id	sid	tid	token	lemma	pos
ap-2092	1	1	acta	acta	PROPN
ap-2092	1	2	polytechnica	polytechnica	PROPN
ap-2092	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2092	1	4	/	/	SYM
ap-2092	1	5	ap.2014.54.0133	ap.2014.54.0133	PROPN
ap-2092	1	6	acta	acta	PROPN
ap-2092	1	7	polytechnica	polytechnica	PROPN
ap-2092	1	8	54(2):133–138	54(2):133–138	PROPN
ap-2092	1	9	,	,	PUNCT
ap-2092	1	10	2014	2014	NUM
ap-2092	1	11	©	©	PROPN
ap-2092	1	12	czech	czech	PROPN
ap-2092	1	13	technical	technical	PROPN
ap-2092	1	14	university	university	PROPN
ap-2092	1	15	in	in	ADP
ap-2092	1	16	prague	prague	PROPN
ap-2092	1	17	,	,	PUNCT
ap-2092	1	18	2014	2014	NUM
ap-2092	1	19	available	available	ADJ
ap-2092	1	20	online	online	ADV
ap-2092	1	21	at	at	ADP
ap-2092	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2092	1	23	stability	stability	NOUN
ap-2092	1	24	of	of	ADP
ap-2092	1	25	bose	bose	NOUN
ap-2092	1	26	-	-	PUNCT
ap-2092	1	27	einstein	einstein	NOUN
ap-2092	1	28	condensates	condensate	NOUN
ap-2092	1	29	in	in	ADP
ap-2092	1	30	a	a	DET
ap-2092	1	31	pt	pt	ADJ
ap-2092	1	32	-	-	ADJ
ap-2092	1	33	symmetric	symmetric	ADJ
ap-2092	1	34	double	double	ADJ
ap-2092	1	35	-	-	PUNCT
ap-2092	1	36	δ	δ	NOUN
ap-2092	1	37	potential	potential	NOUN
ap-2092	1	38	close	close	ADV
ap-2092	1	39	to	to	ADP
ap-2092	1	40	branch	branch	NOUN
ap-2092	1	41	points	point	NOUN
ap-2092	1	42	andreas	andreas	PROPN
ap-2092	1	43	löhle	löhle	PROPN
ap-2092	1	44	,	,	PUNCT
ap-2092	1	45	holger	holger	NOUN
ap-2092	1	46	cartarius∗	cartarius∗	NOUN
ap-2092	1	47	,	,	PUNCT
ap-2092	1	48	daniel	daniel	PROPN
ap-2092	1	49	haag	haag	PROPN
ap-2092	1	50	,	,	PUNCT
ap-2092	1	51	dennis	dennis	PROPN
ap-2092	1	52	dast	dast	PROPN
ap-2092	1	53	,	,	PUNCT
ap-2092	1	54	jörg	jörg	PROPN
ap-2092	1	55	main	main	ADJ
ap-2092	1	56	,	,	PUNCT
ap-2092	1	57	günter	günter	PROPN
ap-2092	1	58	wunner	wunner	PROPN
ap-2092	1	59	institut	institut	PROPN
ap-2092	1	60	für	für	PROPN
ap-2092	1	61	theoretische	theoretische	PROPN
ap-2092	1	62	physik	physik	PROPN
ap-2092	1	63	1	1	NUM
ap-2092	1	64	,	,	PUNCT
ap-2092	1	65	universität	universität	PROPN
ap-2092	1	66	stuttgart	stuttgart	PROPN
ap-2092	1	67	,	,	PUNCT
ap-2092	1	68	70550	70550	NUM
ap-2092	1	69	stuttgart	stuttgart	PROPN
ap-2092	1	70	,	,	PUNCT
ap-2092	1	71	germany	germany	PROPN
ap-2092	1	72	∗	∗	NOUN
ap-2092	1	73	corresponding	correspond	VERB
ap-2092	1	74	author	author	NOUN
ap-2092	1	75	:	:	PUNCT
ap-2092	1	76	holger.cartarius@itp1.uni-stuttgart.de	holger.cartarius@itp1.uni-stuttgart.de	ADJ
ap-2092	1	77	abstract	abstract	NOUN
ap-2092	1	78	.	.	PUNCT
ap-2092	2	1	a	a	DET
ap-2092	2	2	bose	bose	NOUN
ap-2092	2	3	-	-	PUNCT
ap-2092	2	4	einstein	einstein	NOUN
ap-2092	2	5	condensate	condensate	NOUN
ap-2092	2	6	trapped	trap	VERB
ap-2092	2	7	in	in	ADP
ap-2092	2	8	a	a	DET
ap-2092	2	9	double	double	ADJ
ap-2092	2	10	-	-	PUNCT
ap-2092	2	11	well	well	NOUN
ap-2092	2	12	potential	potential	NOUN
ap-2092	2	13	,	,	PUNCT
ap-2092	2	14	where	where	SCONJ
ap-2092	2	15	atoms	atom	NOUN
ap-2092	2	16	are	be	AUX
ap-2092	2	17	incoupled	incouple	VERB
ap-2092	2	18	to	to	ADP
ap-2092	2	19	one	one	NUM
ap-2092	2	20	side	side	NOUN
ap-2092	2	21	and	and	CCONJ
ap-2092	2	22	extracted	extract	VERB
ap-2092	2	23	from	from	ADP
ap-2092	2	24	the	the	DET
ap-2092	2	25	other	other	ADJ
ap-2092	2	26	,	,	PUNCT
ap-2092	2	27	can	can	AUX
ap-2092	2	28	in	in	ADP
ap-2092	2	29	the	the	DET
ap-2092	2	30	mean	mean	ADJ
ap-2092	2	31	-	-	PUNCT
ap-2092	2	32	field	field	NOUN
ap-2092	2	33	limit	limit	NOUN
ap-2092	2	34	be	be	AUX
ap-2092	2	35	described	describe	VERB
ap-2092	2	36	by	by	ADP
ap-2092	2	37	the	the	DET
ap-2092	2	38	nonlinear	nonlinear	ADJ
ap-2092	2	39	gross	gross	ADJ
ap-2092	2	40	-	-	PUNCT
ap-2092	2	41	pitaevskii	pitaevskii	ADJ
ap-2092	2	42	equation	equation	NOUN
ap-2092	2	43	(	(	PUNCT
ap-2092	2	44	gpe	gpe	NOUN
ap-2092	2	45	)	)	PUNCT
ap-2092	2	46	with	with	ADP
ap-2092	2	47	a	a	DET
ap-2092	2	48	pt	pt	INTJ
ap-2092	2	49	symmetric	symmetric	ADJ
ap-2092	2	50	external	external	ADJ
ap-2092	2	51	potential	potential	NOUN
ap-2092	2	52	.	.	PUNCT
ap-2092	3	1	if	if	SCONJ
ap-2092	3	2	the	the	DET
ap-2092	3	3	strength	strength	NOUN
ap-2092	3	4	of	of	ADP
ap-2092	3	5	the	the	DET
ap-2092	3	6	inand	inand	ADJ
ap-2092	3	7	outcoupling	outcoupling	NOUN
ap-2092	3	8	is	be	AUX
ap-2092	3	9	increased	increase	VERB
ap-2092	3	10	two	two	NUM
ap-2092	3	11	pt	pt	NOUN
ap-2092	3	12	broken	break	VERB
ap-2092	3	13	states	state	NOUN
ap-2092	3	14	bifurcate	bifurcate	VERB
ap-2092	3	15	from	from	ADP
ap-2092	3	16	the	the	DET
ap-2092	3	17	pt	pt	PROPN
ap-2092	3	18	symmetric	symmetric	ADJ
ap-2092	3	19	ground	ground	NOUN
ap-2092	3	20	state	state	NOUN
ap-2092	3	21	.	.	PUNCT
ap-2092	4	1	at	at	ADP
ap-2092	4	2	this	this	DET
ap-2092	4	3	bifurcation	bifurcation	NOUN
ap-2092	4	4	point	point	NOUN
ap-2092	4	5	a	a	DET
ap-2092	4	6	stability	stability	NOUN
ap-2092	4	7	change	change	NOUN
ap-2092	4	8	of	of	ADP
ap-2092	4	9	the	the	DET
ap-2092	4	10	ground	ground	NOUN
ap-2092	4	11	state	state	NOUN
ap-2092	4	12	is	be	AUX
ap-2092	4	13	expected	expect	VERB
ap-2092	4	14	.	.	PUNCT
ap-2092	5	1	however	however	ADV
ap-2092	5	2	,	,	PUNCT
ap-2092	5	3	it	it	PRON
ap-2092	5	4	is	be	AUX
ap-2092	5	5	observed	observe	VERB
ap-2092	5	6	that	that	SCONJ
ap-2092	5	7	this	this	DET
ap-2092	5	8	stability	stability	NOUN
ap-2092	5	9	change	change	NOUN
ap-2092	5	10	does	do	AUX
ap-2092	5	11	not	not	PART
ap-2092	5	12	occur	occur	VERB
ap-2092	5	13	exactly	exactly	ADV
ap-2092	5	14	at	at	ADP
ap-2092	5	15	the	the	DET
ap-2092	5	16	bifurcation	bifurcation	NOUN
ap-2092	5	17	but	but	CCONJ
ap-2092	5	18	at	at	ADP
ap-2092	5	19	a	a	DET
ap-2092	5	20	slightly	slightly	ADV
ap-2092	5	21	different	different	ADJ
ap-2092	5	22	strength	strength	NOUN
ap-2092	5	23	of	of	ADP
ap-2092	5	24	the	the	DET
ap-2092	5	25	in-/outcoupling	in-/outcouple	VERB
ap-2092	5	26	effect	effect	NOUN
ap-2092	5	27	.	.	PUNCT
ap-2092	6	1	we	we	PRON
ap-2092	6	2	investigate	investigate	VERB
ap-2092	6	3	a	a	DET
ap-2092	6	4	bose	bose	NOUN
ap-2092	6	5	-	-	PUNCT
ap-2092	6	6	einstein	einstein	NOUN
ap-2092	6	7	condensate	condensate	NOUN
ap-2092	6	8	in	in	ADP
ap-2092	6	9	a	a	DET
ap-2092	6	10	pt	pt	NOUN
ap-2092	6	11	symmetric	symmetric	ADJ
ap-2092	6	12	double	double	ADJ
ap-2092	6	13	-	-	PUNCT
ap-2092	6	14	δ	δ	NOUN
ap-2092	6	15	potential	potential	NOUN
ap-2092	6	16	and	and	CCONJ
ap-2092	6	17	calculate	calculate	VERB
ap-2092	6	18	the	the	DET
ap-2092	6	19	stationary	stationary	ADJ
ap-2092	6	20	states	state	NOUN
ap-2092	6	21	.	.	PUNCT
ap-2092	7	1	the	the	DET
ap-2092	7	2	ground	ground	NOUN
ap-2092	7	3	state	state	NOUN
ap-2092	7	4	’s	’s	PART
ap-2092	7	5	stability	stability	NOUN
ap-2092	7	6	is	be	AUX
ap-2092	7	7	analysed	analyse	VERB
ap-2092	7	8	by	by	ADP
ap-2092	7	9	means	mean	NOUN
ap-2092	7	10	of	of	ADP
ap-2092	7	11	the	the	DET
ap-2092	7	12	bogoliubov	bogoliubov	PROPN
ap-2092	7	13	-	-	PUNCT
ap-2092	7	14	de	de	ADJ
ap-2092	7	15	gennes	genne	NOUN
ap-2092	7	16	equations	equation	NOUN
ap-2092	7	17	and	and	CCONJ
ap-2092	7	18	it	it	PRON
ap-2092	7	19	is	be	AUX
ap-2092	7	20	shown	show	VERB
ap-2092	7	21	that	that	SCONJ
ap-2092	7	22	the	the	DET
ap-2092	7	23	difference	difference	NOUN
ap-2092	7	24	in	in	ADP
ap-2092	7	25	the	the	DET
ap-2092	7	26	strength	strength	NOUN
ap-2092	7	27	of	of	ADP
ap-2092	7	28	the	the	DET
ap-2092	7	29	in-/outcoupling	in-/outcoupling	NOUN
ap-2092	7	30	between	between	ADP
ap-2092	7	31	the	the	DET
ap-2092	7	32	bifurcation	bifurcation	NOUN
ap-2092	7	33	and	and	CCONJ
ap-2092	7	34	the	the	DET
ap-2092	7	35	stability	stability	NOUN
ap-2092	7	36	change	change	NOUN
ap-2092	7	37	can	can	AUX
ap-2092	7	38	be	be	AUX
ap-2092	7	39	completely	completely	ADV
ap-2092	7	40	explained	explain	VERB
ap-2092	7	41	by	by	ADP
ap-2092	7	42	the	the	DET
ap-2092	7	43	norm	norm	NOUN
ap-2092	7	44	-	-	PUNCT
ap-2092	7	45	dependency	dependency	NOUN
ap-2092	7	46	of	of	ADP
ap-2092	7	47	the	the	DET
ap-2092	7	48	nonlinear	nonlinear	ADJ
ap-2092	7	49	term	term	NOUN
ap-2092	7	50	in	in	ADP
ap-2092	7	51	the	the	DET
ap-2092	7	52	gross	gross	ADJ
ap-2092	7	53	-	-	PUNCT
ap-2092	7	54	pitaevskii	pitaevskii	ADJ
ap-2092	7	55	equation	equation	NOUN
ap-2092	7	56	.	.	PUNCT
ap-2092	8	1	keywords	keyword	NOUN
ap-2092	8	2	:	:	PUNCT
ap-2092	8	3	bose	bose	NOUN
ap-2092	8	4	-	-	PUNCT
ap-2092	8	5	einstein	einstein	NOUN
ap-2092	8	6	condensates	condensate	NOUN
ap-2092	8	7	,	,	PUNCT
ap-2092	8	8	pt	pt	NOUN
ap-2092	8	9	symmetry	symmetry	NOUN
ap-2092	8	10	,	,	PUNCT
ap-2092	8	11	stability	stability	NOUN
ap-2092	8	12	,	,	PUNCT
ap-2092	8	13	bogoliubov	bogoliubov	PROPN
ap-2092	8	14	-	-	PUNCT
ap-2092	8	15	de	de	ADJ
ap-2092	8	16	gennes	genne	NOUN
ap-2092	8	17	equations	equation	NOUN
ap-2092	8	18	.	.	PUNCT
ap-2092	9	1	1	1	X
ap-2092	9	2	.	.	X
ap-2092	9	3	introduction	introduction	NOUN
ap-2092	9	4	in	in	ADP
ap-2092	9	5	quantum	quantum	ADJ
ap-2092	9	6	mechanics	mechanic	NOUN
ap-2092	9	7	non	non	ADJ
ap-2092	9	8	-	-	ADJ
ap-2092	9	9	hermitian	hermitian	ADJ
ap-2092	9	10	hamiltonians	hamiltonian	NOUN
ap-2092	9	11	with	with	ADP
ap-2092	9	12	imaginary	imaginary	ADJ
ap-2092	9	13	potentials	potential	NOUN
ap-2092	9	14	have	have	AUX
ap-2092	9	15	become	become	VERB
ap-2092	9	16	an	an	DET
ap-2092	9	17	important	important	ADJ
ap-2092	9	18	tool	tool	NOUN
ap-2092	9	19	to	to	PART
ap-2092	9	20	describe	describe	VERB
ap-2092	9	21	systems	system	NOUN
ap-2092	9	22	with	with	ADP
ap-2092	9	23	loss	loss	NOUN
ap-2092	9	24	or	or	CCONJ
ap-2092	9	25	gain	gain	VERB
ap-2092	9	26	effects	effect	NOUN
ap-2092	9	27	[	[	X
ap-2092	9	28	1	1	NUM
ap-2092	9	29	]	]	PUNCT
ap-2092	9	30	.	.	PUNCT
ap-2092	10	1	non	non	ADJ
ap-2092	10	2	-	-	ADJ
ap-2092	10	3	hermitian	hermitian	ADJ
ap-2092	10	4	pt	pt	PROPN
ap-2092	10	5	symmetric	symmetric	ADJ
ap-2092	10	6	hamiltonians	hamiltonian	NOUN
ap-2092	10	7	,	,	PUNCT
ap-2092	10	8	i.e.	i.e.	X
ap-2092	10	9	hamiltonians	hamiltonian	NOUN
ap-2092	10	10	commuting	commute	VERB
ap-2092	10	11	with	with	ADP
ap-2092	10	12	the	the	DET
ap-2092	10	13	combined	combine	VERB
ap-2092	10	14	action	action	NOUN
ap-2092	10	15	of	of	ADP
ap-2092	10	16	the	the	DET
ap-2092	10	17	parity	parity	NOUN
ap-2092	10	18	(	(	PUNCT
ap-2092	10	19	p	p	X
ap-2092	10	20	:	:	PUNCT
ap-2092	10	21	x→	x→	PUNCT
ap-2092	10	22	−x	−x	NOUN
ap-2092	10	23	,	,	PUNCT
ap-2092	10	24	p→	p→	VERB
ap-2092	10	25	−p	−p	NOUN
ap-2092	10	26	)	)	PUNCT
ap-2092	10	27	and	and	CCONJ
ap-2092	10	28	time	time	NOUN
ap-2092	10	29	reversal	reversal	NOUN
ap-2092	10	30	(	(	PUNCT
ap-2092	10	31	t	t	NOUN
ap-2092	10	32	:	:	PUNCT
ap-2092	10	33	x	x	X
ap-2092	10	34	→	→	SYM
ap-2092	10	35	x	x	SYM
ap-2092	10	36	,	,	PUNCT
ap-2092	10	37	p	p	X
ap-2092	10	38	→	→	SYM
ap-2092	10	39	−p	−p	NOUN
ap-2092	10	40	,	,	PUNCT
ap-2092	10	41	i	i	PROPN
ap-2092	10	42	→	→	SYM
ap-2092	10	43	−i	−i	ADJ
ap-2092	10	44	)	)	PUNCT
ap-2092	10	45	operators	operator	NOUN
ap-2092	10	46	,	,	PUNCT
ap-2092	10	47	possess	possess	VERB
ap-2092	10	48	the	the	DET
ap-2092	10	49	interesting	interesting	ADJ
ap-2092	10	50	property	property	NOUN
ap-2092	10	51	that	that	PRON
ap-2092	10	52	,	,	PUNCT
ap-2092	10	53	in	in	ADP
ap-2092	10	54	spite	spite	NOUN
ap-2092	10	55	of	of	ADP
ap-2092	10	56	the	the	DET
ap-2092	10	57	gain	gain	NOUN
ap-2092	10	58	and	and	CCONJ
ap-2092	10	59	loss	loss	NOUN
ap-2092	10	60	,	,	PUNCT
ap-2092	10	61	they	they	PRON
ap-2092	10	62	can	can	AUX
ap-2092	10	63	exhibit	exhibit	VERB
ap-2092	10	64	stationary	stationary	ADJ
ap-2092	10	65	states	state	NOUN
ap-2092	10	66	with	with	ADP
ap-2092	10	67	real	real	ADJ
ap-2092	10	68	eigenvalues	eigenvalue	NOUN
ap-2092	10	69	[	[	X
ap-2092	10	70	2	2	NUM
ap-2092	10	71	]	]	PUNCT
ap-2092	10	72	.	.	PUNCT
ap-2092	11	1	when	when	SCONJ
ap-2092	11	2	the	the	DET
ap-2092	11	3	strength	strength	NOUN
ap-2092	11	4	of	of	ADP
ap-2092	11	5	the	the	DET
ap-2092	11	6	gain	gain	NOUN
ap-2092	11	7	and	and	CCONJ
ap-2092	11	8	loss	loss	NOUN
ap-2092	11	9	contributions	contribution	NOUN
ap-2092	11	10	is	be	AUX
ap-2092	11	11	increased	increase	VERB
ap-2092	11	12	typically	typically	ADV
ap-2092	11	13	pairs	pair	NOUN
ap-2092	11	14	of	of	ADP
ap-2092	11	15	these	these	DET
ap-2092	11	16	real	real	ADJ
ap-2092	11	17	eigenvalues	eigenvalue	NOUN
ap-2092	11	18	pass	pass	VERB
ap-2092	11	19	through	through	ADP
ap-2092	11	20	an	an	DET
ap-2092	11	21	exceptional	exceptional	ADJ
ap-2092	11	22	point	point	NOUN
ap-2092	11	23	,	,	PUNCT
ap-2092	11	24	i.e.	i.e.	X
ap-2092	11	25	a	a	DET
ap-2092	11	26	branch	branch	NOUN
ap-2092	11	27	point	point	NOUN
ap-2092	11	28	at	at	ADP
ap-2092	11	29	which	which	PRON
ap-2092	11	30	both	both	CCONJ
ap-2092	11	31	the	the	DET
ap-2092	11	32	eigenvalues	eigenvalue	NOUN
ap-2092	11	33	and	and	CCONJ
ap-2092	11	34	the	the	DET
ap-2092	11	35	wave	wave	NOUN
ap-2092	11	36	functions	function	NOUN
ap-2092	11	37	are	be	AUX
ap-2092	11	38	identical	identical	ADJ
ap-2092	11	39	,	,	PUNCT
ap-2092	11	40	and	and	CCONJ
ap-2092	11	41	become	become	VERB
ap-2092	11	42	complex	complex	ADJ
ap-2092	11	43	and	and	CCONJ
ap-2092	11	44	complex	complex	ADJ
ap-2092	11	45	conjugate	conjugate	NOUN
ap-2092	11	46	.	.	PUNCT
ap-2092	12	1	a	a	DET
ap-2092	12	2	promising	promising	ADJ
ap-2092	12	3	candidate	candidate	NOUN
ap-2092	12	4	for	for	ADP
ap-2092	12	5	the	the	DET
ap-2092	12	6	realisation	realisation	NOUN
ap-2092	12	7	of	of	ADP
ap-2092	12	8	a	a	DET
ap-2092	12	9	pt	pt	NOUN
ap-2092	12	10	symmetric	symmetric	ADJ
ap-2092	12	11	quantum	quantum	NOUN
ap-2092	12	12	system	system	NOUN
ap-2092	12	13	are	be	AUX
ap-2092	12	14	bose	bose	NOUN
ap-2092	12	15	-	-	PUNCT
ap-2092	12	16	einstein	einstein	NOUN
ap-2092	12	17	condensates	condensate	NOUN
ap-2092	12	18	.	.	PUNCT
ap-2092	13	1	at	at	ADP
ap-2092	13	2	sufficiently	sufficiently	ADV
ap-2092	13	3	low	low	ADJ
ap-2092	13	4	temperatures	temperature	NOUN
ap-2092	13	5	and	and	CCONJ
ap-2092	13	6	densities	density	NOUN
ap-2092	13	7	they	they	PRON
ap-2092	13	8	can	can	AUX
ap-2092	13	9	in	in	ADP
ap-2092	13	10	the	the	DET
ap-2092	13	11	mean	mean	ADJ
ap-2092	13	12	-	-	PUNCT
ap-2092	13	13	field	field	NOUN
ap-2092	13	14	limit	limit	NOUN
ap-2092	13	15	be	be	AUX
ap-2092	13	16	described	describe	VERB
ap-2092	13	17	by	by	ADP
ap-2092	13	18	the	the	DET
ap-2092	13	19	nonlinear	nonlinear	ADJ
ap-2092	13	20	gross	gross	ADJ
ap-2092	13	21	-	-	PUNCT
ap-2092	13	22	pitaevskii	pitaevskii	ADJ
ap-2092	13	23	equation	equation	NOUN
ap-2092	13	24	[	[	X
ap-2092	13	25	3	3	NUM
ap-2092	13	26	,	,	PUNCT
ap-2092	13	27	4	4	NUM
ap-2092	13	28	]	]	PUNCT
ap-2092	13	29	.	.	PUNCT
ap-2092	14	1	if	if	SCONJ
ap-2092	14	2	a	a	DET
ap-2092	14	3	condensate	condensate	NOUN
ap-2092	14	4	is	be	AUX
ap-2092	14	5	trapped	trap	VERB
ap-2092	14	6	in	in	ADP
ap-2092	14	7	a	a	DET
ap-2092	14	8	double	double	ADJ
ap-2092	14	9	-	-	PUNCT
ap-2092	14	10	well	well	NOUN
ap-2092	14	11	potential	potential	NOUN
ap-2092	14	12	it	it	PRON
ap-2092	14	13	is	be	AUX
ap-2092	14	14	possible	possible	ADJ
ap-2092	14	15	to	to	PART
ap-2092	14	16	add	add	VERB
ap-2092	14	17	atoms	atom	NOUN
ap-2092	14	18	to	to	ADP
ap-2092	14	19	one	one	NUM
ap-2092	14	20	side	side	NOUN
ap-2092	14	21	of	of	ADP
ap-2092	14	22	the	the	DET
ap-2092	14	23	double	double	ADJ
ap-2092	14	24	well	well	NOUN
ap-2092	14	25	and	and	CCONJ
ap-2092	14	26	remove	remove	VERB
ap-2092	14	27	atoms	atom	NOUN
ap-2092	14	28	from	from	ADP
ap-2092	14	29	the	the	DET
ap-2092	14	30	other	other	ADJ
ap-2092	14	31	.	.	PUNCT
ap-2092	15	1	this	this	PRON
ap-2092	15	2	leads	lead	VERB
ap-2092	15	3	to	to	ADP
ap-2092	15	4	a	a	DET
ap-2092	15	5	gain	gain	NOUN
ap-2092	15	6	or	or	CCONJ
ap-2092	15	7	loss	loss	NOUN
ap-2092	15	8	to	to	ADP
ap-2092	15	9	the	the	DET
ap-2092	15	10	condensate	condensate	NOUN
ap-2092	15	11	’s	’s	PART
ap-2092	15	12	probability	probability	NOUN
ap-2092	15	13	amplitude	amplitude	NOUN
ap-2092	15	14	.	.	PUNCT
ap-2092	16	1	if	if	SCONJ
ap-2092	16	2	the	the	DET
ap-2092	16	3	strength	strength	NOUN
ap-2092	16	4	of	of	ADP
ap-2092	16	5	both	both	DET
ap-2092	16	6	contributions	contribution	NOUN
ap-2092	16	7	is	be	AUX
ap-2092	16	8	equal	equal	ADJ
ap-2092	16	9	,	,	PUNCT
ap-2092	16	10	the	the	DET
ap-2092	16	11	process	process	NOUN
ap-2092	16	12	can	can	AUX
ap-2092	16	13	effectively	effectively	ADV
ap-2092	16	14	be	be	AUX
ap-2092	16	15	described	describe	VERB
ap-2092	16	16	by	by	ADP
ap-2092	16	17	a	a	DET
