10	.	.	PUNCT
ap-1797	400	1	the	the	DET
ap-1797	400	2	physics	physics	NOUN
ap-1797	400	3	of	of	ADP
ap-1797	400	4	dipolar	dipolar	ADJ
ap-1797	400	5	bosonic	bosonic	NOUN
ap-1797	400	6	quantum	quantum	NOUN
ap-1797	400	7	gases	gas	NOUN
ap-1797	400	8	.	.	PUNCT
ap-1797	401	1	rep	rep	PROPN
ap-1797	401	2	.	.	PROPN
ap-1797	401	3	prog	prog	PROPN
ap-1797	401	4	.	.	PUNCT
ap-1797	402	1	phys	phy	NOUN
ap-1797	402	2	.	.	PUNCT
ap-1797	403	1	72	72	NUM
ap-1797	403	2	,	,	PUNCT
ap-1797	403	3	126401	126401	NUM
ap-1797	403	4	(	(	PUNCT
ap-1797	403	5	2009	2009	NUM
ap-1797	403	6	)	)	PUNCT
ap-1797	403	7	.	.	PUNCT
ap-1797	404	1	267	267	NUM
ap-1797	404	2	acta	acta	PROPN
ap-1797	404	3	polytechnica	polytechnica	PROPN
ap-1797	404	4	53(3):259–267	53(3):259–267	PROPN
ap-1797	404	5	,	,	PUNCT
ap-1797	404	6	2013	2013	NUM
ap-1797	404	7	1	1	NUM
ap-1797	404	8	introduction	introduction	NOUN
ap-1797	404	9	2	2	NUM
ap-1797	404	10	numerical	numerical	ADJ
ap-1797	404	11	approach	approach	NOUN
ap-1797	404	12	to	to	ADP
ap-1797	404	13	bose	bose	NOUN
ap-1797	404	14	-	-	PUNCT
ap-1797	404	15	einstein	einstein	NOUN
ap-1797	404	16	condensates	condensate	NOUN
ap-1797	404	17	in	in	ADP
ap-1797	404	18	a	a	DET
ap-1797	404	19	pt	pt	NOUN
ap-1797	404	20	symmetric	symmetric	ADJ
ap-1797	404	21	double	double	ADJ
ap-1797	404	22	well	well	NOUN
ap-1797	404	23	2.1	2.1	NUM
ap-1797	404	24	gross	gross	ADJ
ap-1797	404	25	-	-	PUNCT
ap-1797	404	26	pitaevskii	pitaevskii	ADJ
ap-1797	404	27	equation	equation	NOUN
ap-1797	404	28	2.2	2.2	NUM
ap-1797	404	29	two	two	NUM
ap-1797	404	30	methods	method	NOUN
ap-1797	404	31	:	:	PUNCT
ap-1797	404	32	variational	variational	ADJ
ap-1797	404	33	gaussian	gaussian	NOUN
ap-1797	404	34	and	and	CCONJ
ap-1797	404	35	numerically	numerically	ADV
ap-1797	404	36	exact	exact	ADJ
ap-1797	404	37	3	3	NUM
ap-1797	404	38	numerical	numerical	ADJ
ap-1797	404	39	solutions	solution	NOUN
ap-1797	404	40	3.1	3.1	NUM
ap-1797	404	41	energy	energy	NOUN
ap-1797	404	42	eigenvalues	eigenvalue	VERB
ap-1797	404	43	3.2	3.2	NUM
ap-1797	404	44	wave	wave	NOUN
ap-1797	404	45	functions	function	NOUN
ap-1797	404	46	3.3	3.3	NUM
ap-1797	404	47	temporal	temporal	ADJ
ap-1797	404	48	evolution	evolution	NOUN
ap-1797	404	49	and	and	CCONJ
ap-1797	404	50	the	the	DET
ap-1797	404	51	significance	significance	NOUN
ap-1797	404	52	of	of	ADP
ap-1797	404	53	`	`	PUNCT
ap-1797	404	54	`	`	PUNCT
ap-1797	404	55	stationary	stationary	ADJ
ap-1797	404	56	''	''	PUNCT
ap-1797	404	57	solutions	solution	NOUN
ap-1797	404	58	with	with	ADP
ap-1797	404	59	complex	complex	ADJ
ap-1797	404	60	eigenvalues	eigenvalue	VERB
ap-1797	404	61	4	4	NUM
ap-1797	404	62	conclusion	conclusion	NOUN
ap-1797	404	63	references	reference	NOUN