ap-2092	16	18	complex	complex	ADJ
ap-2092	16	19	external	external	ADJ
ap-2092	16	20	potential	potential	ADJ
ap-2092	16	21	v	v	NOUN
ap-2092	16	22	(	(	PUNCT
ap-2092	16	23	−x	−x	NOUN
ap-2092	16	24	)	)	PUNCT
ap-2092	16	25	=	=	SYM
ap-2092	16	26	v	v	ADP
ap-2092	16	27	∗(x	∗(x	PROPN
ap-2092	16	28	)	)	PUNCT
ap-2092	16	29	rendering	render	VERB
ap-2092	16	30	the	the	DET
ap-2092	16	31	hamiltonian	hamiltonian	ADJ
ap-2092	16	32	pt	pt	X
ap-2092	16	33	symmetric	symmetric	ADJ
ap-2092	17	1	[	[	X
ap-2092	17	2	5	5	NUM
ap-2092	17	3	]	]	PUNCT
ap-2092	17	4	.	.	PUNCT
ap-2092	18	1	the	the	DET
ap-2092	18	2	experimental	experimental	ADJ
ap-2092	18	3	realisation	realisation	NOUN
ap-2092	18	4	of	of	ADP
ap-2092	18	5	an	an	DET
ap-2092	18	6	open	open	ADJ
ap-2092	18	7	quantum	quantum	NOUN
ap-2092	18	8	system	system	NOUN
ap-2092	18	9	with	with	ADP
ap-2092	18	10	pt	pt	NOUN
ap-2092	18	11	symmetry	symmetry	NOUN
ap-2092	18	12	will	will	AUX
ap-2092	18	13	be	be	AUX
ap-2092	18	14	an	an	DET
ap-2092	18	15	important	important	ADJ
ap-2092	18	16	step	step	NOUN
ap-2092	18	17	since	since	SCONJ
ap-2092	18	18	the	the	DET
ap-2092	18	19	experimental	experimental	ADJ
ap-2092	18	20	verification	verification	NOUN
ap-2092	18	21	has	have	AUX
ap-2092	18	22	only	only	ADV
ap-2092	18	23	been	be	AUX
ap-2092	18	24	achieved	achieve	VERB
ap-2092	18	25	in	in	ADP
ap-2092	18	26	optics	optic	NOUN
ap-2092	18	27	so	so	ADV
ap-2092	18	28	far	far	ADV
ap-2092	19	1	[	[	X
ap-2092	19	2	6	6	NUM
ap-2092	19	3	,	,	PUNCT
ap-2092	19	4	7	7	NUM
ap-2092	19	5	]	]	PUNCT
ap-2092	19	6	.	.	PUNCT
ap-2092	20	1	the	the	DET
ap-2092	20	2	nonlinearity∝	nonlinearity∝	PROPN
ap-2092	20	3	|ψ(x	|ψ(x	PROPN
ap-2092	20	4	,	,	PUNCT
ap-2092	20	5	t)|2	t)|2	NOUN
ap-2092	20	6	of	of	ADP
ap-2092	20	7	the	the	DET
ap-2092	20	8	gross	gross	ADJ
ap-2092	20	9	-	-	PUNCT
ap-2092	20	10	pitaevskii	pitaevskii	ADJ
ap-2092	20	11	equation	equation	NOUN
ap-2092	20	12	introduces	introduce	VERB
ap-2092	20	13	new	new	ADJ
ap-2092	20	14	interesting	interesting	ADJ
ap-2092	20	15	properties	property	NOUN
ap-2092	21	1	[	[	X
ap-2092	21	2	8–17	8–17	NOUN
ap-2092	21	3	]	]	X
ap-2092	21	4	such	such	ADJ
ap-2092	21	5	as	as	ADP
ap-2092	21	6	pt	pt	PROPN
ap-2092	21	7	broken	break	VERB
ap-2092	21	8	states	state	NOUN
ap-2092	21	9	which	which	PRON
ap-2092	21	10	appear	appear	VERB
ap-2092	21	11	for	for	ADP
ap-2092	21	12	gain	gain	NOUN
ap-2092	21	13	/	/	SYM
ap-2092	21	14	loss	loss	NOUN
ap-2092	21	15	contributions	contribution	NOUN
ap-2092	21	16	lower	low	ADJ
ap-2092	21	17	than	than	ADP
ap-2092	21	18	those	those	PRON
ap-2092	21	19	at	at	ADP
ap-2092	21	20	which	which	PRON
ap-2092	21	21	the	the	DET
ap-2092	21	22	corresponding	correspond	VERB
ap-2092	21	23	pt	pt	NOUN
ap-2092	21	24	symmetric	symmetric	ADJ
ap-2092	21	25	states	state	NOUN
ap-2092	21	26	vanish	vanish	VERB
ap-2092	21	27	.	.	PUNCT
ap-2092	22	1	in	in	ADP
ap-2092	22	2	optics	optic	NOUN
ap-2092	22	3	the	the	DET
ap-2092	22	4	same	same	ADJ
ap-2092	22	5	effect	effect	NOUN
ap-2092	22	6	can	can	AUX
ap-2092	22	7	be	be	AUX
ap-2092	22	8	observed	observe	VERB
ap-2092	22	9	for	for	ADP
ap-2092	22	10	wave	wave	NOUN
ap-2092	22	11	guides	guide	NOUN
ap-2092	22	12	with	with	ADP
ap-2092	22	13	a	a	DET
ap-2092	22	14	kerr	kerr	PROPN
ap-2092	22	15	nonlinearity	nonlinearity	NOUN
ap-2092	22	16	.	.	PUNCT
ap-2092	23	1	they	they	PRON
ap-2092	23	2	are	be	AUX
ap-2092	23	3	described	describe	VERB
ap-2092	23	4	by	by	ADP
ap-2092	23	5	an	an	DET
ap-2092	23	6	equation	equation	NOUN
ap-2092	23	7	that	that	PRON
ap-2092	23	8	is	be	AUX
ap-2092	23	9	mathematically	mathematically	ADV
ap-2092	23	10	equivalent	equivalent	ADJ
ap-2092	23	11	to	to	ADP
ap-2092	23	12	the	the	DET
ap-2092	23	13	grosspitaevskii	grosspitaevskii	ADJ
ap-2092	23	14	equation	equation	NOUN
ap-2092	23	15	.	.	PUNCT
ap-2092	24	1	it	it	PRON
ap-2092	24	2	has	have	AUX
ap-2092	24	3	been	be	AUX
ap-2092	24	4	shown	show	VERB
ap-2092	24	5	that	that	SCONJ
ap-2092	24	6	the	the	DET
ap-2092	24	7	additional	additional	ADJ
ap-2092	24	8	features	feature	NOUN
ap-2092	24	9	appearing	appear	VERB
ap-2092	24	10	in	in	ADP
ap-2092	24	11	the	the	DET
ap-2092	24	12	presence	presence	NOUN
ap-2092	24	13	of	of	ADP
ap-2092	24	14	the	the	DET
ap-2092	24	15	nonlinearity	nonlinearity	NOUN
ap-2092	24	16	might	might	AUX
ap-2092	24	17	be	be	AUX
ap-2092	24	18	exploited	exploit	VERB
ap-2092	24	19	to	to	PART
ap-2092	24	20	create	create	VERB
ap-2092	24	21	uni	uni	ADJ
ap-2092	24	22	-	-	ADJ
ap-2092	24	23	directional	directional	ADJ
ap-2092	24	24	structures	structure	NOUN
ap-2092	25	1	[	[	X
ap-2092	25	2	18	18	NUM
ap-2092	25	3	]	]	PUNCT
ap-2092	25	4	or	or	CCONJ
ap-2092	25	5	solitons	soliton	NOUN
ap-2092	25	6	[	[	X
ap-2092	25	7	19–24	19–24	NUM
ap-2092	25	8	]	]	PUNCT
ap-2092	25	9	.	.	PUNCT
ap-2092	26	1	since	since	SCONJ
ap-2092	26	2	pt	pt	PROPN
ap-2092	26	3	symmetry	symmetry	NOUN
ap-2092	26	4	in	in	ADP
ap-2092	26	5	optics	optic	NOUN
ap-2092	26	6	is	be	AUX
ap-2092	26	7	extensively	extensively	ADV
ap-2092	26	8	studied	study	VERB
ap-2092	26	9	[	[	PUNCT
ap-2092	26	10	5	5	NUM
ap-2092	26	11	,	,	PUNCT
ap-2092	26	12	18–28	18–28	NUM
ap-2092	26	13	]	]	PUNCT
ap-2092	26	14	and	and	CCONJ
ap-2092	26	15	has	have	AUX
ap-2092	26	16	been	be	AUX
ap-2092	26	17	experimentally	experimentally	ADV
ap-2092	26	18	realised	realise	VERB
ap-2092	26	19	[	[	X
ap-2092	26	20	6	6	NUM
ap-2092	26	21	,	,	PUNCT
ap-2092	26	22	7	7	NUM
ap-2092	26	23	]	]	PUNCT
ap-2092	26	24	these	these	DET
ap-2092	26	25	approaches	approach	NOUN
ap-2092	26	26	seem	seem	VERB
ap-2092	26	27	to	to	PART
ap-2092	26	28	be	be	AUX
ap-2092	26	29	very	very	ADV
ap-2092	26	30	promising	promising	ADJ
ap-2092	26	31	.	.	PUNCT
ap-2092	27	1	from	from	ADP
ap-2092	27	2	the	the	DET
ap-2092	27	3	mathematical	mathematical	ADJ
ap-2092	27	4	point	point	NOUN
ap-2092	27	5	of	of	ADP
ap-2092	27	6	view	view	NOUN
ap-2092	27	7	a	a	DET
ap-2092	27	8	new	new	ADJ
ap-2092	27	9	type	type	NOUN
ap-2092	27	10	of	of	ADP
ap-2092	27	11	bifurcation	bifurcation	NOUN
ap-2092	27	12	appearing	appear	VERB
ap-2092	27	13	in	in	ADP
ap-2092	27	14	the	the	DET
ap-2092	27	15	nonlinear	nonlinear	ADJ
ap-2092	27	16	pt	pt	INTJ
ap-2092	27	17	symmetric	symmetric	ADJ
ap-2092	27	18	gross	gross	ADJ
ap-2092	27	19	-	-	PUNCT
ap-2092	27	20	pitaevskii	pitaevskii	ADJ
ap-2092	27	21	equation	equation	NOUN
ap-2092	27	22	is	be	AUX
ap-2092	27	23	of	of	ADP
ap-2092	27	24	special	special	ADJ
ap-2092	27	25	interest	interest	NOUN
ap-2092	28	1	[	[	X
ap-2092	28	2	8–17	8–17	NOUN
ap-2092	28	3	]	]	X
ap-2092	28	4	.	.	PUNCT
ap-2092	29	1	as	as	ADP
ap-2092	29	2	in	in	ADP
ap-2092	29	3	linear	linear	ADJ
ap-2092	29	4	quantum	quantum	NOUN
ap-2092	29	5	systems	system	NOUN
ap-2092	29	6	,	,	PUNCT
ap-2092	29	7	two	two	NUM
ap-2092	29	8	pt	pt	NOUN
ap-2092	29	9	symmetric	symmetric	ADJ
ap-2092	29	10	stationary	stationary	ADJ
ap-2092	29	11	states	state	NOUN
ap-2092	29	12	merge	merge	VERB
ap-2092	29	13	in	in	ADP
ap-2092	29	14	an	an	DET
ap-2092	29	15	exceptional	exceptional	ADJ
ap-2092	29	16	point	point	NOUN
ap-2092	29	17	if	if	SCONJ
ap-2092	29	18	the	the	DET
ap-2092	29	19	strength	strength	NOUN
ap-2092	29	20	of	of	ADP
ap-2092	29	21	a	a	DET
ap-2092	29	22	parameter	parameter	NOUN
ap-2092	29	23	describing	describe	VERB
ap-2092	29	24	the	the	DET
ap-2092	29	25	gain	gain	NOUN
ap-2092	29	26	and	and	CCONJ
ap-2092	29	27	loss	loss	NOUN
ap-2092	29	28	processes	process	NOUN
ap-2092	29	29	is	be	AUX
ap-2092	29	30	increased	increase	VERB
ap-2092	29	31	.	.	PUNCT
ap-2092	30	1	however	however	ADV
ap-2092	30	2	,	,	PUNCT
ap-2092	30	3	in	in	ADP
ap-2092	30	4	contrast	contrast	NOUN
ap-2092	30	5	to	to	ADP
ap-2092	30	6	its	its	PRON
ap-2092	30	7	linear	linear	ADJ
ap-2092	30	8	counterpart	counterpart	NOUN
ap-2092	30	9	,	,	PUNCT
ap-2092	30	10	the	the	DET
ap-2092	30	11	gross	gross	ADJ
ap-2092	30	12	-	-	PUNCT
ap-2092	30	13	pitaevskii	pitaevskii	ADJ
ap-2092	30	14	equation	equation	NOUN
ap-2092	30	15	possesses	possess	VERB
ap-2092	30	16	no	no	DET
ap-2092	30	17	pt	pt	INTJ
ap-2092	30	18	broken	break	VERB
ap-2092	30	19	states	state	NOUN
ap-2092	30	20	emerging	emerge	VERB
ap-2092	30	21	at	at	ADP
ap-2092	30	22	this	this	DET
ap-2092	30	23	exceptional	exceptional	ADJ
ap-2092	30	24	point	point	NOUN
ap-2092	30	25	.	.	PUNCT
ap-2092	31	1	they	they	PRON
ap-2092	31	2	already	already	ADV
ap-2092	31	3	appear	appear	VERB
ap-2092	31	4	for	for	ADP
ap-2092	31	5	lower	low	ADJ
ap-2092	31	6	strengths	strength	NOUN
ap-2092	31	7	of	of	ADP
ap-2092	31	8	the	the	DET
ap-2092	31	9	gain	gain	NOUN
ap-2092	31	10	/	/	SYM
ap-2092	31	11	loss	loss	NOUN
ap-2092	31	12	parameter	parameter	NOUN
ap-2092	31	13	and	and	CCONJ
ap-2092	31	14	bifurcate	bifurcate	VERB
ap-2092	31	15	from	from	ADP
ap-2092	31	16	one	one	NUM
ap-2092	31	17	of	of	ADP
ap-2092	31	18	the	the	DET
ap-2092	31	19	pt	pt	NOUN
ap-2092	31	20	symmetric	symmetric	ADJ
ap-2092	31	21	states	state	NOUN
ap-2092	31	22	in	in	ADP
ap-2092	31	23	a	a	DET
ap-2092	31	24	pitchfork	pitchfork	NOUN
ap-2092	31	25	bifurcation	bifurcation	NOUN
ap-2092	31	26	.	.	PUNCT
ap-2092	32	1	133	133	NUM
ap-2092	32	2	http://dx.doi.org/10.14311/ap.2014.54.0133	http://dx.doi.org/10.14311/ap.2014.54.0133	X
ap-2092	32	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2092	32	4	a.	a.	NOUN
ap-2092	32	5	löhle	löhle	PROPN
ap-2092	32	6	,	,	PUNCT
ap-2092	32	7	h.	h.	PROPN
ap-2092	32	8	cartarius	cartarius	PROPN
ap-2092	32	9	,	,	PUNCT
ap-2092	32	10	d.	d.	PROPN
ap-2092	32	11	haag	haag	PROPN
ap-2092	32	12	et	et	PROPN
ap-2092	32	13	al	al	PROPN
ap-2092	32	14	.	.	PROPN
ap-2092	33	1	acta	acta	PROPN
ap-2092	33	2	polytechnica	polytechnica	PROPN
ap-2092	33	3	the	the	DET
ap-2092	33	4	new	new	ADJ
ap-2092	33	5	bifurcation	bifurcation	NOUN
ap-2092	33	6	point	point	NOUN
ap-2092	33	7	has	have	AUX
ap-2092	33	8	been	be	AUX
ap-2092	33	9	identified	identify	VERB
ap-2092	33	10	to	to	PART
ap-2092	33	11	be	be	AUX
ap-2092	33	12	a	a	DET
ap-2092	33	13	third	third	ADJ
ap-2092	33	14	-	-	PUNCT
ap-2092	33	15	order	order	NOUN
ap-2092	33	16	exceptional	exceptional	ADJ
ap-2092	33	17	point	point	NOUN
ap-2092	33	18	[	[	X
ap-2092	33	19	10	10	NUM
ap-2092	33	20	]	]	PUNCT
ap-2092	33	21	.	.	PUNCT
ap-2092	34	1	for	for	ADP
ap-2092	34	2	attractive	attractive	ADJ
ap-2092	34	3	nonlinearities	nonlinearitie	NOUN
ap-2092	34	4	one	one	NUM
ap-2092	34	5	finds	find	VERB
ap-2092	34	6	that	that	SCONJ
ap-2092	34	7	the	the	DET
ap-2092	34	8	pt	pt	PROPN
ap-2092	34	9	broken	break	VERB
ap-2092	34	10	solutions	solution	NOUN
ap-2092	34	11	bifurcate	bifurcate	NOUN
ap-2092	34	12	from	from	ADP
ap-2092	34	13	the	the	DET
ap-2092	34	14	ground	ground	NOUN
ap-2092	34	15	state	state	NOUN
ap-2092	34	16	.	.	PUNCT
ap-2092	35	1	in	in	ADP
ap-2092	35	2	this	this	DET
ap-2092	35	3	scenario	scenario	NOUN
ap-2092	35	4	the	the	DET
ap-2092	35	5	pt	pt	PROPN
ap-2092	35	6	symmetric	symmetric	ADJ
ap-2092	35	7	ground	ground	NOUN
ap-2092	35	8	state	state	NOUN
ap-2092	35	9	is	be	AUX
ap-2092	35	10	the	the	DET
ap-2092	35	11	only	only	ADJ
ap-2092	35	12	state	state	NOUN
ap-2092	35	13	which	which	PRON
ap-2092	35	14	exists	exist	VERB
ap-2092	35	15	on	on	ADP
ap-2092	35	16	both	both	DET
ap-2092	35	17	sides	side	NOUN
ap-2092	35	18	of	of	ADP
ap-2092	35	19	the	the	DET
ap-2092	35	20	bifurcation	bifurcation	NOUN
ap-2092	35	21	and	and	CCONJ
ap-2092	35	22	always	always	ADV
ap-2092	35	23	possesses	possess	VERB
ap-2092	35	24	a	a	DET
ap-2092	35	25	real	real	ADJ
ap-2092	35	26	energy	energy	NOUN
ap-2092	35	27	eigenvalue	eigenvalue	NOUN
ap-2092	35	28	.	.	PUNCT
ap-2092	36	1	the	the	DET
ap-2092	36	2	pitchfork	pitchfork	NOUN
ap-2092	36	3	bifurcation	bifurcation	NOUN
ap-2092	36	4	is	be	AUX
ap-2092	36	5	expected	expect	VERB
ap-2092	36	6	to	to	PART
ap-2092	36	7	entail	entail	VERB
ap-2092	36	8	a	a	DET
ap-2092	36	9	change	change	NOUN
ap-2092	36	10	of	of	ADP
ap-2092	36	11	its	its	PRON
ap-2092	36	12	stability	stability	NOUN
ap-2092	36	13	.	.	PUNCT
ap-2092	37	1	however	however	ADV
ap-2092	37	2	,	,	PUNCT
ap-2092	37	3	it	it	PRON
ap-2092	37	4	is	be	AUX
ap-2092	37	5	observed	observe	VERB
ap-2092	37	6	that	that	SCONJ
ap-2092	37	7	this	this	DET
ap-2092	37	8	stability	stability	NOUN
ap-2092	37	9	change	change	NOUN
ap-2092	37	10	does	do	AUX
ap-2092	37	11	not	not	PART
ap-2092	37	12	occur	occur	VERB
ap-2092	37	13	exactly	exactly	ADV
ap-2092	37	14	at	at	ADP
ap-2092	37	15	the	the	DET
ap-2092	37	16	bifurcation	bifurcation	NOUN
ap-2092	37	17	but	but	CCONJ
ap-2092	37	18	at	at	ADP
ap-2092	37	19	a	a	DET
ap-2092	37	20	slightly	slightly	ADV
ap-2092	37	21	different	different	ADJ
ap-2092	37	22	value	value	NOUN
ap-2092	37	23	of	of	ADP
ap-2092	37	24	the	the	DET
ap-2092	37	25	gain	gain	NOUN
ap-2092	37	26	/	/	SYM
ap-2092	37	27	loss	loss	NOUN
ap-2092	37	28	parameter	parameter	NOUN
ap-2092	37	29	.	.	PUNCT
ap-2092	38	1	the	the	DET
ap-2092	38	2	discrepancy	discrepancy	NOUN
ap-2092	38	3	between	between	ADP
ap-2092	38	4	the	the	DET
ap-2092	38	5	points	point	NOUN
ap-2092	38	6	of	of	ADP
ap-2092	38	7	bifurcation	bifurcation	NOUN
ap-2092	38	8	and	and	CCONJ
ap-2092	38	9	stability	stability	NOUN
ap-2092	38	10	change	change	NOUN
ap-2092	38	11	seems	seem	VERB
ap-2092	38	12	to	to	PART
ap-2092	38	13	be	be	AUX
ap-2092	38	14	surprising	surprising	ADJ
ap-2092	38	15	and	and	CCONJ
ap-2092	38	16	does	do	AUX
ap-2092	38	17	not	not	PART
ap-2092	38	18	appear	appear	VERB
ap-2092	38	19	in	in	ADP
ap-2092	38	20	all	all	DET
ap-2092	38	21	similar	similar	ADJ
ap-2092	38	22	systems	system	NOUN
ap-2092	38	23	.	.	PUNCT
ap-2092	39	1	the	the	DET
ap-2092	39	2	mean	mean	ADJ
ap-2092	39	3	-	-	PUNCT
ap-2092	39	4	field	field	NOUN
ap-2092	39	5	limit	limit	NOUN
ap-2092	39	6	of	of	ADP
ap-2092	39	7	a	a	DET
ap-2092	39	8	two	two	NUM
ap-2092	39	9	mode	mode	NOUN
ap-2092	39	10	approximation	approximation	NOUN
ap-2092	39	11	with	with	ADP
ap-2092	39	12	a	a	DET
ap-2092	39	13	bose	bose	NOUN
ap-2092	39	14	-	-	PUNCT
ap-2092	39	15	hubbard	hubbard	NOUN
ap-2092	39	16	hamiltonian	hamiltonian	NOUN
ap-2092	39	17	[	[	X
ap-2092	39	18	14–17	14–17	NUM
ap-2092	39	19	]	]	PUNCT
ap-2092	39	20	does	do	AUX
ap-2092	39	21	not	not	PART
ap-2092	39	22	show	show	VERB
ap-2092	39	23	this	this	DET
ap-2092	39	24	effect	effect	NOUN
ap-2092	39	25	.	.	PUNCT
ap-2092	40	1	the	the	DET
ap-2092	40	2	model	model	NOUN
ap-2092	40	3	has	have	VERB
ap-2092	40	4	,	,	PUNCT
ap-2092	40	5	however	however	ADV
ap-2092	40	6	,	,	PUNCT
ap-2092	40	7	two	two	NUM
ap-2092	40	8	crucial	crucial	ADJ
ap-2092	40	9	differences	difference	NOUN
ap-2092	40	10	from	from	ADP
ap-2092	40	11	the	the	DET
ap-2092	40	12	treatment	treatment	NOUN
ap-2092	40	13	of	of	ADP
ap-2092	40	14	bose	bose	NOUN
ap-2092	40	15	-	-	PUNCT
ap-2092	40	16	einstein	einstein	NOUN
ap-2092	40	17	condensates	condensate	NOUN
ap-2092	40	18	with	with	ADP
ap-2092	40	19	the	the	DET
ap-2092	40	20	full	full	ADJ
ap-2092	40	21	gross	gross	ADJ
ap-2092	40	22	-	-	PUNCT
ap-2092	40	23	pitaevskii	pitaevskii	ADJ
ap-2092	40	24	equation	equation	NOUN
ap-2092	40	25	in	in	ADP
ap-2092	40	26	ref	ref	NOUN
ap-2092	40	27	.	.	PUNCT
ap-2092	41	1	[	[	X
ap-2092	41	2	11	11	NUM
ap-2092	41	3	]	]	PUNCT
ap-2092	41	4	.	.	PUNCT
ap-2092	42	1	the	the	DET
ap-2092	42	2	latter	latter	ADJ
ap-2092	42	3	system	system	NOUN
ap-2092	42	4	contains	contain	VERB
ap-2092	42	5	a	a	DET
ap-2092	42	6	harmonic	harmonic	ADJ
ap-2092	42	7	trap	trap	NOUN
ap-2092	42	8	in	in	ADP
ap-2092	42	9	which	which	PRON
ap-2092	42	10	infinitely	infinitely	ADV
ap-2092	42	11	many	many	ADJ
ap-2092	42	12	stationary	stationary	ADJ
ap-2092	42	13	states	state	NOUN
ap-2092	42	14	can	can	AUX
ap-2092	42	15	be	be	AUX
ap-2092	42	16	found	find	VERB
ap-2092	42	17	,	,	PUNCT
ap-2092	42	18	whereas	whereas	SCONJ
ap-2092	42	19	the	the	DET
ap-2092	42	20	nonlinear	nonlinear	ADJ
ap-2092	42	21	two	two	NUM
ap-2092	42	22	-	-	PUNCT
ap-2092	42	23	mode	mode	NOUN
ap-2092	42	24	system	system	NOUN
ap-2092	42	25	exhibits	exhibit	VERB
ap-2092	42	26	only	only	ADV
ap-2092	42	27	four	four	NUM
ap-2092	42	28	states	state	NOUN
ap-2092	42	29	,	,	PUNCT
ap-2092	42	30	viz	viz	PROPN
ap-2092	42	31	.	.	PUNCT
ap-2092	43	1	the	the	DET
ap-2092	43	2	two	two	NUM
ap-2092	43	3	pt	pt	NOUN
ap-2092	43	4	symmetric	symmetric	NOUN
ap-2092	43	5	and	and	CCONJ
ap-2092	43	6	the	the	DET
ap-2092	43	7	two	two	NUM
ap-2092	43	8	pt	pt	NOUN
ap-2092	43	9	broken	break	VERB
ap-2092	43	10	states	state	NOUN
ap-2092	43	11	mentioned	mention	VERB
ap-2092	43	12	above	above	ADV
ap-2092	43	13	.	.	PUNCT
ap-2092	44	1	furthermore	furthermore	ADV
ap-2092	44	2	the	the	DET
ap-2092	44	3	nonlinearity	nonlinearity	NOUN
ap-2092	44	4	derived	derive	VERB
ap-2092	44	5	in	in	ADP
ap-2092	44	6	[	[	X
ap-2092	44	7	14	14	NUM
ap-2092	44	8	,	,	PUNCT
ap-2092	44	9	15	15	NUM
ap-2092	44	10	]	]	PUNCT
ap-2092	44	11	is	be	AUX
ap-2092	44	12	slightly	slightly	ADV
ap-2092	44	13	different	different	ADJ
ap-2092	44	14	from	from	ADP
ap-2092	44	15	that	that	PRON
ap-2092	44	16	of	of	ADP
ap-2092	44	17	the	the	DET
ap-2092	44	18	gross	gross	ADJ
ap-2092	44	19	-	-	PUNCT
ap-2092	44	20	pitaevskii	pitaevskii	ADJ
ap-2092	44	21	equation	equation	NOUN
ap-2092	44	22	.	.	PUNCT
ap-2092	45	1	it	it	PRON
ap-2092	45	2	has	have	VERB
ap-2092	45	3	the	the	DET
ap-2092	45	4	form	form	NOUN
ap-2092	45	5	∝	∝	PROPN
ap-2092	45	6	|ψ|2/||ψ||2	|ψ|2/||ψ||2	PROPN
ap-2092	45	7	,	,	PUNCT
ap-2092	45	8	and	and	CCONJ
ap-2092	45	9	hence	hence	ADV
ap-2092	45	10	does	do	AUX
ap-2092	45	11	not	not	PART
ap-2092	45	12	depend	depend	VERB
ap-2092	45	13	on	on	ADP
ap-2092	45	14	the	the	DET
ap-2092	45	15	norm	norm	NOUN
ap-2092	45	16	of	of	ADP
ap-2092	45	17	the	the	DET
ap-2092	45	18	wave	wave	NOUN
ap-2092	45	19	function	function	NOUN
ap-2092	45	20	.	.	PUNCT
ap-2092	46	1	thus	thus	ADV
ap-2092	46	2	,	,	PUNCT
ap-2092	46	3	there	there	PRON
ap-2092	46	4	might	might	AUX
ap-2092	46	5	be	be	AUX
ap-2092	46	6	two	two	NUM
ap-2092	46	7	reasons	reason	NOUN
ap-2092	46	8	for	for	ADP
ap-2092	46	9	the	the	DET
ap-2092	46	10	appearance	appearance	NOUN
ap-2092	46	11	of	of	ADP
ap-2092	46	12	the	the	DET
ap-2092	46	13	discrepancy	discrepancy	NOUN
ap-2092	46	14	.	.	PUNCT
ap-2092	47	1	it	it	PRON
ap-2092	47	2	could	could	AUX
ap-2092	47	3	have	have	VERB
ap-2092	47	4	its	its	PRON
ap-2092	47	5	origin	origin	NOUN
ap-2092	47	6	in	in	ADP
ap-2092	47	7	the	the	DET
ap-2092	47	8	existence	existence	NOUN
ap-2092	47	9	of	of	ADP
ap-2092	47	10	higher	high	ADJ
ap-2092	47	11	modes	mode	NOUN
ap-2092	47	12	influencing	influence	VERB
ap-2092	47	13	the	the	DET
ap-2092	47	14	ground	ground	NOUN
ap-2092	47	15	state	state	NOUN
ap-2092	47	16	’s	’s	PART
ap-2092	47	17	stability	stability	NOUN
ap-2092	47	18	or	or	CCONJ
ap-2092	47	19	in	in	ADP
ap-2092	47	20	the	the	DET
ap-2092	47	21	norm	norm	NOUN
ap-2092	47	22	-	-	PUNCT
ap-2092	47	23	dependency	dependency	NOUN
ap-2092	47	24	of	of	ADP
ap-2092	47	25	the	the	DET
ap-2092	47	26	gross	gross	ADJ
ap-2092	47	27	-	-	PUNCT
ap-2092	47	28	pitaevskii	pitaevskii	ADJ
ap-2092	47	29	nonlinearity	nonlinearity	NOUN
ap-2092	47	30	.	.	PUNCT
ap-2092	48	1	it	it	PRON
ap-2092	48	2	is	be	AUX
ap-2092	48	3	the	the	DET
ap-2092	48	4	purpose	purpose	NOUN
ap-2092	48	5	of	of	ADP
ap-2092	48	6	this	this	DET
ap-2092	48	7	article	article	NOUN
ap-2092	48	8	to	to	PART
ap-2092	48	9	clarify	clarify	VERB
ap-2092	48	10	this	this	DET
ap-2092	48	11	question	question	NOUN
ap-2092	48	12	.	.	PUNCT
ap-2092	49	1	to	to	PART
ap-2092	49	2	do	do	VERB
ap-2092	49	3	so	so	ADV
ap-2092	49	4	we	we	PRON
ap-2092	49	5	study	study	VERB
ap-2092	49	6	a	a	DET
ap-2092	49	7	bose	bose	NOUN
ap-2092	49	8	-	-	PUNCT
ap-2092	49	9	einstein	einstein	NOUN
ap-2092	49	10	condensate	condensate	NOUN
ap-2092	49	11	in	in	ADP
ap-2092	49	12	an	an	DET
ap-2092	49	13	idealised	idealised	ADJ
ap-2092	49	14	double	double	ADJ
ap-2092	49	15	-	-	PUNCT
ap-2092	49	16	δ	δ	NOUN
ap-2092	49	17	trap	trap	NOUN
ap-2092	49	18	[	[	X
ap-2092	49	19	8–10	8–10	NOUN
ap-2092	49	20	]	]	PUNCT
ap-2092	49	21	,	,	PUNCT
ap-2092	49	22	a	a	DET
ap-2092	49	23	system	system	NOUN
ap-2092	49	24	of	of	ADP
ap-2092	49	25	which	which	PRON
ap-2092	49	26	already	already	ADV
ap-2092	49	27	its	its	PRON
ap-2092	49	28	linear	linear	ADJ
ap-2092	49	29	counterpart	counterpart	NOUN
ap-2092	49	30	helped	help	VERB
ap-2092	49	31	to	to	PART
ap-2092	49	32	understand	understand	VERB
ap-2092	49	33	basic	basic	ADJ
ap-2092	49	34	properties	property	NOUN
ap-2092	49	35	of	of	ADP
ap-2092	49	36	pt	pt	X
ap-2092	49	37	symmetric	symmetric	ADJ
ap-2092	49	38	structures	structure	NOUN
ap-2092	49	39	[	[	X
ap-2092	49	40	29–33	29–33	NUM
ap-2092	49	41	]	]	PUNCT
ap-2092	49	42	.	.	PUNCT
ap-2092	50	1	this	this	DET
ap-2092	50	2	system	system	NOUN
ap-2092	50	3	is	be	AUX
ap-2092	50	4	described	describe	VERB
ap-2092	50	5	by	by	ADP
ap-2092	50	6	the	the	DET
ap-2092	50	7	gross	gross	ADJ
ap-2092	50	8	-	-	PUNCT
ap-2092	50	9	pitaevskii	pitaevskii	ADJ
ap-2092	50	10	equation	equation	NOUN
ap-2092	50	11	,	,	PUNCT
ap-2092	50	12	i.e.	i.e.	X
ap-2092	50	13	the	the	DET
ap-2092	50	14	contact	contact	NOUN
ap-2092	50	15	interaction	interaction	NOUN
ap-2092	50	16	has	have	VERB
ap-2092	50	17	the	the	DET
ap-2092	50	18	norm	norm	NOUN
ap-2092	50	19	-	-	PUNCT
ap-2092	50	20	dependent	dependent	ADJ
ap-2092	50	21	form	form	NOUN
ap-2092	50	22	∝	∝	PROPN
ap-2092	50	23	|ψ(x	|ψ(x	NOUN
ap-2092	50	24	,	,	PUNCT
ap-2092	50	25	t)|2	t)|2	PROPN
ap-2092	50	26	.	.	PUNCT
ap-2092	51	1	however	however	ADV
ap-2092	51	2	,	,	PUNCT
ap-2092	51	3	it	it	PRON
ap-2092	51	4	exhibits	exhibit	VERB
ap-2092	51	5	only	only	ADV
ap-2092	51	6	four	four	NUM
ap-2092	51	7	stationary	stationary	ADJ
ap-2092	51	8	states	state	NOUN
ap-2092	51	9	of	of	ADP
ap-2092	51	10	which	which	PRON
ap-2092	51	11	two	two	NUM
ap-2092	51	12	are	be	AUX
ap-2092	51	13	pt	pt	NOUN
ap-2092	51	14	symmetric	symmetric	ADJ
ap-2092	51	15	and	and	CCONJ
ap-2092	51	16	two	two	NUM
ap-2092	51	17	are	be	AUX
ap-2092	51	18	pt	pt	NOUN
ap-2092	51	19	broken	break	VERB
ap-2092	51	20	as	as	ADP
ap-2092	51	21	in	in	ADP
ap-2092	51	22	the	the	DET
ap-2092	51	23	two	two	NUM
ap-2092	51	24	-	-	PUNCT
ap-2092	51	25	mode	mode	NOUN
ap-2092	51	26	model	model	NOUN
ap-2092	51	27	[	[	X
ap-2092	51	28	14	14	NUM
ap-2092	51	29	–	–	PUNCT
ap-2092	51	30	17	17	NUM
ap-2092	51	31	]	]	PUNCT
ap-2092	51	32	.	.	PUNCT
ap-2092	52	1	additionally	additionally	ADV
ap-2092	52	2	,	,	PUNCT
ap-2092	52	3	in	in	ADP
ap-2092	52	4	a	a	DET
ap-2092	52	5	numerical	numerical	ADJ
ap-2092	52	6	study	study	NOUN
ap-2092	52	7	the	the	DET
ap-2092	52	8	structure	structure	NOUN
ap-2092	52	9	of	of	ADP
ap-2092	52	10	the	the	DET
ap-2092	52	11	nonlinearity	nonlinearity	NOUN
ap-2092	52	12	can	can	AUX
ap-2092	52	13	easily	easily	ADV
ap-2092	52	14	be	be	AUX
ap-2092	52	15	changed	change	VERB
ap-2092	52	16	such	such	ADJ
ap-2092	52	17	that	that	SCONJ
ap-2092	52	18	the	the	DET
ap-2092	52	19	system	system	NOUN
ap-2092	52	20	’s	’s	PART
ap-2092	52	21	mathematical	mathematical	ADJ
ap-2092	52	22	properties	property	NOUN
ap-2092	52	23	can	can	AUX
ap-2092	52	24	be	be	AUX
ap-2092	52	25	brought	bring	VERB
ap-2092	52	26	into	into	ADP
ap-2092	52	27	agreement	agreement	NOUN
ap-2092	52	28	with	with	ADP
ap-2092	52	29	the	the	DET
ap-2092	52	30	mean	mean	ADJ
ap-2092	52	31	-	-	PUNCT
ap-2092	52	32	field	field	NOUN
ap-2092	52	33	limit	limit	NOUN
ap-2092	52	34	of	of	ADP
ap-2092	52	35	the	the	DET
ap-2092	52	36	bosehubbard	bosehubbard	NOUN
ap-2092	52	37	dimer	dimer	NOUN
ap-2092	52	38	.	.	PUNCT
ap-2092	53	1	the	the	DET
ap-2092	53	2	article	article	NOUN
ap-2092	53	3	is	be	AUX
ap-2092	53	4	organised	organise	VERB
ap-2092	53	5	as	as	SCONJ
ap-2092	53	6	follows	follow	VERB
ap-2092	53	7	.	.	PUNCT
ap-2092	54	1	we	we	PRON
ap-2092	54	2	will	will	AUX
ap-2092	54	3	introduce	introduce	VERB
ap-2092	54	4	and	and	CCONJ
ap-2092	54	5	solve	solve	VERB
ap-2092	54	6	the	the	DET
ap-2092	54	7	gross	gross	ADJ
ap-2092	54	8	-	-	PUNCT
ap-2092	54	9	pitaevskii	pitaevskii	ADJ
ap-2092	54	10	equation	equation	NOUN
ap-2092	54	11	of	of	ADP
ap-2092	54	12	a	a	DET
ap-2092	54	13	bose	bose	NOUN
ap-2092	54	14	-	-	PUNCT
ap-2092	54	15	einstein	einstein	NOUN
ap-2092	54	16	condensate	condensate	NOUN
ap-2092	54	17	in	in	ADP
ap-2092	54	18	a	a	DET
ap-2092	54	19	double	double	ADJ
ap-2092	54	20	-	-	PUNCT
ap-2092	54	21	δ	δ	NOUN
ap-2092	54	22	trap	trap	NOUN
ap-2092	54	23	for	for	ADP
ap-2092	54	24	an	an	DET
ap-2092	54	25	attractive	attractive	ADJ
ap-2092	54	26	atom	atom	NOUN
ap-2092	54	27	-	-	PUNCT
ap-2092	54	28	atom	atom	NOUN
ap-2092	54	29	interaction	interaction	NOUN
ap-2092	54	30	in	in	ADP
ap-2092	54	31	section	section	NOUN
ap-2092	54	32	2	2	NUM
ap-2092	54	33	.	.	PUNCT
ap-2092	55	1	some	some	DET
ap-2092	55	2	properties	property	NOUN
ap-2092	55	3	of	of	ADP
ap-2092	55	4	the	the	DET
ap-2092	55	5	stationary	stationary	ADJ
ap-2092	55	6	solutions	solution	NOUN
ap-2092	55	7	which	which	PRON
ap-2092	55	8	are	be	AUX
ap-2092	55	9	important	important	ADJ
ap-2092	55	10	for	for	SCONJ
ap-2092	55	11	the	the	DET
ap-2092	55	12	following	follow	VERB
ap-2092	55	13	discussions	discussion	NOUN
ap-2092	55	14	are	be	AUX
ap-2092	55	15	recapitulated	recapitulate	VERB
ap-2092	55	16	.	.	PUNCT
ap-2092	56	1	then	then	ADV
ap-2092	56	2	we	we	PRON
ap-2092	56	3	will	will	AUX
ap-2092	56	4	investigate	investigate	VERB
ap-2092	56	5	the	the	DET
ap-2092	56	6	ground	ground	NOUN
ap-2092	56	7	state	state	NOUN
ap-2092	56	8	’s	’s	PART
ap-2092	56	9	stability	stability	NOUN
ap-2092	56	10	in	in	ADP
ap-2092	56	11	the	the	DET
ap-2092	56	12	vicinity	vicinity	NOUN
ap-2092	56	13	of	of	ADP
ap-2092	56	14	the	the	DET
ap-2092	56	15	bifurcation	bifurcation	NOUN
ap-2092	56	16	in	in	ADP
ap-2092	56	17	section	section	NOUN
ap-2092	56	18	3	3	NUM
ap-2092	56	19	.	.	PUNCT
ap-2092	57	1	the	the	DET
ap-2092	57	2	bogoliubov	bogoliubov	PROPN
ap-2092	57	3	-	-	PUNCT
ap-2092	57	4	de	de	ADJ
ap-2092	57	5	gennes	genne	NOUN
ap-2092	57	6	equations	equation	NOUN
ap-2092	57	7	are	be	AUX
ap-2092	57	8	solved	solve	VERB
ap-2092	57	9	for	for	ADP
ap-2092	57	10	both	both	DET
ap-2092	57	11	types	type	NOUN
ap-2092	57	12	of	of	ADP
ap-2092	57	13	the	the	DET
ap-2092	57	14	nonlinearity	nonlinearity	NOUN
ap-2092	57	15	,	,	PUNCT
ap-2092	57	16	and	and	CCONJ
ap-2092	57	17	the	the	DET
ap-2092	57	18	origin	origin	NOUN
ap-2092	57	19	of	of	ADP
ap-2092	57	20	the	the	DET
ap-2092	57	21	discrepancy	discrepancy	NOUN
ap-2092	57	22	between	between	ADP
ap-2092	57	23	the	the	DET
ap-2092	57	24	bifurcation	bifurcation	NOUN
ap-2092	57	25	and	and	CCONJ
ap-2092	57	26	the	the	DET
ap-2092	57	27	stability	stability	NOUN
ap-2092	57	28	change	change	NOUN
ap-2092	57	29	is	be	AUX
ap-2092	57	30	discussed	discuss	VERB
ap-2092	57	31	.	.	PUNCT
ap-2092	58	1	conclusions	conclusion	NOUN
ap-2092	58	2	are	be	AUX
ap-2092	58	3	drawn	draw	VERB
ap-2092	58	4	in	in	ADP
ap-2092	58	5	section	section	NOUN
ap-2092	58	6	4	4	NUM
ap-2092	58	7	.	.	NOUN
ap-2092	58	8	2	2	NUM
ap-2092	58	9	.	.	X
ap-2092	58	10	bose	bose	NOUN
ap-2092	58	11	-	-	PUNCT
ap-2092	58	12	einstein	einstein	NOUN
ap-2092	58	13	condensates	condensate	NOUN
ap-2092	58	14	in	in	ADP
ap-2092	58	15	the	the	DET
ap-2092	58	16	pt	pt	NOUN
ap-2092	58	17	symmetric	symmetric	ADJ
ap-2092	58	18	double	double	ADJ
ap-2092	58	19	-	-	PUNCT
ap-2092	58	20	δ	δ	NOUN
ap-2092	58	21	trap	trap	NOUN
ap-2092	58	22	we	we	PRON
ap-2092	58	23	assume	assume	VERB
ap-2092	58	24	the	the	DET
ap-2092	58	25	condensate	condensate	NOUN
ap-2092	58	26	to	to	PART
ap-2092	58	27	be	be	AUX
ap-2092	58	28	trapped	trap	VERB
ap-2092	58	29	in	in	ADP
ap-2092	58	30	an	an	DET
ap-2092	58	31	idealised	idealised	ADJ
ap-2092	58	32	trap	trap	NOUN
ap-2092	58	33	of	of	ADP
ap-2092	58	34	two	two	NUM
ap-2092	58	35	delta	delta	NOUN
ap-2092	58	36	functions	function	NOUN
ap-2092	58	37	,	,	PUNCT
ap-2092	58	38	i.e.	i.e.	X
ap-2092	58	39	the	the	DET
ap-2092	58	40	potential	potential	NOUN
ap-2092	58	41	has	have	VERB
ap-2092	58	42	the	the	DET
ap-2092	58	43	shape	shape	NOUN
ap-2092	58	44	[	[	X
ap-2092	58	45	8	8	NUM
ap-2092	58	46	]	]	SYM
ap-2092	58	47	v	v	NOUN
ap-2092	58	48	(	(	PUNCT
ap-2092	58	49	x	x	NOUN
ap-2092	58	50	)	)	PUNCT
ap-2092	58	51	=	=	SYM
ap-2092	59	1	−	−	PROPN
ap-2092	59	2	(	(	PUNCT
ap-2092	59	3	1−	1−	NUM
ap-2092	59	4	iγ	iγ	NOUN
ap-2092	59	5	)	)	PUNCT
ap-2092	59	6	δ	δ	PROPN
ap-2092	59	7	(	(	PUNCT
ap-2092	59	8	x−	x−	PROPN
ap-2092	59	9	b)−	b)−	PROPN
ap-2092	59	10	(	(	PUNCT
ap-2092	59	11	1	1	NUM
ap-2092	59	12	+	+	CCONJ
ap-2092	59	13	iγ	iγ	NOUN
ap-2092	59	14	)	)	PUNCT
ap-2092	59	15	δ	δ	NOUN
ap-2092	59	16	(	(	PUNCT
ap-2092	59	17	x+	x+	PROPN
ap-2092	59	18	b	b	X
ap-2092	59	19	)	)	PUNCT
ap-2092	59	20	,	,	PUNCT
ap-2092	59	21	(	(	PUNCT
ap-2092	59	22	1	1	X
ap-2092	59	23	)	)	PUNCT
ap-2092	59	24	where	where	SCONJ
ap-2092	59	25	the	the	DET
ap-2092	59	26	units	unit	NOUN
ap-2092	59	27	are	be	AUX
ap-2092	59	28	chosen	choose	VERB
ap-2092	59	29	such	such	ADJ
ap-2092	59	30	that	that	SCONJ
ap-2092	59	31	the	the	DET
ap-2092	59	32	real	real	ADJ
ap-2092	59	33	part	part	NOUN
ap-2092	59	34	due	due	ADP
ap-2092	59	35	to	to	ADP
ap-2092	59	36	the	the	DET
ap-2092	59	37	action	action	NOUN
ap-2092	59	38	of	of	ADP
ap-2092	59	39	the	the	DET
ap-2092	59	40	δ	δ	PROPN
ap-2092	59	41	functions	function	NOUN
ap-2092	59	42	has	have	VERB
ap-2092	59	43	the	the	DET
ap-2092	59	44	value	value	NOUN
ap-2092	59	45	-1	-1	PUNCT
ap-2092	59	46	.	.	PUNCT
ap-2092	60	1	it	it	PRON
ap-2092	60	2	describes	describe	VERB
ap-2092	60	3	two	two	NUM
ap-2092	60	4	symmetric	symmetric	ADJ
ap-2092	60	5	infinitely	infinitely	ADV
ap-2092	60	6	thin	thin	ADJ
ap-2092	60	7	potential	potential	ADJ
ap-2092	60	8	wells	well	NOUN
ap-2092	60	9	at	at	ADP
ap-2092	60	10	positions	position	NOUN
ap-2092	60	11	±b	±b	PROPN
ap-2092	60	12	.	.	PUNCT
ap-2092	61	1	in	in	ADP
ap-2092	61	2	the	the	DET
ap-2092	61	3	left	left	NOUN
ap-2092	61	4	well	well	INTJ
ap-2092	61	5	we	we	PRON
ap-2092	61	6	describe	describe	VERB
ap-2092	61	7	an	an	DET
ap-2092	61	8	outflux	outflux	NOUN
ap-2092	61	9	of	of	ADP
ap-2092	61	10	atoms	atom	NOUN
ap-2092	61	11	by	by	ADP
ap-2092	61	12	a	a	DET
ap-2092	61	13	negative	negative	ADJ
ap-2092	61	14	imaginary	imaginary	ADJ
ap-2092	61	15	contribution	contribution	NOUN
ap-2092	61	16	−iγ	−iγ	NOUN
ap-2092	61	17	,	,	PUNCT
ap-2092	61	18	and	and	CCONJ
ap-2092	61	19	on	on	ADP
ap-2092	61	20	the	the	DET
ap-2092	61	21	right	right	ADJ
ap-2092	61	22	side	side	NOUN
ap-2092	61	23	an	an	DET
ap-2092	61	24	influx	influx	NOUN
ap-2092	61	25	of	of	ADP
ap-2092	61	26	particles	particle	NOUN
ap-2092	61	27	is	be	AUX
ap-2092	61	28	described	describe	VERB
ap-2092	61	29	by	by	ADP
ap-2092	61	30	a	a	DET
ap-2092	61	31	positive	positive	ADJ
ap-2092	61	32	imaginary	imaginary	ADJ
ap-2092	61	33	part	part	NOUN
ap-2092	61	34	+	+	ADJ
ap-2092	61	35	iγ	iγ	NOUN
ap-2092	61	36	of	of	ADP
ap-2092	61	37	the	the	DET
ap-2092	61	38	same	same	ADJ
ap-2092	61	39	strength	strength	NOUN
ap-2092	61	40	.	.	PUNCT
ap-2092	62	1	this	this	PRON
ap-2092	62	2	leads	lead	VERB
ap-2092	62	3	to	to	ADP
ap-2092	62	4	the	the	DET
ap-2092	62	5	time	time	NOUN
ap-2092	62	6	-	-	PUNCT
ap-2092	62	7	independent	independent	ADJ
ap-2092	62	8	gross	gross	ADJ
ap-2092	62	9	-	-	PUNCT
ap-2092	62	10	pitaevskii	pitaevskii	ADJ
ap-2092	62	11	equation	equation	NOUN
ap-2092	62	12	in	in	ADP
ap-2092	62	13	dimensionless	dimensionless	NOUN
ap-2092	62	14	form	form	NOUN
ap-2092	62	15	[	[	X
ap-2092	62	16	8	8	NUM
ap-2092	62	17	]	]	PUNCT
ap-2092	62	18	,	,	PUNCT
ap-2092	62	19	[	[	PUNCT
ap-2092	62	20	−	−	PROPN
ap-2092	62	21	d2	d2	PROPN
ap-2092	62	22	dx2	dx2	PROPN
ap-2092	62	23	−	−	PROPN
ap-2092	62	24	(	(	PUNCT
ap-2092	62	25	1−	1−	NUM
ap-2092	62	26	iγ	iγ	NOUN
ap-2092	62	27	)	)	PUNCT
ap-2092	62	28	δ	δ	PROPN
ap-2092	62	29	(	(	PUNCT
ap-2092	62	30	x−	x−	PROPN
ap-2092	62	31	b)−	b)−	PROPN
ap-2092	62	32	(	(	PUNCT
ap-2092	62	33	1	1	NUM
ap-2092	62	34	+	+	CCONJ
ap-2092	62	35	iγ	iγ	NOUN
ap-2092	62	36	)	)	PUNCT
ap-2092	62	37	δ	δ	NOUN
ap-2092	62	38	(	(	PUNCT
ap-2092	62	39	x+	x+	PROPN
ap-2092	62	40	b	b	X
ap-2092	62	41	)	)	PUNCT
ap-2092	62	42	+	+	CCONJ
ap-2092	62	43	g	g	NOUN
ap-2092	62	44	∣∣ψ(x	∣∣ψ(x	NUM
ap-2092	62	45	)	)	PUNCT
ap-2092	62	46	∣∣2]ψ(x	∣∣2]ψ(x	NUM
ap-2092	62	47	)	)	PUNCT
ap-2092	62	48	=	=	SYM
ap-2092	62	49	−κ2ψ(x	−κ2ψ(x	NOUN
ap-2092	62	50	)	)	PUNCT
ap-2092	62	51	(	(	PUNCT
ap-2092	62	52	2	2	X
ap-2092	62	53	)	)	PUNCT
ap-2092	62	54	with	with	ADP
ap-2092	62	55	the	the	DET
ap-2092	62	56	energy	energy	NOUN
ap-2092	62	57	eigenvalue	eigenvalue	NOUN
ap-2092	62	58	or	or	CCONJ
ap-2092	62	59	chemical	chemical	NOUN
ap-2092	62	60	potential	potential	NOUN
ap-2092	62	61	µ	µ	X
ap-2092	62	62	=	=	SYM
ap-2092	62	63	−κ2	−κ2	PROPN
ap-2092	62	64	.	.	PUNCT
ap-2092	63	1	the	the	DET
ap-2092	63	2	parameter	parameter	NOUN
ap-2092	63	3	g	g	PROPN
ap-2092	63	4	is	be	AUX
ap-2092	63	5	determined	determine	VERB
ap-2092	63	6	by	by	ADP
ap-2092	63	7	the	the	DET
ap-2092	63	8	s	s	NOUN
ap-2092	63	9	-	-	PUNCT
ap-2092	63	10	wave	wave	NOUN
ap-2092	63	11	scattering	scattering	NOUN
ap-2092	63	12	length	length	NOUN
ap-2092	63	13	,	,	PUNCT
ap-2092	63	14	which	which	PRON
ap-2092	63	15	effectively	effectively	ADV
ap-2092	63	16	describes	describe	VERB
ap-2092	63	17	the	the	DET
ap-2092	63	18	van	van	PROPN
ap-2092	63	19	der	der	NOUN
ap-2092	63	20	waals	waal	NOUN
ap-2092	63	21	interaction	interaction	NOUN
ap-2092	63	22	for	for	ADP
ap-2092	63	23	low	low	ADJ
ap-2092	63	24	temperatures	temperature	NOUN
ap-2092	63	25	and	and	CCONJ
ap-2092	63	26	densities	density	NOUN
ap-2092	63	27	.	.	PUNCT
ap-2092	64	1	physically	physically	ADV
ap-2092	64	2	it	it	PRON
ap-2092	64	3	can	can	AUX
ap-2092	64	4	be	be	AUX
ap-2092	64	5	tuned	tune	VERB
ap-2092	64	6	via	via	ADP
ap-2092	64	7	feshbach	feshbach	NOUN
ap-2092	64	8	resonances	resonance	NOUN
ap-2092	64	9	.	.	PUNCT
ap-2092	65	1	throughout	throughout	ADP
ap-2092	65	2	this	this	DET
ap-2092	65	3	article	article	NOUN
ap-2092	65	4	we	we	PRON
ap-2092	65	5	assume	assume	VERB
ap-2092	65	6	g	g	PROPN
ap-2092	65	7	to	to	PART
ap-2092	65	8	be	be	AUX
ap-2092	65	9	negative	negative	ADJ
ap-2092	65	10	,	,	PUNCT
ap-2092	65	11	i.e.	i.e.	X
ap-2092	65	12	the	the	DET
ap-2092	65	13	atom	atom	NOUN
ap-2092	65	14	-	-	PUNCT
ap-2092	65	15	atom	atom	NOUN
ap-2092	65	16	interaction	interaction	NOUN
ap-2092	65	17	is	be	AUX
ap-2092	65	18	attractive	attractive	ADJ
ap-2092	65	19	.	.	PUNCT
ap-2092	66	1	solutions	solution	NOUN
ap-2092	66	2	to	to	ADP
ap-2092	66	3	the	the	DET
ap-2092	66	4	gross	gross	ADJ
ap-2092	66	5	-	-	PUNCT
ap-2092	66	6	pitaevskii	pitaevskii	ADJ
ap-2092	66	7	equation	equation	NOUN
ap-2092	66	8	are	be	AUX
ap-2092	66	9	found	find	VERB
ap-2092	66	10	with	with	ADP
ap-2092	66	11	a	a	DET
ap-2092	66	12	numerical	numerical	ADJ
ap-2092	66	13	exact	exact	ADJ
ap-2092	66	14	integration	integration	NOUN
ap-2092	66	15	.	.	PUNCT
ap-2092	67	1	the	the	DET
ap-2092	67	2	wave	wave	NOUN
ap-2092	67	3	function	function	NOUN
ap-2092	67	4	is	be	AUX
ap-2092	67	5	integrated	integrate	VERB
ap-2092	67	6	outward	outward	ADV
ap-2092	67	7	from	from	ADP
ap-2092	67	8	x	x	X
ap-2092	67	9	=	=	SYM
ap-2092	67	10	0	0	NUM
ap-2092	67	11	in	in	ADP
ap-2092	67	12	positive	positive	ADJ
ap-2092	67	13	and	and	CCONJ
ap-2092	67	14	negative	negative	ADJ
ap-2092	67	15	direction	direction	NOUN
ap-2092	67	16	.	.	PUNCT
ap-2092	68	1	to	to	PART
ap-2092	68	2	do	do	VERB
ap-2092	68	3	so	so	ADV
ap-2092	68	4	the	the	DET
ap-2092	68	5	initial	initial	ADJ
ap-2092	68	6	values	value	NOUN
ap-2092	68	7	ψ(0	ψ(0	NOUN
ap-2092	68	8	)	)	PUNCT
ap-2092	68	9	,	,	PUNCT
ap-2092	68	10	ψ′(0	ψ′(0	NOUN
ap-2092	68	11	)	)	PUNCT
ap-2092	68	12	,	,	PUNCT
ap-2092	68	13	and	and	CCONJ
ap-2092	68	14	κ	κ	X
ap-2092	68	15	have	have	VERB
ap-2092	68	16	to	to	PART
ap-2092	68	17	be	be	AUX
ap-2092	68	18	chosen	choose	VERB
ap-2092	68	19	.	.	PUNCT
ap-2092	69	1	the	the	DET
ap-2092	69	2	arbitrary	arbitrary	ADJ
ap-2092	69	3	global	global	ADJ
ap-2092	69	4	phase	phase	NOUN
ap-2092	69	5	is	be	AUX
ap-2092	69	6	exploited	exploit	VERB
ap-2092	69	7	such	such	ADJ
ap-2092	69	8	that	that	PRON
ap-2092	69	9	ψ(0	ψ(0	NOUN
ap-2092	69	10	)	)	PUNCT
ap-2092	69	11	is	be	AUX
ap-2092	69	12	chosen	choose	VERB
ap-2092	69	13	to	to	PART
ap-2092	69	14	be	be	AUX
ap-2092	69	15	real	real	ADJ
ap-2092	69	16	.	.	PUNCT
ap-2092	70	1	together	together	ADV
ap-2092	70	2	with	with	ADP
ap-2092	70	3	ψ′(0	ψ′(0	NOUN
ap-2092	70	4	)	)	PUNCT
ap-2092	70	5	∈	∈	PROPN
ap-2092	70	6	c	c	NOUN
ap-2092	70	7	and	and	CCONJ
ap-2092	70	8	κ	κ	PROPN
ap-2092	70	9	∈	∈	PROPN
ap-2092	71	1	c	c	X
ap-2092	71	2	we	we	PRON
ap-2092	71	3	have	have	VERB
ap-2092	71	4	five	five	NUM
ap-2092	71	5	parameters	parameter	NOUN
ap-2092	71	6	which	which	PRON
ap-2092	71	7	have	have	VERB
ap-2092	71	8	to	to	PART
ap-2092	71	9	be	be	AUX
ap-2092	71	10	set	set	VERB
ap-2092	71	11	such	such	ADJ
ap-2092	71	12	that	that	SCONJ
ap-2092	71	13	physically	physically	ADV
ap-2092	71	14	relevant	relevant	ADJ
ap-2092	71	15	wave	wave	NOUN
ap-2092	71	16	functions	function	NOUN
ap-2092	71	17	are	be	AUX
ap-2092	71	18	obtained	obtain	VERB
ap-2092	71	19	.	.	PUNCT
ap-2092	72	1	these	these	PRON
ap-2092	72	2	have	have	VERB
ap-2092	72	3	to	to	PART
ap-2092	72	4	be	be	AUX
ap-2092	72	5	square	square	NOUN
ap-2092	72	6	-	-	PUNCT
ap-2092	72	7	integrable	integrable	ADJ
ap-2092	72	8	and	and	CCONJ
ap-2092	72	9	normalised	normalise	VERB
ap-2092	72	10	in	in	ADP
ap-2092	72	11	the	the	DET
ap-2092	72	12	nonlinear	nonlinear	ADJ
ap-2092	72	13	system	system	NOUN
ap-2092	72	14	.	.	PUNCT
ap-2092	73	1	the	the	DET
ap-2092	73	2	five	five	NUM
ap-2092	73	3	conditions	condition	NOUN
ap-2092	73	4	ψ(∞)→	ψ(∞)→	PROPN
ap-2092	73	5	0	0	NUM
ap-2092	73	6	,	,	PUNCT
ap-2092	73	7	ψ(−∞)→	ψ(−∞)→	ADJ
ap-2092	73	8	0	0	NUM
ap-2092	73	9	,	,	PUNCT
ap-2092	73	10	and	and	CCONJ
ap-2092	73	11	||ψ||	||ψ||	NOUN
ap-2092	73	12	=	=	SYM
ap-2092	73	13	1	1	NUM
ap-2092	73	14	ensure	ensure	VERB
ap-2092	73	15	that	that	SCONJ
ap-2092	73	16	these	these	DET
ap-2092	73	17	conditions	condition	NOUN
ap-2092	73	18	are	be	AUX
ap-2092	73	19	fulfilled	fulfil	VERB
ap-2092	73	20	,	,	PUNCT
ap-2092	73	21	and	and	CCONJ
ap-2092	73	22	,	,	PUNCT
ap-2092	73	23	together	together	ADV
ap-2092	73	24	with	with	ADP
ap-2092	73	25	the	the	DET
ap-2092	73	26	five	five	NUM
ap-2092	73	27	initial	initial	ADJ
ap-2092	73	28	parameters	parameter	NOUN
ap-2092	73	29	,	,	PUNCT
ap-2092	73	30	define	define	VERB
ap-2092	73	31	a	a	DET
ap-2092	73	32	five	five	NUM
ap-2092	73	33	-	-	PUNCT
ap-2092	73	34	dimensional	dimensional	ADJ
ap-2092	73	35	root	root	NOUN
ap-2092	73	36	search	search	NOUN
ap-2092	73	37	problem	problem	NOUN
ap-2092	73	38	,	,	PUNCT
ap-2092	73	39	which	which	PRON
ap-2092	73	40	is	be	AUX
ap-2092	73	41	solved	solve	VERB
ap-2092	73	42	numerically	numerically	ADV
ap-2092	73	43	.	.	PUNCT
ap-2092	74	1	figure	figure	NOUN
ap-2092	74	2	1	1	NUM
ap-2092	74	3	shows	show	VERB
ap-2092	74	4	a	a	DET
ap-2092	74	5	typical	typical	ADJ
ap-2092	74	6	example	example	NOUN
ap-2092	74	7	for	for	ADP
ap-2092	74	8	all	all	DET
ap-2092	74	9	stationary	stationary	ADJ
ap-2092	74	10	states	state	NOUN
ap-2092	74	11	found	find	VERB
ap-2092	74	12	in	in	ADP
ap-2092	74	13	the	the	DET
ap-2092	74	14	case	case	NOUN
ap-2092	74	15	g	g	NOUN
ap-2092	74	16	=	=	SYM
ap-2092	74	17	−1	−1	NOUN
ap-2092	74	18	(	(	PUNCT
ap-2092	74	19	red	red	ADJ
ap-2092	74	20	solid	solid	ADJ
ap-2092	74	21	lines	line	NOUN
ap-2092	74	22	)	)	PUNCT
ap-2092	74	23	.	.	PUNCT
ap-2092	75	1	two	two	NUM
ap-2092	75	2	states	state	NOUN
ap-2092	75	3	with	with	ADP
ap-2092	75	4	purely	purely	ADV
ap-2092	75	5	real	real	ADJ
ap-2092	75	6	eigenvalues	eigenvalue	NOUN
ap-2092	75	7	vanish	vanish	VERB
ap-2092	75	8	for	for	ADP
ap-2092	75	9	increasing	increase	VERB
ap-2092	75	10	γ	γ	NOUN
ap-2092	75	11	in	in	ADP
ap-2092	75	12	an	an	DET
ap-2092	75	13	exceptional	exceptional	ADJ
ap-2092	75	14	point	point	NOUN
ap-2092	75	15	.	.	PUNCT
ap-2092	76	1	since	since	SCONJ
ap-2092	76	2	κ	κ	PROPN
ap-2092	76	3	is	be	AUX
ap-2092	76	4	plotted	plot	VERB
ap-2092	76	5	and	and	CCONJ
ap-2092	76	6	µ	µ	X
ap-2092	76	7	=	=	SYM
ap-2092	76	8	−κ2	−κ2	PROPN
ap-2092	76	9	is	be	AUX
ap-2092	76	10	the	the	DET
ap-2092	76	11	energy	energy	NOUN
ap-2092	76	12	eigenvalue	eigenvalue	NOUN
ap-2092	76	13	,	,	PUNCT
ap-2092	76	14	the	the	DET
ap-2092	76	15	upper	upper	ADJ
ap-2092	76	16	line	line	NOUN
ap-2092	76	17	corresponds	correspond	VERB
ap-2092	76	18	to	to	ADP
ap-2092	76	19	the	the	DET
ap-2092	76	20	ground	ground	NOUN
ap-2092	76	21	state	state	NOUN
ap-2092	76	22	.	.	PUNCT
ap-2092	77	1	two	two	NUM
ap-2092	77	2	complex	complex	ADJ
ap-2092	77	3	and	and	CCONJ
ap-2092	77	4	complex	complex	ADJ
ap-2092	77	5	conjugate	conjugate	ADJ
ap-2092	77	6	eigenvalues	eigenvalue	NOUN
ap-2092	77	7	bifurcate	bifurcate	NOUN
ap-2092	77	8	from	from	ADP
ap-2092	77	9	this	this	DET
ap-2092	77	10	ground	ground	NOUN
ap-2092	77	11	state	state	NOUN
ap-2092	77	12	in	in	ADP
ap-2092	77	13	a	a	DET
ap-2092	77	14	pitchfork	pitchfork	NOUN
ap-2092	77	15	bifurcation	bifurcation	NOUN
ap-2092	77	16	at	at	ADP
ap-2092	77	17	a	a	DET
ap-2092	77	18	critical	critical	ADJ
ap-2092	77	19	value	value	NOUN
ap-2092	77	20	γκ	γκ	ADJ
ap-2092	78	1	≈	≈	PROPN
ap-2092	78	2	0.3071	0.3071	PROPN
ap-2092	78	3	.	.	PUNCT
ap-2092	79	1	the	the	DET
ap-2092	79	2	same	same	ADJ
ap-2092	79	3	plots	plot	NOUN
ap-2092	79	4	for	for	ADP
ap-2092	79	5	g	g	NOUN
ap-2092	79	6	=	=	SYM
ap-2092	79	7	−0.5	−0.5	PROPN
ap-2092	79	8	(	(	PUNCT
ap-2092	79	9	blue	blue	ADJ
ap-2092	79	10	dotted	dotted	ADJ
ap-2092	79	11	lines	line	NOUN
ap-2092	79	12	)	)	PUNCT
ap-2092	79	13	and	and	CCONJ
ap-2092	79	14	g	g	NOUN
ap-2092	79	15	=	=	SYM
ap-2092	79	16	0	0	PROPN
ap-2092	80	1	(	(	PUNCT
ap-2092	80	2	green	green	ADJ
ap-2092	80	3	dashed	dash	VERB
ap-2092	80	4	lines	line	NOUN
ap-2092	80	5	)	)	PUNCT
ap-2092	80	6	demonstrate	demonstrate	VERB
ap-2092	80	7	how	how	SCONJ
ap-2092	80	8	the	the	DET
ap-2092	80	9	pitchfork	pitchfork	NOUN
ap-2092	80	10	bifurcation	bifurcation	NOUN
ap-2092	80	11	is	be	AUX
ap-2092	80	12	introduced	introduce	VERB
ap-2092	80	13	by	by	ADP
ap-2092	80	14	the	the	DET
ap-2092	80	15	nonlinearity	nonlinearity	NOUN
ap-2092	80	16	.	.	PUNCT
ap-2092	81	1	134	134	NUM
ap-2092	81	2	vol	vol	NOUN
ap-2092	81	3	.	.	PUNCT
ap-2092	82	1	54	54	NUM
ap-2092	82	2	no	no	NOUN
ap-2092	82	3	.	.	PUNCT
ap-2092	83	1	2/2014	2/2014	NUM
ap-2092	83	2	stability	stability	NOUN
ap-2092	83	3	of	of	ADP
ap-2092	83	4	becs	becs	PROPN
ap-2092	83	5	in	in	ADP
ap-2092	83	6	a	a	DET
ap-2092	83	7	pt	pt	ADJ
ap-2092	83	8	-	-	ADJ
ap-2092	83	9	symmetric	symmetric	ADJ
ap-2092	83	10	double	double	ADJ
ap-2092	83	11	-	-	PUNCT
ap-2092	83	12	δ	δ	NOUN
ap-2092	83	13	potential	potential	NOUN
ap-2092	83	14	0	0	NUM
ap-2092	83	15	0.1	0.1	NUM
ap-2092	83	16	0.2	0.2	NUM
ap-2092	83	17	0.3	0.3	NUM
ap-2092	83	18	0.4	0.4	NUM
ap-2092	83	19	0.5	0.5	NUM
ap-2092	83	20	0.6	0.6	NUM
ap-2092	83	21	0.7	0.7	NUM
ap-2092	84	1	0.8	0.8	NUM
ap-2092	84	2	0	0	NUM
ap-2092	84	3	0.1	0.1	NUM
ap-2092	84	4	0.2	0.2	NUM
ap-2092	84	5	0.3	0.3	NUM
ap-2092	84	6	0.4	0.4	NUM
ap-2092	84	7	0.5	0.5	NUM
ap-2092	84	8	0.6	0.6	NUM
ap-2092	84	9	r	r	NOUN
ap-2092	84	10	e	e	X
ap-2092	84	11	(	(	PUNCT
ap-2092	84	12	κ	κ	NOUN
ap-2092	84	13	)	)	PUNCT
ap-2092	84	14	γ	γ	X
ap-2092	84	15	(	(	PUNCT
ap-2092	84	16	a	a	NOUN
ap-2092	84	17	)	)	PUNCT
ap-2092	84	18	γ	γ	NOUN
ap-2092	84	19	κ	κ	ADP
ap-2092	84	20	g	g	NOUN
ap-2092	84	21	=	=	PUNCT
ap-2092	84	22	-1.0	-1.0	PROPN
ap-2092	84	23	g	g	PROPN
ap-2092	84	24	=	=	SYM
ap-2092	84	25	-0.5	-0.5	PROPN
ap-2092	84	26	g	g	NOUN
ap-2092	84	27	=	=	SYM
ap-2092	84	28	0	0	PROPN
ap-2092	84	29	-0.3	-0.3	PROPN
ap-2092	84	30	-0.2	-0.2	PROPN
ap-2092	84	31	-0.1	-0.1	PROPN
ap-2092	84	32	0	0	NUM
ap-2092	84	33	0.1	0.1	NUM
ap-2092	84	34	0.2	0.2	NUM
ap-2092	84	35	0.3	0.3	NUM
ap-2092	84	36	0	0	NUM
ap-2092	84	37	0.1	0.1	NUM
ap-2092	84	38	0.2	0.2	NUM
ap-2092	84	39	0.3	0.3	NUM
ap-2092	84	40	0.4	0.4	NUM
ap-2092	84	41	0.5	0.5	NUM
ap-2092	84	42	0.6	0.6	NUM
ap-2092	85	1	i	i	PRON
ap-2092	85	2	m	m	VERB
ap-2092	85	3	(	(	PUNCT
ap-2092	85	4	κ	κ	NOUN
ap-2092	85	5	)	)	PUNCT
ap-2092	85	6	γ	γ	PROPN
ap-2092	85	7	(	(	PUNCT
ap-2092	85	8	b	b	NOUN
ap-2092	85	9	)	)	PUNCT
ap-2092	85	10	γ	γ	PROPN
ap-2092	85	11	κ	κ	NOUN
ap-2092	85	12	figure	figure	NOUN
ap-2092	85	13	1	1	NUM
ap-2092	85	14	.	.	PUNCT
ap-2092	86	1	real	real	ADJ
ap-2092	86	2	(	(	PUNCT
ap-2092	86	3	a	a	NOUN
ap-2092	86	4	)	)	PUNCT
ap-2092	86	5	and	and	CCONJ
ap-2092	86	6	imaginary	imaginary	ADJ
ap-2092	86	7	(	(	PUNCT
ap-2092	86	8	b	b	NOUN
ap-2092	86	9	)	)	PUNCT
ap-2092	86	10	parts	part	NOUN
ap-2092	86	11	of	of	ADP
ap-2092	86	12	the	the	DET
ap-2092	86	13	stationary	stationary	ADJ
ap-2092	86	14	solutions	solution	NOUN
ap-2092	86	15	found	find	VERB
ap-2092	86	16	for	for	ADP
ap-2092	86	17	the	the	DET
ap-2092	86	18	gross	gross	ADJ
ap-2092	86	19	-	-	PUNCT
ap-2092	86	20	pitaevskii	pitaevskii	ADJ
ap-2092	86	21	equation	equation	NOUN
ap-2092	86	22	(	(	PUNCT
ap-2092	86	23	2	2	NUM
ap-2092	86	24	)	)	PUNCT
ap-2092	86	25	for	for	ADP
ap-2092	86	26	the	the	DET
ap-2092	86	27	case	case	NOUN
ap-2092	86	28	g	g	NOUN
ap-2092	86	29	=	=	SYM
ap-2092	86	30	−1	−1	NOUN
ap-2092	86	31	(	(	PUNCT
ap-2092	86	32	red	red	ADJ
ap-2092	86	33	solid	solid	ADJ
ap-2092	86	34	lines	line	NOUN
ap-2092	86	35	)	)	PUNCT
ap-2092	86	36	,	,	PUNCT
ap-2092	86	37	which	which	PRON
ap-2092	86	38	is	be	AUX
ap-2092	86	39	compared	compare	VERB
ap-2092	86	40	with	with	ADP
ap-2092	86	41	its	its	PRON
ap-2092	86	42	linear	linear	ADJ
ap-2092	86	43	counterpart	counterpart	NOUN
ap-2092	86	44	g	g	PROPN
ap-2092	86	45	=	=	SYM
ap-2092	86	46	0	0	PROPN
ap-2092	87	1	(	(	PUNCT
ap-2092	87	2	green	green	ADJ
ap-2092	87	3	dashed	dash	VERB
ap-2092	87	4	lines	line	NOUN
ap-2092	87	5	)	)	PUNCT
ap-2092	87	6	and	and	CCONJ
ap-2092	87	7	the	the	DET
ap-2092	87	8	weaker	weak	ADJ
ap-2092	87	9	interaction	interaction	NOUN
ap-2092	87	10	g	g	NOUN
ap-2092	87	11	=	=	SYM
ap-2092	87	12	−0.5	−0.5	PROPN
ap-2092	87	13	(	(	PUNCT
ap-2092	87	14	blue	blue	ADJ
ap-2092	87	15	dotted	dotted	ADJ
ap-2092	87	16	lines	line	NOUN
ap-2092	87	17	)	)	PUNCT
ap-2092	87	18	.	.	PUNCT
ap-2092	88	1	in	in	ADP
ap-2092	88	2	the	the	DET
ap-2092	88	3	nonlinear	nonlinear	ADJ
ap-2092	88	4	case	case	NOUN
ap-2092	88	5	we	we	PRON
ap-2092	88	6	observe	observe	VERB
ap-2092	88	7	two	two	NUM
ap-2092	88	8	complex	complex	ADJ
ap-2092	88	9	conjugate	conjugate	ADJ
ap-2092	88	10	states	state	NOUN
ap-2092	88	11	bifurcating	bifurcate	VERB
ap-2092	88	12	from	from	ADP
ap-2092	88	13	the	the	DET
ap-2092	88	14	ground	ground	NOUN
ap-2092	88	15	state	state	NOUN
ap-2092	88	16	in	in	ADP
ap-2092	88	17	a	a	DET
ap-2092	88	18	pitchfork	pitchfork	NOUN
ap-2092	88	19	bifurcation	bifurcation	NOUN
ap-2092	88	20	.	.	PUNCT
ap-2092	89	1	for	for	ADP
ap-2092	89	2	g	g	NOUN
ap-2092	89	3	=	=	SYM
ap-2092	89	4	−1	−1	NOUN
ap-2092	89	5	this	this	PRON
ap-2092	89	6	occurs	occur	VERB
ap-2092	89	7	at	at	ADP
ap-2092	89	8	γκ	γκ	PROPN
ap-2092	89	9	≈	≈	PROPN
ap-2092	89	10	0.3071	0.3071	PROPN
ap-2092	89	11	.	.	PUNCT
ap-2092	90	1	this	this	DET
ap-2092	90	2	eigenvalue	eigenvalue	NOUN
ap-2092	90	3	structure	structure	NOUN
ap-2092	90	4	is	be	AUX
ap-2092	90	5	very	very	ADV
ap-2092	90	6	generic	generic	ADJ
ap-2092	90	7	for	for	ADP
ap-2092	90	8	pt	pt	X
ap-2092	90	9	symmetric	symmetric	ADJ
ap-2092	90	10	systems	system	NOUN
ap-2092	90	11	with	with	ADP
ap-2092	90	12	a	a	DET
ap-2092	90	13	quadratic	quadratic	ADJ
ap-2092	90	14	term	term	NOUN
ap-2092	90	15	in	in	ADP
ap-2092	90	16	the	the	DET
ap-2092	90	17	hamiltonian	hamiltonian	NOUN
ap-2092	90	18	.	.	PUNCT
ap-2092	91	1	it	it	PRON
ap-2092	91	2	is	be	AUX
ap-2092	91	3	found	find	VERB
ap-2092	91	4	for	for	ADP
ap-2092	91	5	bose	bose	NOUN
ap-2092	91	6	-	-	PUNCT
ap-2092	91	7	einstein	einstein	NOUN
ap-2092	91	8	condensates	condensate	NOUN
ap-2092	91	9	in	in	ADP
ap-2092	91	10	a	a	DET
ap-2092	91	11	true	true	ADJ
ap-2092	91	12	spatially	spatially	ADV
ap-2092	91	13	extended	extend	VERB
ap-2092	91	14	double	double	ADJ
ap-2092	91	15	well	well	ADV
ap-2092	91	16	in	in	ADP
ap-2092	91	17	one	one	NUM
ap-2092	91	18	and	and	CCONJ
ap-2092	91	19	three	three	NUM
ap-2092	91	20	dimensions	dimension	NOUN
ap-2092	91	21	[	[	X
ap-2092	91	22	11	11	NUM
ap-2092	91	23	,	,	PUNCT
ap-2092	91	24	12	12	NUM
ap-2092	91	25	]	]	PUNCT
ap-2092	91	26	which	which	PRON
ap-2092	91	27	contain	contain	VERB
ap-2092	91	28	the	the	DET
ap-2092	91	29	nonlinearity	nonlinearity	NOUN
ap-2092	91	30	∝	∝	NOUN
ap-2092	91	31	|ψ|2	|ψ|2	PROPN
ap-2092	91	32	as	as	ADV
ap-2092	91	33	well	well	ADV
ap-2092	91	34	as	as	ADP
ap-2092	91	35	for	for	ADP
ap-2092	91	36	the	the	DET
ap-2092	91	37	mean	mean	ADJ
ap-2092	91	38	-	-	PUNCT
ap-2092	91	39	field	field	NOUN
ap-2092	91	40	limit	limit	NOUN
ap-2092	91	41	of	of	ADP
ap-2092	91	42	the	the	DET
ap-2092	91	43	bosehubbard	bosehubbard	NOUN
ap-2092	91	44	dimer	dimer	NOUN
ap-2092	92	1	[	[	X
ap-2092	92	2	14–17	14–17	NUM
ap-2092	92	3	]	]	PUNCT
ap-2092	92	4	with	with	ADP
ap-2092	92	5	a	a	DET
ap-2092	92	6	term	term	NOUN
ap-2092	92	7	∝	∝	PROPN
ap-2092	92	8	|ψ|2/||ψ||2	|ψ|2/||ψ||2	PROPN
ap-2092	92	9	.	.	PUNCT
ap-2092	93	1	the	the	DET
ap-2092	93	2	difference	difference	NOUN
ap-2092	93	3	in	in	ADP
ap-2092	93	4	the	the	DET
ap-2092	93	5	norm	norm	NOUN
ap-2092	93	6	-	-	PUNCT
ap-2092	93	7	dependency	dependency	NOUN
ap-2092	93	8	of	of	ADP
ap-2092	93	9	the	the	DET
ap-2092	93	10	nonlinearity	nonlinearity	NOUN
ap-2092	93	11	between	between	ADP
ap-2092	93	12	the	the	DET
ap-2092	93	13	two	two	NUM
ap-2092	93	14	systems	system	NOUN
ap-2092	93	15	does	do	AUX
ap-2092	93	16	not	not	PART
ap-2092	93	17	lead	lead	VERB
ap-2092	93	18	to	to	ADP
ap-2092	93	19	different	different	ADJ
ap-2092	93	20	eigenvalues	eigenvalue	NOUN
ap-2092	93	21	,	,	PUNCT
ap-2092	93	22	as	as	SCONJ
ap-2092	93	23	has	have	AUX
ap-2092	93	24	already	already	ADV
ap-2092	93	25	been	be	AUX
ap-2092	93	26	mentioned	mention	VERB
ap-2092	93	27	[	[	X
ap-2092	93	28	17	17	NUM
ap-2092	93	29	]	]	PUNCT
ap-2092	93	30	.	.	PUNCT
ap-2092	94	1	the	the	DET
ap-2092	94	2	difference	difference	NOUN
ap-2092	94	3	appears	appear	VERB
ap-2092	94	4	,	,	PUNCT
ap-2092	94	5	however	however	ADV
ap-2092	94	6	,	,	PUNCT
ap-2092	94	7	for	for	ADP
ap-2092	94	8	the	the	DET
ap-2092	94	9	dynamics	dynamic	NOUN
ap-2092	94	10	,	,	PUNCT
ap-2092	94	11	where	where	SCONJ
ap-2092	94	12	the	the	DET
ap-2092	94	13	norm	norm	NOUN
ap-2092	94	14	plays	play	VERB
ap-2092	94	15	a	a	DET
ap-2092	94	16	crucial	crucial	ADJ
ap-2092	94	17	role	role	NOUN
ap-2092	94	18	in	in	ADP
ap-2092	94	19	the	the	DET
ap-2092	94	20	presence	presence	NOUN
ap-2092	94	21	of	of	ADP
ap-2092	94	22	gain	gain	NOUN
ap-2092	94	23	and	and	CCONJ
ap-2092	94	24	loss	loss	NOUN
ap-2092	94	25	[	[	X
ap-2092	94	26	13	13	NUM
ap-2092	94	27	]	]	PUNCT
ap-2092	94	28	.	.	PUNCT
ap-2092	95	1	3	3	X
ap-2092	95	2	.	.	X
ap-2092	95	3	stability	stability	NOUN
ap-2092	95	4	analysis	analysis	NOUN
ap-2092	95	5	of	of	ADP
ap-2092	95	6	the	the	DET
ap-2092	95	7	ground	ground	NOUN
ap-2092	95	8	state	state	NOUN
ap-2092	95	9	the	the	DET
ap-2092	95	10	linear	linear	ADJ
ap-2092	95	11	stability	stability	NOUN
ap-2092	95	12	is	be	AUX
ap-2092	95	13	analysed	analyse	VERB
ap-2092	95	14	with	with	ADP
ap-2092	95	15	the	the	DET
ap-2092	95	16	bogoliubov	bogoliubov	PROPN
ap-2092	95	17	-	-	PUNCT
ap-2092	95	18	de	de	ADJ
ap-2092	95	19	gennes	genne	NOUN
ap-2092	95	20	equations	equation	NOUN
ap-2092	95	21	.	.	PUNCT
ap-2092	96	1	they	they	PRON
ap-2092	96	2	are	be	AUX
ap-2092	96	3	derived	derive	VERB
ap-2092	96	4	under	under	ADP
ap-2092	96	5	the	the	DET
ap-2092	96	6	assumption	assumption	NOUN
ap-2092	96	7	that	that	SCONJ
ap-2092	96	8	a	a	DET
ap-2092	96	9	stationary	stationary	ADJ
ap-2092	96	10	state	state	NOUN
ap-2092	96	11	ψ0(x	ψ0(x	SYM
ap-2092	96	12	,	,	PUNCT
ap-2092	96	13	t	t	PROPN
ap-2092	96	14	)	)	PUNCT
ap-2092	96	15	is	be	AUX
ap-2092	96	16	perturbed	perturb	VERB
ap-2092	96	17	by	by	ADP
ap-2092	96	18	a	a	DET
ap-2092	96	19	small	small	ADJ
ap-2092	96	20	fluctuation	fluctuation	NOUN
ap-2092	96	21	θ(x	θ(x	PROPN
ap-2092	96	22	,	,	PUNCT
ap-2092	96	23	t	t	PROPN
ap-2092	96	24	)	)	PUNCT
ap-2092	96	25	,	,	PUNCT
ap-2092	96	26	i.e.	i.e.	X
ap-2092	96	27	ψ(x	ψ(x	PROPN
ap-2092	96	28	,	,	PUNCT
ap-2092	96	29	t	t	PROPN
ap-2092	96	30	)	)	PUNCT
ap-2092	96	31	=	=	SYM
ap-2092	96	32	eiκ2	eiκ2	PROPN
ap-2092	96	33	t	t	PROPN
ap-2092	96	34	[	[	PUNCT
ap-2092	96	35	ψ0(x	ψ0(x	NOUN
ap-2092	96	36	)	)	PUNCT
ap-2092	97	1	+	+	CCONJ
ap-2092	97	2	θ(x	θ(x	PROPN
ap-2092	97	3	,	,	PUNCT
ap-2092	97	4	t	t	PROPN
ap-2092	97	5	)	)	PUNCT
ap-2092	97	6	]	]	PUNCT
ap-2092	97	7	,	,	PUNCT
ap-2092	97	8	(	(	PUNCT
ap-2092	97	9	3a	3a	NUM
ap-2092	97	10	)	)	PUNCT
ap-2092	97	11	where	where	SCONJ
ap-2092	97	12	θ(x	θ(x	PROPN
ap-2092	97	13	,	,	PUNCT
ap-2092	97	14	t	t	PROPN
ap-2092	97	15	)	)	PUNCT
ap-2092	98	1	=	=	PUNCT
ap-2092	99	1	u(x)e−iωt	u(x)e−iωt	PROPN
ap-2092	99	2	+	+	X
ap-2092	99	3	v∗(x)eiω∗t	v∗(x)eiω∗t	ADJ
ap-2092	99	4	.	.	PUNCT
ap-2092	100	1	(	(	PUNCT
ap-2092	100	2	3b	3b	NUM
ap-2092	100	3	)	)	PUNCT
ap-2092	100	4	with	with	ADP
ap-2092	100	5	this	this	DET
ap-2092	100	6	ansatz	ansatz	NOUN
ap-2092	100	7	and	and	CCONJ
ap-2092	100	8	a	a	DET
ap-2092	100	9	linearisation	linearisation	NOUN
ap-2092	100	10	in	in	ADP
ap-2092	100	11	the	the	DET
ap-2092	100	12	small	small	ADJ
ap-2092	100	13	quantities	quantity	NOUN
ap-2092	100	14	u	u	NOUN
ap-2092	100	15	and	and	CCONJ
ap-2092	100	16	v	v	ADP
ap-2092	100	17	one	one	NUM
ap-2092	100	18	obtains	obtain	VERB
ap-2092	100	19	from	from	ADP
ap-2092	100	20	the	the	DET
ap-2092	100	21	gross	gross	ADJ
ap-2092	100	22	-	-	PUNCT
ap-2092	100	23	pitaevskii	pitaevskii	ADJ
ap-2092	100	24	equation	equation	NOUN
ap-2092	100	25	the	the	DET
ap-2092	100	26	coupled	couple	VERB
ap-2092	100	27	system	system	NOUN
ap-2092	100	28	of	of	ADP
ap-2092	100	29	the	the	DET
ap-2092	100	30	bogoliubov	bogoliubov	PROPN
ap-2092	100	31	-	-	PUNCT
ap-2092	100	32	de	de	ADJ
ap-2092	100	33	gennes	genne	NOUN
ap-2092	100	34	differential	differential	NOUN
ap-2092	100	35	equations	equation	NOUN
ap-2092	100	36	,	,	PUNCT
ap-2092	100	37	d2	d2	NOUN
ap-2092	100	38	dx2u(x	dx2u(x	NOUN
ap-2092	100	39	)	)	PUNCT
ap-2092	101	1	=	=	SYM
ap-2092	101	2	[	[	PUNCT
ap-2092	101	3	−(1	−(1	NOUN
ap-2092	101	4	+	+	CCONJ
ap-2092	102	1	iγ)δ(x+	iγ)δ(x+	PROPN
ap-2092	102	2	b)−	b)−	PROPN
ap-2092	102	3	(	(	PUNCT
ap-2092	102	4	1−	1−	NUM
ap-2092	102	5	iγ)δ(x−	iγ)δ(x−	PROPN
ap-2092	102	6	b	b	PROPN
ap-2092	102	7	)	)	PUNCT
ap-2092	102	8	+	+	NUM
ap-2092	102	9	κ2	κ2	NOUN
ap-2092	102	10	−	−	PROPN
ap-2092	102	11	ω	ω	PROPN
ap-2092	102	12	+	+	CCONJ
ap-2092	102	13	2	2	NUM
ap-2092	102	14	g	g	NOUN
ap-2092	102	15	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	102	16	)	)	PUNCT
ap-2092	102	17	∣∣2]u(x	∣∣2]u(x	NOUN
ap-2092	102	18	)	)	PUNCT
ap-2092	102	19	+	+	CCONJ
ap-2092	102	20	gψ0(x)2v(x	gψ0(x)2v(x	NOUN
ap-2092	102	21	)	)	PUNCT
ap-2092	102	22	,	,	PUNCT
ap-2092	102	23	(	(	PUNCT
ap-2092	102	24	4a	4a	X
ap-2092	102	25	)	)	PUNCT
ap-2092	102	26	d2	d2	PROPN
ap-2092	102	27	dx2	dx2	PROPN
ap-2092	102	28	v(x	v(x	PROPN
ap-2092	102	29	)	)	PUNCT
ap-2092	103	1	=	=	NOUN
ap-2092	103	2	[	[	PUNCT
ap-2092	103	3	−(1−	−(1−	X
ap-2092	103	4	iγ)δ(x+	iγ)δ(x+	PROPN
ap-2092	103	5	b)−	b)−	PROPN
ap-2092	103	6	(	(	PUNCT
ap-2092	103	7	1	1	NUM
ap-2092	103	8	+	+	NUM
ap-2092	103	9	iγ)δ(x−	iγ)δ(x−	PROPN
ap-2092	103	10	b	b	PROPN
ap-2092	103	11	)	)	PUNCT
ap-2092	104	1	+	+	CCONJ
ap-2092	104	2	(	(	PUNCT
ap-2092	104	3	κ2)∗	κ2)∗	NOUN
ap-2092	104	4	+	+	PROPN
ap-2092	104	5	ω	ω	NUM
ap-2092	104	6	+	+	NOUN
ap-2092	104	7	2	2	NUM
ap-2092	104	8	g	g	NOUN
ap-2092	104	9	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	104	10	)	)	PUNCT
ap-2092	104	11	∣∣2]v(x	∣∣2]v(x	NUM
ap-2092	104	12	)	)	PUNCT
ap-2092	105	1	+	+	CCONJ
ap-2092	105	2	gψ∗0(x)2u(x	gψ∗0(x)2u(x	NOUN
ap-2092	105	3	)	)	PUNCT
ap-2092	105	4	.	.	PUNCT
ap-2092	106	1	(	(	PUNCT
ap-2092	106	2	4b	4b	PROPN
ap-2092	106	3	)	)	PUNCT
ap-2092	106	4	in	in	ADP
ap-2092	106	5	equation	equation	NOUN
ap-2092	106	6	(	(	PUNCT
ap-2092	106	7	3b	3b	NUM
ap-2092	106	8	)	)	PUNCT
ap-2092	106	9	it	it	PRON
ap-2092	106	10	can	can	AUX
ap-2092	106	11	be	be	AUX
ap-2092	106	12	seen	see	VERB
ap-2092	106	13	that	that	SCONJ
ap-2092	106	14	ω	ω	PROPN
ap-2092	106	15	decides	decide	VERB
ap-2092	106	16	on	on	ADP
ap-2092	106	17	the	the	DET
ap-2092	106	18	temporal	temporal	ADJ
ap-2092	106	19	evolution	evolution	NOUN
ap-2092	106	20	of	of	ADP
ap-2092	106	21	the	the	DET
ap-2092	106	22	fluctuation	fluctuation	NOUN
ap-2092	106	23	.	.	PUNCT
ap-2092	107	1	real	real	ADJ
ap-2092	107	2	values	value	NOUN
ap-2092	107	3	of	of	ADP
ap-2092	107	4	ω	ω	NUM
ap-2092	107	5	describe	describe	VERB
ap-2092	107	6	stable	stable	ADJ
ap-2092	107	7	oscillations	oscillation	NOUN
ap-2092	107	8	,	,	PUNCT
ap-2092	107	9	whereas	whereas	SCONJ
ap-2092	107	10	imaginary	imaginary	ADJ
ap-2092	107	11	parts	part	NOUN
ap-2092	107	12	lead	lead	VERB
ap-2092	107	13	to	to	ADP
ap-2092	107	14	a	a	DET
ap-2092	107	15	growth	growth	NOUN
ap-2092	107	16	or	or	CCONJ
ap-2092	107	17	decay	decay	NOUN
ap-2092	107	18	of	of	ADP
ap-2092	107	19	the	the	DET
ap-2092	107	20	fluctuation	fluctuation	NOUN
ap-2092	107	21	’s	’s	PART
ap-2092	107	22	amplitude	amplitude	NOUN
ap-2092	107	23	.	.	PUNCT
ap-2092	108	1	thus	thus	ADV
ap-2092	108	2	,	,	PUNCT
ap-2092	108	3	ω	ω	PROPN
ap-2092	108	4	measures	measure	VERB
ap-2092	108	5	the	the	DET
ap-2092	108	6	stability	stability	NOUN
ap-2092	108	7	of	of	ADP
ap-2092	108	8	the	the	DET
ap-2092	108	9	stationary	stationary	ADJ
ap-2092	108	10	solution	solution	NOUN
ap-2092	108	11	ψ0	ψ0	ADV
ap-2092	108	12	against	against	ADP
ap-2092	108	13	small	small	ADJ
ap-2092	108	14	fluctuations	fluctuation	NOUN
ap-2092	108	15	.	.	PUNCT
ap-2092	109	1	numerically	numerically	ADV
ap-2092	109	2	the	the	DET
ap-2092	109	3	bogoliubov	bogoliubov	PROPN
ap-2092	109	4	-	-	PUNCT
ap-2092	109	5	de	de	ADJ
ap-2092	109	6	gennes	genne	NOUN
ap-2092	109	7	equations	equation	NOUN
ap-2092	109	8	are	be	AUX
ap-2092	109	9	solved	solve	VERB
ap-2092	109	10	with	with	ADP
ap-2092	109	11	the	the	DET
ap-2092	109	12	same	same	ADJ
ap-2092	109	13	method	method	NOUN
ap-2092	109	14	as	as	SCONJ
ap-2092	109	15	the	the	DET
ap-2092	109	16	stationary	stationary	ADJ
ap-2092	109	17	states	state	NOUN
ap-2092	109	18	,	,	PUNCT
ap-2092	109	19	i.e.	i.e.	X
ap-2092	109	20	the	the	DET
ap-2092	109	21	wave	wave	NOUN
ap-2092	109	22	functions	function	NOUN
ap-2092	109	23	u	u	NOUN
ap-2092	109	24	and	and	CCONJ
ap-2092	109	25	v	v	NOUN
ap-2092	109	26	are	be	AUX
ap-2092	109	27	integrated	integrate	VERB
ap-2092	109	28	outward	outward	ADV
ap-2092	109	29	from	from	ADP
ap-2092	109	30	x	x	X
ap-2092	109	31	=	=	NOUN
ap-2092	109	32	0	0	NUM
ap-2092	109	33	.	.	PUNCT
ap-2092	110	1	it	it	PRON
ap-2092	110	2	can	can	AUX
ap-2092	110	3	easily	easily	ADV
ap-2092	110	4	be	be	AUX
ap-2092	110	5	seen	see	VERB
ap-2092	110	6	that	that	SCONJ
ap-2092	110	7	the	the	DET
ap-2092	110	8	bogoliubov	bogoliubov	PROPN
ap-2092	110	9	-	-	PUNCT
ap-2092	110	10	de	de	ADJ
ap-2092	110	11	gennes	genne	NOUN
ap-2092	110	12	equations	equation	NOUN
ap-2092	110	13	(	(	PUNCT
ap-2092	110	14	4	4	X
ap-2092	110	15	)	)	PUNCT
ap-2092	110	16	are	be	AUX
ap-2092	110	17	invariant	invariant	ADJ
ap-2092	110	18	under	under	ADP
ap-2092	110	19	the	the	DET
ap-2092	110	20	transformation	transformation	NOUN
ap-2092	110	21	u(x	u(x	NOUN
ap-2092	110	22	)	)	PUNCT
ap-2092	110	23	→	→	SYM
ap-2092	110	24	u(x)eiχ	u(x)eiχ	PROPN
ap-2092	110	25	,	,	PUNCT
ap-2092	110	26	v(x)→	v(x)→	PUNCT
ap-2092	110	27	v(x)eiχ	v(x)eiχ	ADV
ap-2092	110	28	with	with	ADP
ap-2092	110	29	a	a	DET
ap-2092	110	30	real	real	ADJ
ap-2092	110	31	phase	phase	NOUN
ap-2092	110	32	χ	χ	NOUN
ap-2092	110	33	.	.	PUNCT
ap-2092	111	1	similarly	similarly	ADV
ap-2092	111	2	to	to	ADP
ap-2092	111	3	the	the	DET
ap-2092	111	4	procedure	procedure	NOUN
ap-2092	111	5	for	for	ADP
ap-2092	111	6	the	the	DET
ap-2092	111	7	integration	integration	NOUN
ap-2092	111	8	of	of	ADP
ap-2092	111	9	the	the	DET
ap-2092	111	10	stationary	stationary	ADJ
ap-2092	111	11	states	state	NOUN
ap-2092	111	12	this	this	DET
ap-2092	111	13	symmetry	symmetry	NOUN
ap-2092	111	14	can	can	AUX
ap-2092	111	15	be	be	AUX
ap-2092	111	16	exploited	exploit	VERB
ap-2092	111	17	.	.	PUNCT
ap-2092	112	1	the	the	DET
ap-2092	112	2	remaining	remain	VERB
ap-2092	112	3	initial	initial	ADJ
ap-2092	112	4	values	value	NOUN
ap-2092	112	5	with	with	ADP
ap-2092	112	6	which	which	PRON
ap-2092	112	7	the	the	DET
ap-2092	112	8	integration	integration	NOUN
ap-2092	112	9	has	have	VERB
ap-2092	112	10	to	to	PART
ap-2092	112	11	be	be	AUX
ap-2092	112	12	started	start	VERB
ap-2092	112	13	are	be	AUX
ap-2092	112	14	u(0	u(0	NOUN
ap-2092	112	15	)	)	PUNCT
ap-2092	112	16	∈	∈	PROPN
ap-2092	112	17	c	c	X
ap-2092	112	18	,	,	PUNCT
ap-2092	112	19	re(v(0	re(v(0	PROPN
ap-2092	112	20	)	)	PUNCT
ap-2092	112	21	)	)	PUNCT
ap-2092	112	22	,	,	PUNCT
ap-2092	112	23	u′(0	u′(0	PROPN
ap-2092	112	24	)	)	PUNCT
ap-2092	112	25	∈	∈	PROPN
ap-2092	112	26	c	c	X
ap-2092	112	27	,	,	PUNCT
ap-2092	112	28	v′(0	v′(0	ADJ
ap-2092	112	29	)	)	PUNCT
ap-2092	112	30	∈	∈	PROPN
ap-2092	112	31	c	c	X
ap-2092	112	32	,	,	PUNCT
ap-2092	112	33	ω	ω	PROPN
ap-2092	112	34	∈	∈	PROPN
ap-2092	112	35	c.	c.	NOUN
ap-2092	112	36	in	in	ADP
ap-2092	112	37	a	a	DET
ap-2092	112	38	nine	nine	NUM
ap-2092	112	39	-	-	PUNCT
ap-2092	112	40	dimensional	dimensional	ADJ
ap-2092	112	41	root	root	NOUN
ap-2092	112	42	search	search	NOUN
ap-2092	112	43	they	they	PRON
ap-2092	112	44	have	have	VERB
ap-2092	112	45	to	to	PART
ap-2092	112	46	be	be	AUX
ap-2092	112	47	chosen	choose	VERB
ap-2092	112	48	such	such	ADJ
ap-2092	112	49	that	that	SCONJ
ap-2092	112	50	the	the	DET
ap-2092	112	51	conditions	condition	NOUN
ap-2092	112	52	u(±∞	u(±∞	NUM
ap-2092	112	53	)	)	PUNCT
ap-2092	112	54	→	→	SYM
ap-2092	112	55	0	0	NUM
ap-2092	112	56	,	,	PUNCT
ap-2092	112	57	v(±∞	v(±∞	NOUN
ap-2092	112	58	)	)	PUNCT
ap-2092	112	59	→	→	SYM
ap-2092	112	60	0	0	NUM
ap-2092	112	61	,	,	PUNCT
ap-2092	112	62	and	and	CCONJ
ap-2092	112	63	∫	∫	PROPN
ap-2092	112	64	∞	∞	PROPN
ap-2092	112	65	−∞	−∞	ADP
ap-2092	112	66	∣∣u(x	∣∣u(x	NOUN
ap-2092	112	67	)	)	PUNCT
ap-2092	113	1	+	+	NUM
ap-2092	113	2	v∗(x	v∗(x	NOUN
ap-2092	113	3	)	)	PUNCT
ap-2092	113	4	∣∣2	∣∣2	PROPN
ap-2092	113	5	dx	dx	NOUN
ap-2092	113	6	=	=	SYM
ap-2092	113	7	1	1	NUM
ap-2092	113	8	are	be	AUX
ap-2092	113	9	fulfilled	fulfil	VERB
ap-2092	113	10	[	[	PUNCT
ap-2092	113	11	11	11	NUM
ap-2092	113	12	]	]	PUNCT
ap-2092	113	13	.	.	PUNCT
ap-2092	114	1	two	two	NUM
ap-2092	114	2	further	further	ADJ
ap-2092	114	3	symmetries	symmetry	NOUN
ap-2092	114	4	can	can	AUX
ap-2092	114	5	be	be	AUX
ap-2092	114	6	exploited	exploit	VERB
ap-2092	114	7	to	to	PART
ap-2092	114	8	reduce	reduce	VERB
ap-2092	114	9	the	the	DET
ap-2092	114	10	number	number	NOUN
ap-2092	114	11	of	of	ADP
ap-2092	114	12	independent	independent	ADJ
ap-2092	114	13	stability	stability	NOUN
ap-2092	114	14	eigenvalues	eigenvalue	VERB
ap-2092	114	15	that	that	PRON
ap-2092	114	16	have	have	VERB
ap-2092	114	17	to	to	PART
ap-2092	114	18	be	be	AUX
ap-2092	114	19	calculated	calculate	VERB
ap-2092	114	20	.	.	PUNCT
ap-2092	115	1	the	the	DET
ap-2092	115	2	replacement	replacement	NOUN
ap-2092	115	3	(	(	PUNCT
ap-2092	115	4	u	u	NOUN
ap-2092	115	5	,	,	PUNCT
ap-2092	115	6	v	v	NOUN
ap-2092	115	7	,	,	PUNCT
ap-2092	115	8	ω)→	ω)→	PROPN
ap-2092	115	9	(	(	PUNCT
ap-2092	115	10	v∗	v∗	PROPN
ap-2092	115	11	,	,	PUNCT
ap-2092	115	12	u∗,−ω∗	u∗,−ω∗	NOUN
ap-2092	115	13	)	)	PUNCT
ap-2092	115	14	leaves	leave	VERB
ap-2092	115	15	the	the	DET
ap-2092	115	16	ansatz	ansatz	ADJ
ap-2092	115	17	(	(	PUNCT
ap-2092	115	18	3b	3b	NUM
ap-2092	115	19	)	)	PUNCT
ap-2092	115	20	invariant	invariant	ADJ
ap-2092	115	21	.	.	PUNCT
ap-2092	116	1	thus	thus	ADV
ap-2092	116	2	,	,	PUNCT
ap-2092	116	3	if	if	SCONJ
ap-2092	116	4	ω	ω	PROPN
ap-2092	116	5	is	be	AUX
ap-2092	116	6	a	a	DET
ap-2092	116	7	stability	stability	NOUN
ap-2092	116	8	eigenvalue	eigenvalue	NOUN
ap-2092	116	9	also	also	ADV
ap-2092	116	10	−ω∗	−ω∗	PROPN
ap-2092	116	11	is	be	AUX
ap-2092	116	12	a	a	DET
ap-2092	116	13	valid	valid	ADJ
ap-2092	116	14	solution	solution	NOUN
ap-2092	116	15	.	.	PUNCT
ap-2092	117	1	furthermore	furthermore	ADV
ap-2092	117	2	for	for	ADP
ap-2092	117	3	every	every	DET
ap-2092	117	4	eigenvalue	eigenvalue	PROPN
ap-2092	117	5	ω	ω	PROPN
ap-2092	117	6	there	there	PRON
ap-2092	117	7	is	be	VERB
ap-2092	117	8	also	also	ADV
ap-2092	117	9	one	one	NUM
ap-2092	117	10	solution	solution	NOUN
ap-2092	117	11	with	with	ADP
ap-2092	117	12	the	the	DET
ap-2092	117	13	eigenvalue	eigenvalue	PROPN
ap-2092	117	14	ω∗	ω∗	NOUN
ap-2092	117	15	if	if	SCONJ
ap-2092	117	16	the	the	DET
ap-2092	117	17	stationary	stationary	ADJ
ap-2092	117	18	state	state	NOUN
ap-2092	117	19	ψ0	ψ0	ADV
ap-2092	117	20	is	be	AUX
ap-2092	117	21	pt	pt	X
ap-2092	117	22	symmetric	symmetric	NOUN
ap-2092	117	23	.	.	PUNCT
ap-2092	118	1	this	this	PRON
ap-2092	118	2	can	can	AUX
ap-2092	118	3	be	be	AUX
ap-2092	118	4	verified	verify	VERB
ap-2092	118	5	by	by	ADP
ap-2092	118	6	applying	apply	VERB
ap-2092	118	7	the	the	DET
ap-2092	118	8	pt	pt	NOUN
ap-2092	118	9	operator	operator	NOUN
ap-2092	118	10	to	to	ADP
ap-2092	118	11	the	the	DET
ap-2092	118	12	bogoliubov	bogoliubov	PROPN
ap-2092	118	13	-	-	PUNCT
ap-2092	118	14	de	de	ADJ
ap-2092	118	15	gennes	genne	NOUN
ap-2092	118	16	equations	equation	NOUN
ap-2092	118	17	(	(	PUNCT
ap-2092	118	18	4	4	NUM
ap-2092	118	19	)	)	PUNCT
ap-2092	118	20	.	.	PUNCT
ap-2092	119	1	due	due	ADP
ap-2092	119	2	to	to	ADP
ap-2092	119	3	these	these	DET
ap-2092	119	4	two	two	NUM
ap-2092	119	5	symmetries	symmetry	NOUN
ap-2092	119	6	it	it	PRON
ap-2092	119	7	is	be	AUX
ap-2092	119	8	sufficient	sufficient	ADJ
ap-2092	119	9	to	to	PART
ap-2092	119	10	search	search	VERB
ap-2092	119	11	for	for	ADP
ap-2092	119	12	stability	stability	NOUN
ap-2092	119	13	eigenvalues	eigenvalue	VERB
ap-2092	119	14	with	with	ADP
ap-2092	119	15	re(ω	re(ω	NOUN
ap-2092	119	16	)	)	PUNCT
ap-2092	119	17	>	>	X
ap-2092	119	18	0	0	PUNCT
ap-2092	119	19	and	and	CCONJ
ap-2092	119	20	im(ω	im(ω	NOUN
ap-2092	119	21	)	)	PUNCT
ap-2092	119	22	>	>	X
ap-2092	120	1	0	0	X
ap-2092	120	2	.	.	NOUN
ap-2092	120	3	3.1	3.1	NUM
ap-2092	120	4	.	.	PUNCT
ap-2092	121	1	stability	stability	NOUN
ap-2092	121	2	in	in	ADP
ap-2092	121	3	the	the	DET
ap-2092	121	4	vicinity	vicinity	NOUN
ap-2092	121	5	of	of	ADP
ap-2092	121	6	the	the	DET
ap-2092	121	7	bifurcation	bifurcation	NOUN
ap-2092	121	8	the	the	DET
ap-2092	121	9	relevant	relevant	ADJ
ap-2092	121	10	question	question	NOUN
ap-2092	121	11	which	which	PRON
ap-2092	121	12	has	have	VERB
ap-2092	121	13	to	to	PART
ap-2092	121	14	be	be	AUX
ap-2092	121	15	answered	answer	VERB
ap-2092	121	16	by	by	ADP
ap-2092	121	17	our	our	PRON
ap-2092	121	18	calculation	calculation	NOUN
ap-2092	121	19	is	be	AUX
ap-2092	121	20	whether	whether	SCONJ
ap-2092	121	21	or	or	CCONJ
ap-2092	121	22	not	not	PART
ap-2092	121	23	the	the	DET
ap-2092	121	24	discrepancy	discrepancy	NOUN
ap-2092	121	25	between	between	ADP
ap-2092	121	26	the	the	DET
ap-2092	121	27	γ	γ	PROPN
ap-2092	121	28	values	value	NOUN
ap-2092	121	29	of	of	ADP
ap-2092	121	30	the	the	DET
ap-2092	121	31	pitchfork	pitchfork	NOUN
ap-2092	121	32	bifurcation	bifurcation	NOUN
ap-2092	121	33	and	and	CCONJ
ap-2092	121	34	the	the	DET
ap-2092	121	35	stability	stability	NOUN
ap-2092	121	36	change	change	NOUN
ap-2092	121	37	appears	appear	VERB
ap-2092	121	38	for	for	ADP
ap-2092	121	39	the	the	DET
ap-2092	121	40	double	double	ADJ
ap-2092	121	41	-	-	PUNCT
ap-2092	121	42	δ	δ	NOUN
ap-2092	121	43	potential	potential	NOUN
ap-2092	121	44	.	.	PUNCT
ap-2092	122	1	thus	thus	ADV
ap-2092	122	2	we	we	PRON
ap-2092	122	3	calculated	calculate	VERB
ap-2092	122	4	the	the	DET
ap-2092	122	5	stability	stability	NOUN
ap-2092	122	6	eigenvalue	eigenvalue	VERB
ap-2092	122	7	with	with	ADP
ap-2092	122	8	re(ω	re(ω	NOUN
ap-2092	122	9	)	)	PUNCT
ap-2092	122	10	>	>	X
ap-2092	122	11	0	0	NUM
ap-2092	122	12	,	,	PUNCT
ap-2092	122	13	im(ω	im(ω	NOUN
ap-2092	122	14	)	)	PUNCT
ap-2092	122	15	>	>	X
ap-2092	122	16	0	0	PUNCT
ap-2092	123	1	for	for	ADP
ap-2092	123	2	a	a	DET
ap-2092	123	3	range	range	NOUN
ap-2092	123	4	of	of	ADP
ap-2092	123	5	γ	γ	NOUN
ap-2092	123	6	around	around	ADP
ap-2092	123	7	the	the	DET
ap-2092	123	8	bifurcation	bifurcation	NOUN
ap-2092	123	9	,	,	PUNCT
ap-2092	123	10	which	which	PRON
ap-2092	123	11	is	be	AUX
ap-2092	123	12	shown	show	VERB
ap-2092	123	13	in	in	ADP
ap-2092	123	14	figure	figure	NOUN
ap-2092	123	15	2	2	NUM
ap-2092	123	16	for	for	ADP
ap-2092	123	17	g	g	NOUN
ap-2092	123	18	=	=	SYM
ap-2092	123	19	−1	−1	NOUN
ap-2092	123	20	.	.	PUNCT
ap-2092	124	1	for	for	ADP
ap-2092	124	2	increasing	increase	VERB
ap-2092	124	3	135	135	NUM
ap-2092	124	4	a.	a.	NOUN
ap-2092	124	5	löhle	löhle	PROPN
ap-2092	124	6	,	,	PUNCT
ap-2092	124	7	h.	h.	PROPN
ap-2092	124	8	cartarius	cartarius	PROPN
ap-2092	124	9	,	,	PUNCT
ap-2092	124	10	d.	d.	PROPN
ap-2092	124	11	haag	haag	PROPN
ap-2092	124	12	et	et	PROPN
ap-2092	124	13	al	al	PROPN
ap-2092	124	14	.	.	PROPN
ap-2092	124	15	acta	acta	PROPN
ap-2092	124	16	polytechnica	polytechnica	PROPN
ap-2092	124	17	0	0	NUM
ap-2092	124	18	0.1	0.1	NUM
ap-2092	124	19	0.2	0.2	NUM
ap-2092	124	20	0.3	0.3	NUM
ap-2092	124	21	0.4	0.4	NUM
ap-2092	124	22	0.5	0.5	NUM
ap-2092	124	23	0.6	0.6	NUM
ap-2092	124	24	0.7	0.7	NUM
ap-2092	124	25	0.8	0.8	NUM
ap-2092	124	26	0	0	NUM
ap-2092	124	27	0.05	0.05	NUM
ap-2092	124	28	0.1	0.1	NUM
ap-2092	124	29	0.15	0.15	NUM
ap-2092	124	30	0.2	0.2	NUM
ap-2092	124	31	0.25	0.25	NUM
ap-2092	124	32	0.3	0.3	NUM
ap-2092	124	33	0.35	0.35	NUM
ap-2092	124	34	0.4	0.4	NUM
ap-2092	124	35	κ	κ	NOUN
ap-2092	124	36	,	,	PUNCT
ap-2092	124	37	ω	ω	PROPN
ap-2092	124	38	γ	γ	X
ap-2092	124	39	γ	γ	X
ap-2092	124	40	κ	κ	PROPN
ap-2092	124	41	re(ω	re(ω	X
ap-2092	124	42	)	)	PUNCT
ap-2092	124	43	im(ω	im(ω	PROPN
ap-2092	124	44	)	)	PUNCT
ap-2092	124	45	re(κ	re(κ	X
ap-2092	124	46	)	)	PUNCT
ap-2092	124	47	figure	figure	NOUN
ap-2092	124	48	2	2	NUM
ap-2092	124	49	.	.	PUNCT
ap-2092	124	50	real	real	ADJ
ap-2092	124	51	(	(	PUNCT
ap-2092	124	52	red	red	ADJ
ap-2092	124	53	solid	solid	ADJ
ap-2092	124	54	line	line	NOUN
ap-2092	124	55	)	)	PUNCT
ap-2092	124	56	and	and	CCONJ
ap-2092	124	57	imaginary	imaginary	ADJ
ap-2092	124	58	(	(	PUNCT
ap-2092	124	59	green	green	ADJ
ap-2092	124	60	dashed	dash	VERB
ap-2092	124	61	line	line	NOUN
ap-2092	124	62	)	)	PUNCT
ap-2092	124	63	part	part	NOUN
ap-2092	124	64	of	of	ADP
ap-2092	124	65	the	the	DET
ap-2092	124	66	stability	stability	NOUN
ap-2092	124	67	eigenvalue	eigenvalue	PROPN
ap-2092	124	68	ω	ω	PROPN
ap-2092	124	69	for	for	ADP
ap-2092	124	70	the	the	DET
ap-2092	124	71	stationary	stationary	ADJ
ap-2092	124	72	ground	ground	NOUN
ap-2092	124	73	state	state	NOUN
ap-2092	124	74	in	in	ADP
ap-2092	124	75	the	the	DET
ap-2092	124	76	case	case	NOUN
ap-2092	124	77	g	g	NOUN
ap-2092	124	78	=	=	SYM
ap-2092	124	79	−1	−1	NOUN
ap-2092	124	80	.	.	PUNCT
ap-2092	125	1	the	the	DET
ap-2092	125	2	stability	stability	NOUN
ap-2092	125	3	change	change	NOUN
ap-2092	125	4	occurs	occur	VERB
ap-2092	125	5	at	at	ADP
ap-2092	125	6	γω	γω	PROPN
ap-2092	125	7	≈	≈	PROPN
ap-2092	125	8	0.3138	0.3138	NUM
ap-2092	125	9	.	.	PUNCT
ap-2092	126	1	to	to	PART
ap-2092	126	2	illustrate	illustrate	VERB
ap-2092	126	3	the	the	DET
ap-2092	126	4	pitchfork	pitchfork	NOUN
ap-2092	126	5	bifurcation	bifurcation	NOUN
ap-2092	126	6	the	the	DET
ap-2092	126	7	real	real	ADJ
ap-2092	126	8	parts	part	NOUN
ap-2092	126	9	of	of	ADP
ap-2092	126	10	κ	κ	NOUN
ap-2092	126	11	of	of	ADP
ap-2092	126	12	all	all	DET
ap-2092	126	13	stationary	stationary	ADJ
ap-2092	126	14	states	state	NOUN
ap-2092	126	15	are	be	AUX
ap-2092	126	16	also	also	ADV
ap-2092	126	17	shown	show	VERB
ap-2092	126	18	(	(	PUNCT
ap-2092	126	19	blue	blue	ADJ
ap-2092	126	20	dotted	dotted	ADJ
ap-2092	126	21	lines	line	NOUN
ap-2092	126	22	)	)	PUNCT
ap-2092	126	23	.	.	PUNCT
ap-2092	127	1	the	the	DET
ap-2092	127	2	value	value	NOUN
ap-2092	127	3	γκ	γκ	ADJ
ap-2092	128	1	≈	≈	PROPN
ap-2092	128	2	0.307	0.307	NUM
ap-2092	128	3	is	be	AUX
ap-2092	128	4	marked	mark	VERB
ap-2092	128	5	by	by	ADP
ap-2092	128	6	the	the	DET
ap-2092	128	7	black	black	ADJ
ap-2092	128	8	dasheddotted	dasheddotte	VERB
ap-2092	128	9	line	line	NOUN
ap-2092	128	10	.	.	PUNCT
ap-2092	129	1	obviously	obviously	ADV
ap-2092	129	2	there	there	PRON
ap-2092	129	3	is	be	VERB
ap-2092	129	4	a	a	DET
ap-2092	129	5	discrepancy	discrepancy	NOUN
ap-2092	129	6	between	between	ADP
ap-2092	129	7	the	the	DET
ap-2092	129	8	two	two	NUM
ap-2092	129	9	values	value	NOUN
ap-2092	129	10	.	.	PUNCT
ap-2092	130	1	γ	γ	X
ap-2092	130	2	the	the	DET
ap-2092	130	3	eigenvalue	eigenvalue	PROPN
ap-2092	130	4	ω	ω	PROPN
ap-2092	130	5	switches	switch	NOUN
ap-2092	130	6	from	from	ADP
ap-2092	130	7	real	real	ADV
ap-2092	130	8	to	to	ADP
ap-2092	130	9	imaginary	imaginary	ADJ
ap-2092	130	10	at	at	ADP
ap-2092	130	11	γω	γω	ADP
ap-2092	130	12	≈	≈	PROPN
ap-2092	130	13	0.3138	0.3138	NUM
ap-2092	130	14	marking	mark	VERB
ap-2092	130	15	the	the	DET
ap-2092	130	16	stability	stability	NOUN
ap-2092	130	17	change	change	NOUN
ap-2092	130	18	.	.	PUNCT
ap-2092	131	1	the	the	DET
ap-2092	131	2	pitchfork	pitchfork	NOUN
ap-2092	131	3	bifurcation	bifurcation	NOUN
ap-2092	131	4	is	be	AUX
ap-2092	131	5	visible	visible	ADJ
ap-2092	131	6	in	in	ADP
ap-2092	131	7	the	the	DET
ap-2092	131	8	real	real	ADJ
ap-2092	131	9	parts	part	NOUN
ap-2092	131	10	of	of	ADP
ap-2092	131	11	κ	κ	NOUN
ap-2092	131	12	of	of	ADP
ap-2092	131	13	all	all	DET
ap-2092	131	14	stationary	stationary	ADJ
ap-2092	131	15	states	state	NOUN
ap-2092	131	16	of	of	ADP
ap-2092	131	17	the	the	DET
ap-2092	131	18	system	system	NOUN
ap-2092	131	19	.	.	PUNCT
ap-2092	132	1	it	it	PRON
ap-2092	132	2	is	be	AUX
ap-2092	132	3	marked	mark	VERB
ap-2092	132	4	by	by	ADP
ap-2092	132	5	the	the	DET
ap-2092	132	6	black	black	NOUN
ap-2092	132	7	dashed	dash	VERB
ap-2092	132	8	-	-	PUNCT
ap-2092	132	9	dotted	dot	VERB
ap-2092	132	10	line	line	NOUN
ap-2092	132	11	.	.	PUNCT
ap-2092	133	1	obviously	obviously	ADV
ap-2092	133	2	there	there	PRON
ap-2092	133	3	is	be	VERB
ap-2092	133	4	a	a	DET
ap-2092	133	5	discrepancy	discrepancy	NOUN
ap-2092	133	6	between	between	ADP
ap-2092	133	7	γκ	γκ	ADJ
ap-2092	133	8	and	and	CCONJ
ap-2092	133	9	γω	γω	NOUN
ap-2092	133	10	.	.	PUNCT
ap-2092	134	1	the	the	DET
ap-2092	134	2	difference	difference	NOUN
ap-2092	134	3	∆γ	∆γ	VERB
ap-2092	134	4	=	=	PUNCT
ap-2092	134	5	γκ	γκ	ADJ
ap-2092	134	6	−	−	PROPN
ap-2092	134	7	γω	γω	ADP
ap-2092	134	8	(	(	PUNCT
ap-2092	134	9	5	5	NUM
ap-2092	134	10	)	)	PUNCT
ap-2092	134	11	is	be	AUX
ap-2092	134	12	∆γ	∆γ	PROPN
ap-2092	134	13	≈	≈	PROPN
ap-2092	134	14	−0.0067	−0.0067	PROPN
ap-2092	134	15	.	.	PUNCT
ap-2092	135	1	the	the	DET
ap-2092	135	2	system	system	NOUN
ap-2092	135	3	does	do	AUX
ap-2092	135	4	not	not	PART
ap-2092	135	5	possess	possess	VERB
ap-2092	135	6	any	any	DET
ap-2092	135	7	further	further	ADJ
ap-2092	135	8	stationary	stationary	ADJ
ap-2092	135	9	states	state	NOUN
ap-2092	135	10	besides	besides	SCONJ
ap-2092	135	11	those	those	PRON
ap-2092	135	12	shown	show	VERB
ap-2092	135	13	in	in	ADP
ap-2092	135	14	figure	figure	NOUN
ap-2092	135	15	1	1	NUM
ap-2092	135	16	.	.	PUNCT
ap-2092	135	17	three	three	NUM
ap-2092	135	18	of	of	ADP
ap-2092	135	19	these	these	DET
ap-2092	135	20	four	four	NUM
ap-2092	135	21	states	state	NOUN
ap-2092	135	22	are	be	AUX
ap-2092	135	23	participating	participate	VERB
ap-2092	135	24	in	in	ADP
ap-2092	135	25	the	the	DET
ap-2092	135	26	pitchfork	pitchfork	NOUN
ap-2092	135	27	bifurcation	bifurcation	NOUN
ap-2092	135	28	.	.	PUNCT
ap-2092	136	1	only	only	ADV
ap-2092	136	2	the	the	DET
ap-2092	136	3	excited	excited	ADJ
ap-2092	136	4	pt	pt	NOUN
ap-2092	136	5	symmetric	symmetric	ADJ
ap-2092	136	6	solution	solution	NOUN
ap-2092	136	7	would	would	AUX
ap-2092	136	8	be	be	AUX
ap-2092	136	9	able	able	ADJ
ap-2092	136	10	to	to	PART
ap-2092	136	11	influence	influence	VERB
ap-2092	136	12	the	the	DET
ap-2092	136	13	dynamics	dynamic	NOUN
ap-2092	136	14	of	of	ADP
ap-2092	136	15	the	the	DET
ap-2092	136	16	ground	ground	NOUN
ap-2092	136	17	state	state	NOUN
ap-2092	136	18	at	at	ADP
ap-2092	136	19	a	a	DET
ap-2092	136	20	value	value	NOUN
ap-2092	136	21	γ	γ	X
ap-2092	136	22	6=	6=	SYM
ap-2092	136	23	γω	γω	PROPN
ap-2092	136	24	.	.	PUNCT
ap-2092	137	1	however	however	ADV
ap-2092	137	2	,	,	PUNCT
ap-2092	137	3	it	it	PRON
ap-2092	137	4	stays	stay	VERB
ap-2092	137	5	real	real	ADJ
ap-2092	137	6	for	for	SCONJ
ap-2092	137	7	all	all	DET
ap-2092	137	8	parameters	parameter	NOUN
ap-2092	137	9	γ	γ	NOUN
ap-2092	137	10	shown	show	VERB
ap-2092	137	11	in	in	ADP
ap-2092	137	12	figure	figure	NOUN
ap-2092	137	13	2	2	NUM
ap-2092	137	14	and	and	CCONJ
ap-2092	137	15	can	can	AUX
ap-2092	137	16	not	not	PART
ap-2092	137	17	cause	cause	VERB
ap-2092	137	18	any	any	DET
ap-2092	137	19	qualitatively	qualitatively	ADV
ap-2092	137	20	different	different	ADJ
ap-2092	137	21	behaviour	behaviour	NOUN
ap-2092	137	22	of	of	ADP
ap-2092	137	23	the	the	DET
ap-2092	137	24	ground	ground	NOUN
ap-2092	137	25	state	state	NOUN
ap-2092	137	26	’s	’s	PART
ap-2092	137	27	dynamics	dynamic	NOUN
ap-2092	137	28	.	.	PUNCT
ap-2092	138	1	thus	thus	ADV
ap-2092	138	2	,	,	PUNCT
ap-2092	138	3	an	an	DET
ap-2092	138	4	influence	influence	NOUN
ap-2092	138	5	of	of	ADP
ap-2092	138	6	further	further	ADJ
ap-2092	138	7	states	state	NOUN
ap-2092	138	8	can	can	AUX
ap-2092	138	9	be	be	AUX
ap-2092	138	10	ruled	rule	VERB
ap-2092	138	11	out	out	ADP
ap-2092	138	12	as	as	ADP
ap-2092	138	13	the	the	DET
ap-2092	138	14	reason	reason	NOUN
ap-2092	138	15	for	for	ADP
ap-2092	138	16	the	the	DET
ap-2092	138	17	discrepancy	discrepancy	NOUN
ap-2092	138	18	in	in	ADP
ap-2092	138	19	the	the	DET
ap-2092	138	20	double	double	ADJ
ap-2092	138	21	-	-	PUNCT
ap-2092	138	22	well	well	NOUN
ap-2092	138	23	system	system	NOUN
ap-2092	138	24	of	of	ADP
ap-2092	138	25	refs	ref	NOUN
ap-2092	138	26	.	.	PUNCT
ap-2092	139	1	[	[	X
ap-2092	139	2	11	11	NUM
ap-2092	139	3	,	,	PUNCT
ap-2092	139	4	12	12	NUM
ap-2092	139	5	]	]	PUNCT
ap-2092	139	6	.	.	PUNCT
ap-2092	140	1	the	the	DET
ap-2092	140	2	remaining	remain	VERB
ap-2092	140	3	difference	difference	NOUN
ap-2092	140	4	between	between	ADP
ap-2092	140	5	the	the	DET
ap-2092	140	6	grosspitaevskii	grosspitaevskii	ADJ
ap-2092	140	7	equation	equation	NOUN
ap-2092	140	8	(	(	PUNCT
ap-2092	140	9	2	2	NUM
ap-2092	140	10	)	)	PUNCT
ap-2092	140	11	and	and	CCONJ
ap-2092	140	12	the	the	DET
ap-2092	140	13	two	two	NUM
ap-2092	140	14	mode	mode	NOUN
ap-2092	140	15	system	system	NOUN
ap-2092	140	16	of	of	ADP
ap-2092	140	17	refs	ref	NOUN
ap-2092	140	18	.	.	PUNCT
ap-2092	141	1	[	[	X
ap-2092	141	2	14–17	14–17	NUM
ap-2092	141	3	]	]	PUNCT
ap-2092	141	4	is	be	AUX
ap-2092	141	5	the	the	DET
ap-2092	141	6	norm	norm	NOUN
ap-2092	141	7	-	-	PUNCT
ap-2092	141	8	dependency	dependency	NOUN
ap-2092	141	9	of	of	ADP
ap-2092	141	10	the	the	DET
ap-2092	141	11	nonlinearity	nonlinearity	NOUN
ap-2092	141	12	.	.	PUNCT
ap-2092	142	1	indeed	indeed	ADV
ap-2092	142	2	,	,	PUNCT
ap-2092	142	3	an	an	DET
ap-2092	142	4	influence	influence	NOUN
ap-2092	142	5	of	of	ADP
ap-2092	142	6	the	the	DET
ap-2092	142	7	norm	norm	NOUN
ap-2092	142	8	is	be	AUX
ap-2092	142	9	already	already	ADV
ap-2092	142	10	present	present	ADJ
ap-2092	142	11	if	if	SCONJ
ap-2092	142	12	the	the	DET
ap-2092	142	13	study	study	NOUN
ap-2092	142	14	done	do	VERB
ap-2092	142	15	in	in	ADP
ap-2092	142	16	figure	figure	NOUN
ap-2092	142	17	2	2	NUM
ap-2092	142	18	is	be	AUX
ap-2092	142	19	repeated	repeat	VERB
ap-2092	142	20	for	for	ADP
ap-2092	142	21	different	different	ADJ
ap-2092	142	22	values	value	NOUN
ap-2092	142	23	of	of	ADP
ap-2092	142	24	the	the	DET
ap-2092	142	25	nonlinearity	nonlinearity	NOUN
ap-2092	142	26	parameter	parameter	NOUN
ap-2092	142	27	g.	g.	PROPN
ap-2092	142	28	figure	figure	PROPN
ap-2092	142	29	3	3	NUM
ap-2092	142	30	shows	show	VERB
ap-2092	142	31	∆γ	∆γ	PROPN
ap-2092	142	32	as	as	ADP
ap-2092	142	33	a	a	DET
ap-2092	142	34	function	function	NOUN
ap-2092	142	35	of	of	ADP
ap-2092	142	36	g.	g.	PROPN
ap-2092	142	37	a	a	DET
ap-2092	142	38	strong	strong	ADJ
ap-2092	142	39	dependency	dependency	NOUN
ap-2092	142	40	is	be	AUX
ap-2092	142	41	visible	visible	ADJ
ap-2092	142	42	.	.	PUNCT
ap-2092	143	1	even	even	ADV
ap-2092	143	2	the	the	DET
ap-2092	143	3	sign	sign	NOUN
ap-2092	143	4	changes	change	NOUN
ap-2092	143	5	.	.	PUNCT
ap-2092	144	1	for	for	ADP
ap-2092	144	2	g	g	PROPN
ap-2092	144	3	/	/	SYM
ap-2092	144	4	0.4	0.4	NUM
ap-2092	144	5	the	the	DET
ap-2092	144	6	ground	ground	NOUN
ap-2092	144	7	state	state	NOUN
ap-2092	144	8	becomes	become	VERB
ap-2092	144	9	unstable	unstable	ADJ
ap-2092	144	10	at	at	ADP
ap-2092	144	11	γω	γω	ADP
ap-2092	144	12	<	<	X
ap-2092	144	13	γκ	γκ	PRON
ap-2092	144	14	.	.	PUNCT
ap-2092	144	15	for	for	ADP
ap-2092	144	16	g	g	PROPN
ap-2092	144	17	→	→	SYM
ap-2092	144	18	0	0	NUM
ap-2092	144	19	the	the	DET
ap-2092	144	20	discrepancy	discrepancy	NOUN
ap-2092	144	21	vanishes	vanish	VERB
ap-2092	144	22	as	as	SCONJ
ap-2092	144	23	expected	expect	VERB
ap-2092	144	24	.	.	PUNCT
ap-2092	145	1	3.2	3.2	NUM
ap-2092	145	2	.	.	PUNCT
ap-2092	146	1	norm	norm	NOUN
ap-2092	146	2	-	-	PUNCT
ap-2092	146	3	independent	independent	ADJ
ap-2092	146	4	variant	variant	NOUN
ap-2092	146	5	of	of	ADP
ap-2092	146	6	the	the	DET
ap-2092	146	7	gross	gross	ADJ
ap-2092	146	8	-	-	PUNCT
ap-2092	146	9	pitaevskii	pitaevskii	ADJ
ap-2092	146	10	equation	equation	NOUN
ap-2092	146	11	an	an	DET
ap-2092	146	12	even	even	ADV
ap-2092	146	13	clearer	clear	ADJ
ap-2092	146	14	identification	identification	NOUN
ap-2092	146	15	of	of	ADP
ap-2092	146	16	∆γ	∆γ	NOUN
ap-2092	146	17	with	with	ADP
ap-2092	146	18	the	the	DET
ap-2092	146	19	normdependency	normdependency	NOUN
ap-2092	146	20	of	of	ADP
ap-2092	146	21	the	the	DET
ap-2092	146	22	nonlinearity	nonlinearity	NOUN
ap-2092	146	23	in	in	ADP
ap-2092	146	24	the	the	DET
ap-2092	146	25	gross	gross	ADJ
ap-2092	146	26	-	-	PUNCT
ap-2092	146	27	pitaevskii	pitaevskii	ADJ
ap-2092	146	28	-0.007	-0.007	PROPN
ap-2092	146	29	-0.006	-0.006	X
ap-2092	146	30	-0.005	-0.005	X
ap-2092	146	31	-0.004	-0.004	PUNCT
ap-2092	146	32	-0.003	-0.003	NOUN
ap-2092	146	33	-0.002	-0.002	PUNCT
ap-2092	146	34	-0.001	-0.001	NOUN
ap-2092	146	35	0	0	NUM
ap-2092	146	36	0.001	0.001	NUM
ap-2092	146	37	0	0	NUM
ap-2092	146	38	0.1	0.1	NUM
ap-2092	146	39	0.2	0.2	NUM
ap-2092	146	40	0.3	0.3	NUM
ap-2092	146	41	0.4	0.4	NUM
ap-2092	146	42	0.5	0.5	NUM
ap-2092	146	43	0.6	0.6	NUM
ap-2092	146	44	0.7	0.7	NUM
ap-2092	146	45	0.8	0.8	NUM
ap-2092	146	46	0.9	0.9	NUM
ap-2092	146	47	1	1	NUM
ap-2092	146	48	∆	∆	PROPN
ap-2092	146	49	γ	γ	X
ap-2092	146	50	-g	-g	PUNCT
ap-2092	146	51	figure	figure	NOUN
ap-2092	146	52	3	3	NUM
ap-2092	146	53	.	.	NOUN
ap-2092	146	54	difference	difference	NOUN
ap-2092	146	55	between	between	ADP
ap-2092	146	56	γκ	γκ	ADJ
ap-2092	146	57	and	and	CCONJ
ap-2092	146	58	γω	γω	NOUN
ap-2092	146	59	as	as	SCONJ
ap-2092	146	60	defined	define	VERB
ap-2092	146	61	in	in	ADP
ap-2092	146	62	equation	equation	NOUN
ap-2092	146	63	(	(	PUNCT
ap-2092	146	64	5	5	NUM
ap-2092	146	65	)	)	PUNCT
ap-2092	146	66	as	as	ADP
ap-2092	146	67	a	a	DET
ap-2092	146	68	function	function	NOUN
ap-2092	146	69	of	of	ADP
ap-2092	146	70	g.	g.	PROPN
ap-2092	146	71	a	a	DET
ap-2092	146	72	strong	strong	ADJ
ap-2092	146	73	dependency	dependency	NOUN
ap-2092	146	74	is	be	AUX
ap-2092	146	75	clearly	clearly	ADV
ap-2092	146	76	visible	visible	ADJ
ap-2092	146	77	.	.	PUNCT
ap-2092	147	1	equation	equation	NOUN
ap-2092	147	2	(	(	PUNCT
ap-2092	147	3	2	2	X
ap-2092	147	4	)	)	PUNCT
ap-2092	147	5	can	can	AUX
ap-2092	147	6	be	be	AUX
ap-2092	147	7	given	give	VERB
ap-2092	147	8	with	with	ADP
ap-2092	147	9	a	a	DET
ap-2092	147	10	small	small	ADJ
ap-2092	147	11	modification	modification	NOUN
ap-2092	147	12	.	.	PUNCT
ap-2092	148	1	the	the	DET
ap-2092	148	2	replacement	replacement	NOUN
ap-2092	148	3	g|ψ|2	g|ψ|2	NOUN
ap-2092	148	4	→	→	SYM
ap-2092	148	5	g|ψ|2∫	g|ψ|2∫	NOUN
ap-2092	148	6	|ψ|2	|ψ|2	PROPN
ap-2092	148	7	dx	dx	PROPN
ap-2092	148	8	(	(	PUNCT
ap-2092	148	9	6	6	NUM
ap-2092	148	10	)	)	PUNCT
ap-2092	148	11	makes	make	VERB
ap-2092	148	12	the	the	DET
ap-2092	148	13	gross	gross	ADJ
ap-2092	148	14	-	-	PUNCT
ap-2092	148	15	pitaevskii	pitaevskii	ADJ
ap-2092	148	16	equation	equation	NOUN
ap-2092	148	17	(	(	PUNCT
ap-2092	148	18	2	2	X
ap-2092	148	19	)	)	PUNCT
ap-2092	148	20	normindependent	normindependent	NOUN
ap-2092	148	21	.	.	PUNCT
ap-2092	149	1	note	note	VERB
ap-2092	149	2	that	that	SCONJ
ap-2092	149	3	this	this	PRON
ap-2092	149	4	is	be	AUX
ap-2092	149	5	exactly	exactly	ADV
ap-2092	149	6	the	the	DET
ap-2092	149	7	form	form	NOUN
ap-2092	149	8	of	of	ADP
ap-2092	149	9	the	the	DET
ap-2092	149	10	mean	mean	ADJ
ap-2092	149	11	-	-	PUNCT
ap-2092	149	12	field	field	NOUN
ap-2092	149	13	limit	limit	NOUN
ap-2092	149	14	of	of	ADP
ap-2092	149	15	refs	ref	NOUN
ap-2092	149	16	.	.	PUNCT
ap-2092	150	1	[	[	X
ap-2092	150	2	14–17	14–17	NUM
ap-2092	150	3	]	]	PUNCT
ap-2092	150	4	.	.	PUNCT
ap-2092	151	1	since	since	SCONJ
ap-2092	151	2	the	the	DET
ap-2092	151	3	stationary	stationary	ADJ
ap-2092	151	4	states	state	NOUN
ap-2092	151	5	are	be	AUX
ap-2092	151	6	normalised	normalise	VERB
ap-2092	151	7	to	to	ADP
ap-2092	151	8	1	1	NUM
ap-2092	151	9	they	they	PRON
ap-2092	151	10	are	be	AUX
ap-2092	151	11	not	not	PART
ap-2092	151	12	influenced	influence	VERB
ap-2092	151	13	by	by	ADP
ap-2092	151	14	the	the	DET
ap-2092	151	15	replacement	replacement	NOUN
ap-2092	151	16	.	.	PUNCT
ap-2092	152	1	however	however	ADV
ap-2092	152	2	,	,	PUNCT
ap-2092	152	3	it	it	PRON
ap-2092	152	4	influences	influence	VERB
ap-2092	152	5	the	the	DET
ap-2092	152	6	dynamics	dynamic	NOUN
ap-2092	152	7	and	and	CCONJ
ap-2092	152	8	also	also	ADV
ap-2092	152	9	the	the	DET
ap-2092	152	10	linear	linear	ADJ
ap-2092	152	11	stability	stability	NOUN
ap-2092	152	12	.	.	PUNCT
ap-2092	153	1	the	the	DET
ap-2092	153	2	bogoliubov	bogoliubov	PROPN
ap-2092	153	3	-	-	PUNCT
ap-2092	153	4	de	de	X
ap-2092	153	5	gennes	genne	NOUN
ap-2092	153	6	equations	equation	NOUN
ap-2092	153	7	have	have	VERB
ap-2092	153	8	to	to	PART
ap-2092	153	9	be	be	AUX
ap-2092	153	10	adapted	adapt	VERB
ap-2092	153	11	.	.	PUNCT
ap-2092	154	1	assuming	assume	VERB
ap-2092	154	2	again	again	ADV
ap-2092	154	3	a	a	DET
ap-2092	154	4	small	small	ADJ
ap-2092	154	5	perturbation	perturbation	NOUN
ap-2092	154	6	of	of	ADP
ap-2092	154	7	the	the	DET
ap-2092	154	8	form	form	NOUN
ap-2092	154	9	(	(	PUNCT
ap-2092	154	10	3a	3a	NUM
ap-2092	154	11	)	)	PUNCT
ap-2092	154	12	and	and	CCONJ
ap-2092	154	13	(	(	PUNCT
ap-2092	154	14	3b	3b	NUM
ap-2092	154	15	)	)	PUNCT
ap-2092	154	16	a	a	DET
ap-2092	154	17	linearisation	linearisation	NOUN
ap-2092	154	18	in	in	ADP
ap-2092	154	19	u	u	NOUN
ap-2092	154	20	and	and	CCONJ
ap-2092	154	21	v	v	NOUN
ap-2092	154	22	leads	lead	VERB
ap-2092	154	23	us	we	PRON
ap-2092	154	24	to	to	PART
ap-2092	154	25	d2	d2	VERB
ap-2092	154	26	dx2u(x	dx2u(x	NOUN
ap-2092	154	27	)	)	PUNCT
ap-2092	155	1	=	=	SYM
ap-2092	155	2	[	[	PUNCT
ap-2092	155	3	−(1	−(1	NOUN
ap-2092	155	4	+	+	CCONJ
ap-2092	156	1	iγ)δ(x+	iγ)δ(x+	PROPN
ap-2092	156	2	b)−	b)−	PROPN
ap-2092	156	3	(	(	PUNCT
ap-2092	156	4	1−	1−	NUM
ap-2092	156	5	iγ)δ(x−	iγ)δ(x−	PROPN
ap-2092	156	6	b	b	PROPN
ap-2092	156	7	)	)	PUNCT
ap-2092	156	8	+	+	NUM
ap-2092	156	9	κ2	κ2	NOUN
ap-2092	156	10	−	−	PROPN
ap-2092	156	11	ω	ω	PROPN
ap-2092	156	12	+	+	CCONJ
ap-2092	156	13	2	2	NUM
ap-2092	156	14	g	g	NOUN
ap-2092	156	15	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	156	16	)	)	PUNCT
ap-2092	156	17	∣∣2]u(x	∣∣2]u(x	NOUN
ap-2092	156	18	)	)	PUNCT
ap-2092	156	19	+	+	CCONJ
ap-2092	156	20	gψ0(x)2v(x	gψ0(x)2v(x	NOUN
ap-2092	156	21	)	)	PUNCT
ap-2092	156	22	−	−	ADP
ap-2092	156	23	g	g	PROPN
ap-2092	156	24	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	156	25	)	)	PUNCT
ap-2092	156	26	∣∣2ψ0(x)s	∣∣2ψ0(x)s	NOUN
ap-2092	156	27	,	,	PUNCT
ap-2092	156	28	(	(	PUNCT
ap-2092	156	29	7a	7a	X
ap-2092	156	30	)	)	PUNCT
ap-2092	156	31	d2	d2	PROPN
ap-2092	156	32	dx2	dx2	PROPN
ap-2092	156	33	v(x	v(x	PROPN
ap-2092	156	34	)	)	PUNCT
ap-2092	156	35	=	=	NOUN
ap-2092	157	1	[	[	PUNCT
ap-2092	157	2	−(1−	−(1−	X
ap-2092	157	3	iγ)δ(x+	iγ)δ(x+	PROPN
ap-2092	157	4	b)−	b)−	PROPN
ap-2092	157	5	(	(	PUNCT
ap-2092	157	6	1	1	NUM
ap-2092	157	7	+	+	NUM
ap-2092	157	8	iγ)δ(x−	iγ)δ(x−	PROPN
ap-2092	157	9	b	b	PROPN
ap-2092	157	10	)	)	PUNCT
ap-2092	157	11	+	+	CCONJ
ap-2092	157	12	(	(	PUNCT
ap-2092	157	13	κ2)∗	κ2)∗	NOUN
ap-2092	157	14	+	+	PROPN
ap-2092	157	15	ω	ω	NUM
ap-2092	157	16	+	+	NOUN
ap-2092	157	17	2	2	NUM
ap-2092	157	18	g	g	NOUN
ap-2092	157	19	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	157	20	)	)	PUNCT
ap-2092	157	21	∣∣2]v(x	∣∣2]v(x	NUM
ap-2092	157	22	)	)	PUNCT
ap-2092	158	1	+	+	CCONJ
ap-2092	158	2	gψ∗0(x)2u(x	gψ∗0(x)2u(x	NOUN
ap-2092	158	3	)	)	PUNCT
ap-2092	158	4	−	−	PROPN
ap-2092	158	5	g	g	PROPN
ap-2092	158	6	∣∣ψ0(x	∣∣ψ0(x	NOUN
ap-2092	158	7	)	)	PUNCT
ap-2092	158	8	∣∣2ψ∗0(x)s	∣∣2ψ∗0(x)s	PROPN
ap-2092	158	9	(	(	PUNCT
ap-2092	158	10	7b	7b	NUM
ap-2092	158	11	)	)	PUNCT
ap-2092	158	12	with	with	ADP
ap-2092	158	13	the	the	DET
ap-2092	158	14	integral	integral	ADJ
ap-2092	158	15	s	s	X
ap-2092	158	16	=	=	X
ap-2092	158	17	∫	∫	PROPN
ap-2092	158	18	[	[	PUNCT
ap-2092	158	19	v(x)ψ0(x	v(x)ψ0(x	NOUN
ap-2092	158	20	)	)	PUNCT
ap-2092	159	1	+	+	CCONJ
ap-2092	159	2	u(x)ψ∗0(x	u(x)ψ∗0(x	PROPN
ap-2092	159	3	)	)	PUNCT
ap-2092	159	4	]	]	PUNCT
ap-2092	160	1	dx	dx	PROPN
ap-2092	160	2	.	.	PUNCT
ap-2092	160	3	(	(	PUNCT
ap-2092	160	4	7c	7c	PROPN
ap-2092	160	5	)	)	PUNCT
ap-2092	160	6	for	for	ADP
ap-2092	160	7	a	a	DET
ap-2092	160	8	numerical	numerical	ADJ
ap-2092	160	9	solution	solution	NOUN
ap-2092	160	10	of	of	ADP
ap-2092	160	11	the	the	DET
ap-2092	160	12	modified	modify	VERB
ap-2092	160	13	bogoliubovde	bogoliubovde	NOUN
ap-2092	160	14	gennes	genne	NOUN
ap-2092	160	15	equations	equation	VERB
ap-2092	160	16	the	the	DET
ap-2092	160	17	value	value	NOUN
ap-2092	160	18	of	of	ADP
ap-2092	160	19	s	s	NOUN
ap-2092	160	20	is	be	AUX
ap-2092	160	21	included	include	VERB
ap-2092	160	22	in	in	ADP
ap-2092	160	23	the	the	DET
ap-2092	160	24	root	root	NOUN
ap-2092	160	25	search	search	NOUN
ap-2092	160	26	,	,	PUNCT
ap-2092	160	27	i.e.	i.e.	X
ap-2092	160	28	for	for	ADP
ap-2092	160	29	the	the	DET
ap-2092	160	30	integration	integration	NOUN
ap-2092	160	31	of	of	ADP
ap-2092	160	32	equations	equation	NOUN
ap-2092	160	33	(	(	PUNCT
ap-2092	160	34	7a	7a	NUM
ap-2092	160	35	)	)	PUNCT
ap-2092	160	36	and	and	CCONJ
ap-2092	160	37	(	(	PUNCT
ap-2092	160	38	7c	7c	NUM
ap-2092	160	39	)	)	PUNCT
ap-2092	160	40	a	a	DET
ap-2092	160	41	value	value	NOUN
ap-2092	160	42	for	for	ADP
ap-2092	160	43	s	s	PROPN
ap-2092	160	44	is	be	AUX
ap-2092	160	45	guessed	guess	VERB
ap-2092	160	46	and	and	CCONJ
ap-2092	160	47	subsequently	subsequently	ADV
ap-2092	160	48	compared	compare	VERB
ap-2092	160	49	with	with	ADP
ap-2092	160	50	the	the	DET
ap-2092	160	51	result	result	NOUN
ap-2092	160	52	of	of	ADP
ap-2092	160	53	equation	equation	NOUN
ap-2092	160	54	(	(	PUNCT
ap-2092	160	55	7c	7c	PROPN
ap-2092	160	56	)	)	PUNCT
ap-2092	160	57	.	.	PUNCT
ap-2092	161	1	since	since	SCONJ
ap-2092	161	2	s	s	NOUN
ap-2092	161	3	is	be	AUX
ap-2092	161	4	in	in	ADP
ap-2092	161	5	general	general	ADJ
ap-2092	161	6	a	a	DET
ap-2092	161	7	complex	complex	ADJ
ap-2092	161	8	value	value	NOUN
ap-2092	161	9	this	this	PRON
ap-2092	161	10	increases	increase	VERB
ap-2092	161	11	the	the	DET
ap-2092	161	12	dimension	dimension	NOUN
ap-2092	161	13	of	of	ADP
ap-2092	161	14	the	the	DET
ap-2092	161	15	root	root	NOUN
ap-2092	161	16	search	search	NOUN
ap-2092	161	17	to	to	ADP
ap-2092	161	18	11	11	NUM
ap-2092	161	19	.	.	PUNCT
ap-2092	162	1	an	an	DET
ap-2092	162	2	example	example	NOUN
ap-2092	162	3	for	for	ADP
ap-2092	162	4	a	a	DET
ap-2092	162	5	typical	typical	ADJ
ap-2092	162	6	result	result	NOUN
ap-2092	162	7	is	be	AUX
ap-2092	162	8	shown	show	VERB
ap-2092	162	9	in	in	ADP
ap-2092	162	10	figure	figure	NOUN
ap-2092	162	11	4	4	NUM
ap-2092	162	12	.	.	PUNCT
ap-2092	163	1	the	the	DET
ap-2092	163	2	discrepancy	discrepancy	NOUN
ap-2092	163	3	between	between	ADP
ap-2092	163	4	the	the	DET
ap-2092	163	5	γ	γ	PROPN
ap-2092	163	6	values	value	NOUN
ap-2092	163	7	at	at	ADP
ap-2092	163	8	which	which	PRON
ap-2092	163	9	the	the	DET
ap-2092	163	10	pitchfork	pitchfork	NOUN
ap-2092	163	11	bifurcation	bifurcation	NOUN
ap-2092	163	12	and	and	CCONJ
ap-2092	163	13	the	the	DET
ap-2092	163	14	stability	stability	NOUN
ap-2092	163	15	change	change	NOUN
ap-2092	163	16	occur	occur	VERB
ap-2092	163	17	vanishes	vanish	VERB
ap-2092	163	18	.	.	PUNCT
ap-2092	164	1	the	the	DET
ap-2092	164	2	two	two	NUM
ap-2092	164	3	values	value	NOUN
ap-2092	164	4	agree	agree	VERB
ap-2092	164	5	,	,	PUNCT
ap-2092	164	6	as	as	SCONJ
ap-2092	164	7	is	be	AUX
ap-2092	164	8	expected	expect	VERB
ap-2092	164	9	for	for	ADP
ap-2092	164	10	a	a	DET
ap-2092	164	11	pitchfork	pitchfork	NOUN
ap-2092	164	12	bifurcation	bifurcation	NOUN
ap-2092	164	13	.	.	PUNCT
ap-2092	165	1	this	this	PRON
ap-2092	165	2	is	be	AUX
ap-2092	165	3	true	true	ADJ
ap-2092	165	4	for	for	ADP
ap-2092	165	5	all	all	DET
ap-2092	165	6	values	value	NOUN
ap-2092	165	7	of	of	ADP
ap-2092	165	8	g.	g.	PROPN
ap-2092	165	9	136	136	NUM
ap-2092	165	10	vol	vol	NOUN
ap-2092	165	11	.	.	PUNCT
ap-2092	166	1	54	54	NUM
ap-2092	166	2	no	no	NOUN
ap-2092	166	3	.	.	PUNCT
ap-2092	167	1	2/2014	2/2014	NUM
ap-2092	167	2	stability	stability	NOUN
ap-2092	167	3	of	of	ADP
ap-2092	167	4	becs	becs	PROPN
ap-2092	167	5	in	in	ADP
ap-2092	167	6	a	a	DET
ap-2092	167	7	pt	pt	ADJ
ap-2092	167	8	-	-	ADJ
ap-2092	167	9	symmetric	symmetric	ADJ
ap-2092	167	10	double	double	ADJ
ap-2092	167	11	-	-	PUNCT
ap-2092	167	12	δ	δ	NOUN
ap-2092	167	13	potential	potential	NOUN
ap-2092	167	14	0	0	NUM
ap-2092	167	15	0.1	0.1	NUM
ap-2092	167	16	0.2	0.2	NUM
ap-2092	167	17	0.3	0.3	NUM
ap-2092	167	18	0.4	0.4	NUM
ap-2092	167	19	0.5	0.5	NUM
ap-2092	167	20	0.6	0.6	NUM
ap-2092	167	21	0.7	0.7	NUM
ap-2092	168	1	0.8	0.8	NUM
ap-2092	168	2	0	0	NUM
ap-2092	168	3	0.05	0.05	NUM
ap-2092	168	4	0.1	0.1	NUM
ap-2092	168	5	0.15	0.15	NUM
ap-2092	168	6	0.2	0.2	NUM
ap-2092	168	7	0.25	0.25	NUM
ap-2092	168	8	0.3	0.3	NUM
ap-2092	168	9	0.35	0.35	NUM
ap-2092	168	10	0.4	0.4	NUM
ap-2092	168	11	κ	κ	NOUN
ap-2092	168	12	,	,	PUNCT
ap-2092	168	13	ω	ω	PROPN
ap-2092	168	14	γ	γ	X
ap-2092	168	15	γ	γ	X
ap-2092	168	16	κ	κ	NOUN
ap-2092	168	17	=	=	SYM
ap-2092	168	18	γ	γ	X
ap-2092	168	19	ω	ω	PROPN
ap-2092	168	20	re(ω	re(ω	X
ap-2092	168	21	)	)	PUNCT
ap-2092	168	22	im(ω	im(ω	PROPN
ap-2092	168	23	)	)	PUNCT
ap-2092	168	24	re(κ	re(κ	X
ap-2092	168	25	)	)	PUNCT
ap-2092	168	26	figure	figure	NOUN
ap-2092	168	27	4	4	NUM
ap-2092	168	28	.	.	PUNCT
ap-2092	169	1	the	the	DET
ap-2092	169	2	same	same	ADJ
ap-2092	169	3	as	as	ADP
ap-2092	169	4	in	in	ADP
ap-2092	169	5	figure	figure	NOUN
ap-2092	169	6	2	2	NUM
ap-2092	169	7	but	but	CCONJ
ap-2092	169	8	for	for	ADP
ap-2092	169	9	the	the	DET
ap-2092	169	10	modified	modify	VERB
ap-2092	169	11	bogoliubov	bogoliubov	PROPN
ap-2092	169	12	-	-	PUNCT
ap-2092	169	13	de	de	X
ap-2092	169	14	gennes	genne	NOUN
ap-2092	169	15	equations	equation	NOUN
ap-2092	169	16	(	(	PUNCT
ap-2092	169	17	7a)-(7c	7a)-(7c	NUM
ap-2092	169	18	)	)	PUNCT
ap-2092	169	19	.	.	PUNCT
ap-2092	170	1	now	now	ADV
ap-2092	170	2	the	the	DET
ap-2092	170	3	γ	γ	PROPN
ap-2092	170	4	values	value	NOUN
ap-2092	170	5	at	at	ADP
ap-2092	170	6	which	which	PRON
ap-2092	170	7	the	the	DET
ap-2092	170	8	pitchfork	pitchfork	NOUN
ap-2092	170	9	bifurcation	bifurcation	NOUN
ap-2092	170	10	and	and	CCONJ
ap-2092	170	11	the	the	DET
ap-2092	170	12	stability	stability	NOUN
ap-2092	170	13	change	change	NOUN
ap-2092	170	14	occur	occur	VERB
ap-2092	170	15	are	be	AUX
ap-2092	170	16	in	in	ADP
ap-2092	170	17	perfect	perfect	ADJ
ap-2092	170	18	agreement	agreement	NOUN
ap-2092	170	19	.	.	PUNCT
ap-2092	171	1	thus	thus	ADV
ap-2092	171	2	,	,	PUNCT
ap-2092	171	3	we	we	PRON
ap-2092	171	4	conclude	conclude	VERB
ap-2092	171	5	that	that	SCONJ
ap-2092	171	6	the	the	DET
ap-2092	171	7	discrepancy	discrepancy	NOUN
ap-2092	171	8	appearing	appear	VERB
ap-2092	171	9	in	in	ADP
ap-2092	171	10	figure	figure	NOUN
ap-2092	171	11	2	2	NUM
ap-2092	171	12	for	for	ADP
ap-2092	171	13	the	the	DET
ap-2092	171	14	gross	gross	ADJ
ap-2092	171	15	-	-	PUNCT
ap-2092	171	16	pitaevskii	pitaevskii	ADJ
ap-2092	171	17	equation	equation	NOUN
ap-2092	171	18	is	be	AUX
ap-2092	171	19	solely	solely	ADV
ap-2092	171	20	a	a	DET
ap-2092	171	21	result	result	NOUN
ap-2092	171	22	of	of	ADP
ap-2092	171	23	the	the	DET
ap-2092	171	24	norm	norm	NOUN
ap-2092	171	25	-	-	PUNCT
ap-2092	171	26	dependent	dependent	ADJ
ap-2092	171	27	nonlinearity	nonlinearity	NOUN
ap-2092	171	28	∝	∝	PROPN
ap-2092	171	29	|ψ|2	|ψ|2	PROPN
ap-2092	171	30	in	in	ADP
ap-2092	171	31	the	the	DET
ap-2092	171	32	hamiltonian	hamiltonian	NOUN
ap-2092	171	33	and	and	CCONJ
ap-2092	171	34	is	be	AUX
ap-2092	171	35	not	not	PART
ap-2092	171	36	a	a	DET
ap-2092	171	37	consequence	consequence	NOUN
ap-2092	171	38	of	of	ADP
ap-2092	171	39	the	the	DET
ap-2092	171	40	interaction	interaction	NOUN
ap-2092	171	41	with	with	ADP
ap-2092	171	42	higher	high	ADJ
ap-2092	171	43	excited	excited	ADJ
ap-2092	171	44	states	state	NOUN
ap-2092	171	45	.	.	PUNCT
ap-2092	172	1	3.3	3.3	NUM
ap-2092	172	2	.	.	PUNCT
ap-2092	172	3	discussion	discussion	NOUN
ap-2092	172	4	the	the	DET
ap-2092	172	5	reason	reason	NOUN
ap-2092	172	6	why	why	SCONJ
ap-2092	172	7	the	the	DET
ap-2092	172	8	stability	stability	NOUN
ap-2092	172	9	change	change	NOUN
ap-2092	172	10	does	do	AUX
ap-2092	172	11	not	not	PART
ap-2092	172	12	occur	occur	VERB
ap-2092	172	13	exactly	exactly	ADV
ap-2092	172	14	at	at	ADP
ap-2092	172	15	the	the	DET
ap-2092	172	16	bifurcation	bifurcation	NOUN
ap-2092	172	17	can	can	AUX
ap-2092	172	18	also	also	ADV
ap-2092	172	19	be	be	AUX
ap-2092	172	20	understood	understand	VERB
ap-2092	172	21	intuitively	intuitively	ADV
ap-2092	172	22	.	.	PUNCT
ap-2092	173	1	figure	figure	NOUN
ap-2092	173	2	1	1	NUM
ap-2092	173	3	indicates	indicate	VERB
ap-2092	173	4	that	that	SCONJ
ap-2092	173	5	the	the	DET
ap-2092	173	6	values	value	NOUN
ap-2092	173	7	γκ	γκ	ADJ
ap-2092	173	8	of	of	ADP
ap-2092	173	9	the	the	DET
ap-2092	173	10	pitchfork	pitchfork	NOUN
ap-2092	173	11	bifurcation	bifurcation	NOUN
ap-2092	173	12	are	be	AUX
ap-2092	173	13	not	not	PART
ap-2092	173	14	equal	equal	ADJ
ap-2092	173	15	for	for	ADP
ap-2092	173	16	all	all	DET
ap-2092	173	17	values	value	NOUN
ap-2092	173	18	of	of	ADP
ap-2092	173	19	g.	g.	NOUN
ap-2092	173	20	for	for	ADP
ap-2092	173	21	g	g	PROPN
ap-2092	173	22	=	=	SYM
ap-2092	173	23	0	0	NUM
ap-2092	174	1	there	there	PRON
ap-2092	174	2	is	be	VERB
ap-2092	174	3	no	no	DET
ap-2092	174	4	pitchfork	pitchfork	NOUN
ap-2092	174	5	bifurcation	bifurcation	NOUN
ap-2092	174	6	.	.	PUNCT
ap-2092	175	1	the	the	DET
ap-2092	175	2	two	two	NUM
ap-2092	175	3	real	real	ADJ
ap-2092	175	4	eigenvalues	eigenvalue	NOUN
ap-2092	175	5	κ	κ	NOUN
ap-2092	175	6	vanish	vanish	NOUN
ap-2092	175	7	in	in	ADP
ap-2092	175	8	a	a	DET
ap-2092	175	9	tangent	tangent	ADJ
ap-2092	175	10	bifurcation	bifurcation	NOUN
ap-2092	175	11	and	and	CCONJ
ap-2092	175	12	two	two	NUM
ap-2092	175	13	complex	complex	ADJ
ap-2092	175	14	eigenvalues	eigenvalue	NOUN
ap-2092	175	15	emerge	emerge	VERB
ap-2092	175	16	.	.	PUNCT
ap-2092	176	1	only	only	ADV
ap-2092	176	2	for	for	ADP
ap-2092	176	3	nonvanishing	nonvanishe	VERB
ap-2092	176	4	g	g	ADP
ap-2092	176	5	the	the	DET
ap-2092	176	6	pitchfork	pitchfork	NOUN
ap-2092	176	7	bifurcation	bifurcation	NOUN
ap-2092	176	8	exists	exist	VERB
ap-2092	176	9	and	and	CCONJ
ap-2092	176	10	moves	move	NOUN
ap-2092	176	11	to	to	ADP
ap-2092	176	12	smaller	small	ADJ
ap-2092	176	13	values	value	NOUN
ap-2092	176	14	of	of	ADP
ap-2092	176	15	γ	γ	NOUN
ap-2092	176	16	for	for	ADP
ap-2092	176	17	increasing	increase	VERB
ap-2092	176	18	|g|	|g|	ADJ
ap-2092	176	19	.	.	PUNCT
ap-2092	177	1	if	if	SCONJ
ap-2092	177	2	now	now	ADV
ap-2092	177	3	the	the	DET
ap-2092	177	4	norm	norm	NOUN
ap-2092	177	5	of	of	ADP
ap-2092	177	6	a	a	DET
ap-2092	177	7	wave	wave	NOUN
ap-2092	177	8	function	function	NOUN
ap-2092	177	9	changes	change	NOUN
ap-2092	177	10	,	,	PUNCT
ap-2092	177	11	this	this	PRON
ap-2092	177	12	can	can	AUX
ap-2092	177	13	also	also	ADV
ap-2092	177	14	be	be	AUX
ap-2092	177	15	understood	understand	VERB
ap-2092	177	16	as	as	ADP
ap-2092	177	17	a	a	DET
ap-2092	177	18	variation	variation	NOUN
ap-2092	177	19	of	of	ADP
ap-2092	177	20	g	g	NOUN
ap-2092	177	21	,	,	PUNCT
ap-2092	177	22	i.e.	i.e.	X
ap-2092	177	23	a	a	DET
ap-2092	177	24	wave	wave	NOUN
ap-2092	177	25	function	function	NOUN
ap-2092	177	26	with	with	ADP
ap-2092	177	27	a	a	DET
ap-2092	177	28	norm	norm	NOUN
ap-2092	177	29	n	n	NOUN
ap-2092	177	30	=	=	PRON
ap-2092	177	31	||ψ||2	||ψ||2	NOUN
ap-2092	177	32	has	have	VERB
ap-2092	177	33	the	the	DET
ap-2092	177	34	same	same	ADJ
ap-2092	177	35	effect	effect	NOUN
ap-2092	177	36	as	as	ADP
ap-2092	177	37	a	a	DET
ap-2092	177	38	wave	wave	NOUN
ap-2092	177	39	function	function	NOUN
ap-2092	177	40	with	with	ADP
ap-2092	177	41	the	the	DET
ap-2092	177	42	norm	norm	NOUN
ap-2092	177	43	1	1	NUM
ap-2092	177	44	and	and	CCONJ
ap-2092	177	45	a	a	DET
ap-2092	177	46	modified	modify	VERB
ap-2092	177	47	value	value	NOUN
ap-2092	177	48	g̃	g̃	PROPN
ap-2092	177	49	=	=	SYM
ap-2092	177	50	ng	ng	PROPN
ap-2092	177	51	.	.	PUNCT
ap-2092	178	1	the	the	DET
ap-2092	178	2	values	value	NOUN
ap-2092	178	3	γκ	γκ	ADJ
ap-2092	178	4	of	of	ADP
ap-2092	178	5	the	the	DET
ap-2092	178	6	pitchfork	pitchfork	NOUN
ap-2092	178	7	bifurcation	bifurcation	NOUN
ap-2092	178	8	are	be	AUX
ap-2092	178	9	obviously	obviously	ADV
ap-2092	178	10	different	different	ADJ
ap-2092	178	11	for	for	ADP
ap-2092	178	12	g	g	NOUN
ap-2092	178	13	and	and	CCONJ
ap-2092	178	14	g̃.	g̃.	PROPN
ap-2092	178	15	with	with	ADP
ap-2092	178	16	this	this	DET
ap-2092	178	17	relation	relation	NOUN
ap-2092	178	18	in	in	ADP
ap-2092	178	19	mind	mind	NOUN
ap-2092	178	20	it	it	PRON
ap-2092	178	21	is	be	AUX
ap-2092	178	22	not	not	PART
ap-2092	178	23	surprising	surprising	ADJ
ap-2092	178	24	that	that	SCONJ
ap-2092	178	25	a	a	DET
ap-2092	178	26	fluctuation	fluctuation	NOUN
ap-2092	178	27	changing	change	VERB
ap-2092	178	28	the	the	DET
ap-2092	178	29	norm	norm	NOUN
ap-2092	178	30	of	of	ADP
ap-2092	178	31	the	the	DET
ap-2092	178	32	wave	wave	NOUN
ap-2092	178	33	function	function	NOUN
ap-2092	178	34	may	may	AUX
ap-2092	178	35	cause	cause	VERB
ap-2092	178	36	a	a	DET
ap-2092	178	37	qualitative	qualitative	ADJ
ap-2092	178	38	change	change	NOUN
ap-2092	178	39	of	of	ADP
ap-2092	178	40	the	the	DET
ap-2092	178	41	condensate	condensate	NOUN
ap-2092	178	42	’s	’s	PART
ap-2092	178	43	stability	stability	NOUN
ap-2092	178	44	properties	property	NOUN
ap-2092	178	45	in	in	ADP
ap-2092	178	46	the	the	DET
ap-2092	178	47	vicinity	vicinity	NOUN
ap-2092	178	48	of	of	ADP
ap-2092	178	49	γκ	γκ	PROPN
ap-2092	178	50	.	.	NOUN
ap-2092	178	51	4	4	NUM
ap-2092	178	52	.	.	PUNCT
ap-2092	179	1	conclusions	conclusion	NOUN
ap-2092	179	2	we	we	PRON
ap-2092	179	3	investigated	investigate	VERB
ap-2092	179	4	the	the	DET
ap-2092	179	5	origin	origin	NOUN
ap-2092	179	6	of	of	ADP
ap-2092	179	7	the	the	DET
ap-2092	179	8	discrepancy	discrepancy	NOUN
ap-2092	179	9	between	between	ADP
ap-2092	179	10	the	the	DET
ap-2092	179	11	value	value	NOUN
ap-2092	179	12	of	of	ADP
ap-2092	179	13	the	the	DET
ap-2092	179	14	gain	gain	NOUN
ap-2092	179	15	/	/	SYM
ap-2092	179	16	loss	loss	NOUN
ap-2092	179	17	parameters	parameter	NOUN
ap-2092	179	18	at	at	ADP
ap-2092	179	19	which	which	PRON
ap-2092	179	20	the	the	DET
ap-2092	179	21	ground	ground	NOUN
ap-2092	179	22	state	state	NOUN
ap-2092	179	23	of	of	ADP
ap-2092	179	24	a	a	DET
ap-2092	179	25	bose	bose	NOUN
ap-2092	179	26	-	-	PUNCT
ap-2092	179	27	einstein	einstein	NOUN
ap-2092	179	28	condensate	condensate	NOUN
ap-2092	179	29	in	in	ADP
ap-2092	179	30	a	a	DET
ap-2092	179	31	doublewell	doublewell	NOUN
ap-2092	179	32	trap	trap	NOUN
ap-2092	179	33	passes	pass	VERB
ap-2092	179	34	through	through	ADP
ap-2092	179	35	a	a	DET
ap-2092	179	36	pitchfork	pitchfork	NOUN
ap-2092	179	37	bifurcation	bifurcation	NOUN
ap-2092	179	38	and	and	CCONJ
ap-2092	179	39	at	at	ADP
ap-2092	179	40	which	which	PRON
ap-2092	179	41	its	its	PRON
ap-2092	179	42	stability	stability	NOUN
ap-2092	179	43	changes	change	NOUN
ap-2092	179	44	.	.	PUNCT
ap-2092	180	1	in	in	ADP
ap-2092	180	2	a	a	DET
ap-2092	180	3	naive	naive	ADJ
ap-2092	180	4	expectation	expectation	NOUN
ap-2092	180	5	these	these	DET
ap-2092	180	6	γ	γ	PROPN
ap-2092	180	7	values	value	NOUN
ap-2092	180	8	should	should	AUX
ap-2092	180	9	be	be	AUX
ap-2092	180	10	identical	identical	ADJ
ap-2092	180	11	.	.	PUNCT
ap-2092	181	1	however	however	ADV
ap-2092	181	2	,	,	PUNCT
ap-2092	181	3	it	it	PRON
ap-2092	181	4	is	be	AUX
ap-2092	181	5	found	find	VERB
ap-2092	181	6	that	that	SCONJ
ap-2092	181	7	this	this	PRON
ap-2092	181	8	is	be	AUX
ap-2092	181	9	not	not	PART
ap-2092	181	10	exactly	exactly	ADV
ap-2092	181	11	fulfilled	fulfil	VERB
ap-2092	181	12	.	.	PUNCT
ap-2092	182	1	since	since	SCONJ
ap-2092	182	2	this	this	DET
ap-2092	182	3	discrepancy	discrepancy	NOUN
ap-2092	182	4	does	do	AUX
ap-2092	182	5	not	not	PART
ap-2092	182	6	occur	occur	VERB
ap-2092	182	7	for	for	ADP
ap-2092	182	8	a	a	DET
ap-2092	182	9	similar	similar	ADJ
ap-2092	182	10	system	system	NOUN
ap-2092	182	11	,	,	PUNCT
ap-2092	182	12	viz	viz	PROPN
ap-2092	182	13	.	.	PUNCT
ap-2092	183	1	the	the	DET
ap-2092	183	2	mean	mean	ADJ
ap-2092	183	3	-	-	PUNCT
ap-2092	183	4	field	field	NOUN
ap-2092	183	5	limit	limit	NOUN
ap-2092	183	6	of	of	ADP
ap-2092	183	7	a	a	DET
ap-2092	183	8	bose	bose	NOUN
ap-2092	183	9	-	-	PUNCT
ap-2092	183	10	hubbard	hubbard	NOUN
ap-2092	183	11	dimer	dimer	NOUN
ap-2092	184	1	[	[	X
ap-2092	184	2	14–17	14–17	NUM
ap-2092	184	3	]	]	PUNCT
ap-2092	184	4	,	,	PUNCT
ap-2092	184	5	we	we	PRON
ap-2092	184	6	investigated	investigate	VERB
ap-2092	184	7	the	the	DET
ap-2092	184	8	differences	difference	NOUN
ap-2092	184	9	between	between	ADP
ap-2092	184	10	the	the	DET
ap-2092	184	11	equations	equation	NOUN
ap-2092	184	12	describing	describe	VERB
ap-2092	184	13	the	the	DET
ap-2092	184	14	two	two	NUM
ap-2092	184	15	systems	system	NOUN
ap-2092	184	16	.	.	PUNCT
ap-2092	185	1	it	it	PRON
ap-2092	185	2	was	be	AUX
ap-2092	185	3	found	find	VERB
ap-2092	185	4	that	that	SCONJ
ap-2092	185	5	the	the	DET
ap-2092	185	6	norm	norm	NOUN
ap-2092	185	7	-	-	PUNCT
ap-2092	185	8	dependency	dependency	NOUN
ap-2092	185	9	of	of	ADP
ap-2092	185	10	the	the	DET
ap-2092	185	11	nonlinearity	nonlinearity	NOUN
ap-2092	185	12	in	in	ADP
ap-2092	185	13	the	the	DET
ap-2092	185	14	hamiltonian	hamiltonian	ADJ
ap-2092	185	15	∝	∝	PROPN
ap-2092	185	16	|ψ|2	|ψ|2	PROPN
ap-2092	185	17	is	be	AUX
ap-2092	185	18	unambiguously	unambiguously	ADV
ap-2092	185	19	the	the	DET
ap-2092	185	20	origin	origin	NOUN
ap-2092	185	21	of	of	ADP
ap-2092	185	22	the	the	DET
ap-2092	185	23	discrepancy	discrepancy	NOUN
ap-2092	185	24	.	.	PUNCT
ap-2092	186	1	it	it	PRON
ap-2092	186	2	can	can	AUX
ap-2092	186	3	be	be	AUX
ap-2092	186	4	completely	completely	ADV
ap-2092	186	5	removed	remove	VERB
ap-2092	186	6	with	with	ADP
ap-2092	186	7	the	the	DET
ap-2092	186	8	replacement	replacement	NOUN
ap-2092	186	9	|ψ|2	|ψ|2	PROPN
ap-2092	186	10	→	→	SYM
ap-2092	186	11	|ψ|2/||ψ||2	|ψ|2/||ψ||2	PROPN
ap-2092	186	12	.	.	PUNCT
ap-2092	187	1	an	an	DET
ap-2092	187	2	intuitive	intuitive	ADJ
ap-2092	187	3	explanation	explanation	NOUN
ap-2092	187	4	can	can	AUX
ap-2092	187	5	be	be	AUX
ap-2092	187	6	given	give	VERB
ap-2092	187	7	.	.	PUNCT
ap-2092	188	1	fluctuations	fluctuation	NOUN
ap-2092	188	2	which	which	PRON
ap-2092	188	3	change	change	VERB
ap-2092	188	4	the	the	DET
ap-2092	188	5	norm	norm	NOUN
ap-2092	188	6	of	of	ADP
ap-2092	188	7	a	a	DET
ap-2092	188	8	stationary	stationary	ADJ
ap-2092	188	9	state	state	NOUN
ap-2092	188	10	are	be	AUX
ap-2092	188	11	able	able	ADJ
ap-2092	188	12	to	to	PART
ap-2092	188	13	shift	shift	VERB
ap-2092	188	14	the	the	DET
ap-2092	188	15	position	position	NOUN
ap-2092	188	16	γκ	γκ	ADJ
ap-2092	188	17	of	of	ADP
ap-2092	188	18	the	the	DET
ap-2092	188	19	bifurcation	bifurcation	NOUN
ap-2092	188	20	.	.	PUNCT
ap-2092	189	1	since	since	SCONJ
ap-2092	189	2	the	the	DET
ap-2092	189	3	dynamical	dynamical	ADJ
ap-2092	189	4	properties	property	NOUN
ap-2092	189	5	of	of	ADP
ap-2092	189	6	the	the	DET
ap-2092	189	7	wave	wave	NOUN
ap-2092	189	8	functions	function	NOUN
ap-2092	189	9	are	be	AUX
ap-2092	189	10	crucial	crucial	ADJ
ap-2092	189	11	for	for	ADP
ap-2092	189	12	the	the	DET
ap-2092	189	13	experimental	experimental	ADJ
ap-2092	189	14	observability	observability	NOUN
ap-2092	189	15	of	of	ADP
ap-2092	189	16	a	a	DET
ap-2092	189	17	pt	pt	X
ap-2092	189	18	symmetric	symmetric	ADJ
ap-2092	189	19	bose	bose	PROPN
ap-2092	189	20	-	-	PUNCT
ap-2092	189	21	einstein	einstein	NOUN
ap-2092	189	22	condensate	condensate	NOUN
ap-2092	189	23	it	it	PRON
ap-2092	189	24	is	be	AUX
ap-2092	189	25	important	important	ADJ
ap-2092	189	26	to	to	PART
ap-2092	189	27	know	know	VERB
ap-2092	189	28	about	about	ADP
ap-2092	189	29	all	all	DET
ap-2092	189	30	processes	process	NOUN
ap-2092	189	31	introducing	introduce	VERB
ap-2092	189	32	possible	possible	ADJ
ap-2092	189	33	instabilities	instability	NOUN
ap-2092	189	34	.	.	PUNCT
ap-2092	190	1	as	as	SCONJ
ap-2092	190	2	has	have	AUX
ap-2092	190	3	been	be	AUX
ap-2092	190	4	shown	show	VERB
ap-2092	190	5	in	in	ADP
ap-2092	190	6	this	this	DET
ap-2092	190	7	article	article	NOUN
ap-2092	190	8	the	the	DET
ap-2092	190	9	stability	stability	NOUN
ap-2092	190	10	relations	relation	NOUN
ap-2092	190	11	are	be	AUX
ap-2092	190	12	nontrivial	nontrivial	ADJ
ap-2092	190	13	close	close	ADV
ap-2092	190	14	to	to	ADP
ap-2092	190	15	branch	branch	NOUN
ap-2092	190	16	points	point	NOUN
ap-2092	190	17	in	in	ADP
ap-2092	190	18	condensate	condensate	NOUN
ap-2092	190	19	setups	setup	NOUN
ap-2092	190	20	with	with	ADP
ap-2092	190	21	gain	gain	NOUN
ap-2092	190	22	and	and	CCONJ
ap-2092	190	23	loss	loss	NOUN
ap-2092	190	24	.	.	PUNCT
ap-2092	191	1	the	the	DET
ap-2092	191	2	gross	gross	ADJ
ap-2092	191	3	-	-	PUNCT
ap-2092	191	4	pitaevskii	pitaevskii	PROPN
ap-2092	191	5	has	have	VERB
ap-2092	191	6	a	a	DET
ap-2092	191	7	norm	norm	NOUN
ap-2092	191	8	-	-	PUNCT
ap-2092	191	9	dependent	dependent	ADJ
ap-2092	191	10	nonlinearity	nonlinearity	NOUN
ap-2092	191	11	,	,	PUNCT
ap-2092	191	12	and	and	CCONJ
ap-2092	191	13	therefore	therefore	ADV
ap-2092	191	14	it	it	PRON
ap-2092	191	15	should	should	AUX
ap-2092	191	16	be	be	AUX
ap-2092	191	17	clarified	clarify	VERB
ap-2092	191	18	in	in	ADP
ap-2092	191	19	future	future	ADJ
ap-2092	191	20	work	work	NOUN
ap-2092	191	21	which	which	DET
ap-2092	191	22	type	type	NOUN
ap-2092	191	23	of	of	ADP
ap-2092	191	24	fluctuation	fluctuation	NOUN
ap-2092	191	25	influences	influence	VERB
ap-2092	191	26	the	the	DET
ap-2092	191	27	wave	wave	NOUN
ap-2092	191	28	function	function	NOUN
ap-2092	191	29	’s	’s	PART
ap-2092	191	30	norm	norm	NOUN
ap-2092	191	31	such	such	ADJ
ap-2092	191	32	that	that	SCONJ
ap-2092	191	33	additional	additional	ADJ
ap-2092	191	34	instabilities	instability	NOUN
ap-2092	191	35	appear	appear	VERB
ap-2092	191	36	.	.	PUNCT
ap-2092	192	1	in	in	ADP
ap-2092	192	2	particular	particular	ADJ
ap-2092	192	3	,	,	PUNCT
ap-2092	192	4	it	it	PRON
ap-2092	192	5	would	would	AUX
ap-2092	192	6	be	be	AUX
ap-2092	192	7	interesting	interesting	ADJ
ap-2092	192	8	to	to	PART
ap-2092	192	9	see	see	VERB
ap-2092	192	10	,	,	PUNCT
ap-2092	192	11	how	how	SCONJ
ap-2092	192	12	the	the	DET
ap-2092	192	13	amplitude	amplitude	NOUN
ap-2092	192	14	of	of	ADP
ap-2092	192	15	a	a	DET
ap-2092	192	16	fluctuation	fluctuation	NOUN
ap-2092	192	17	is	be	AUX
ap-2092	192	18	related	relate	VERB
ap-2092	192	19	to	to	ADP
ap-2092	192	20	the	the	DET
ap-2092	192	21	size	size	NOUN
ap-2092	192	22	of	of	ADP
ap-2092	192	23	the	the	DET
ap-2092	192	24	difference	difference	NOUN
ap-2092	192	25	∆γ	∆γ	PROPN
ap-2092	192	26	.	.	PUNCT
ap-2092	193	1	a	a	DET
ap-2092	193	2	deeper	deep	ADJ
ap-2092	193	3	understanding	understanding	NOUN
ap-2092	193	4	of	of	ADP
ap-2092	193	5	how	how	SCONJ
ap-2092	193	6	this	this	DET
ap-2092	193	7	effect	effect	NOUN
ap-2092	193	8	influences	influence	VERB
ap-2092	193	9	realistic	realistic	ADJ
ap-2092	193	10	setups	setup	NOUN
ap-2092	193	11	generating	generate	VERB
ap-2092	193	12	the	the	DET
ap-2092	193	13	pt	pt	NOUN
ap-2092	193	14	symmetric	symmetric	ADJ
ap-2092	193	15	external	external	ADJ
ap-2092	193	16	potential	potential	NOUN
ap-2092	194	1	[	[	X
ap-2092	194	2	34	34	NUM
ap-2092	194	3	]	]	PUNCT
ap-2092	194	4	,	,	PUNCT
ap-2092	194	5	would	would	AUX
ap-2092	194	6	also	also	ADV
ap-2092	194	7	be	be	AUX
ap-2092	194	8	of	of	ADP
ap-2092	194	9	high	high	ADJ
ap-2092	194	10	value	value	NOUN
ap-2092	194	11	.	.	PUNCT
ap-2092	195	1	acknowledgements	acknowledgement	NOUN
ap-2092	195	2	we	we	PRON
ap-2092	195	3	thank	thank	VERB
ap-2092	195	4	eva	eva	PROPN
ap-2092	195	5	-	-	PUNCT
ap-2092	195	6	maria	maria	PROPN
ap-2092	195	7	graefe	graefe	NOUN
ap-2092	195	8	for	for	ADP
ap-2092	195	9	stimulating	stimulate	VERB
ap-2092	195	10	discussions	discussion	NOUN
ap-2092	195	11	.	.	PUNCT
ap-2092	196	1	references	reference	NOUN
ap-2092	196	2	[	[	X
ap-2092	196	3	1	1	NUM
ap-2092	196	4	]	]	X
ap-2092	196	5	n.	n.	PROPN
ap-2092	196	6	moiseyev	moiseyev	PROPN
ap-2092	196	7	.	.	PUNCT
ap-2092	197	1	non	non	ADJ
ap-2092	197	2	-	-	ADJ
ap-2092	197	3	hermitian	hermitian	ADJ
ap-2092	197	4	quantum	quantum	ADJ
ap-2092	197	5	mechanics	mechanic	NOUN
ap-2092	197	6	.	.	PUNCT
ap-2092	198	1	cambridge	cambridge	PROPN
ap-2092	198	2	university	university	PROPN
ap-2092	198	3	press	press	PROPN
ap-2092	198	4	,	,	PUNCT
ap-2092	198	5	cambridge	cambridge	PROPN
ap-2092	198	6	,	,	PUNCT
ap-2092	198	7	2011	2011	NUM
ap-2092	198	8	.	.	PUNCT
ap-2092	199	1	[	[	X
ap-2092	199	2	2	2	NUM
ap-2092	199	3	]	]	PUNCT
ap-2092	199	4	c.	c.	PROPN
ap-2092	199	5	m.	m.	PROPN
ap-2092	199	6	bender	bender	PROPN
ap-2092	199	7	,	,	PUNCT
ap-2092	199	8	et	et	PROPN
ap-2092	199	9	al	al	PROPN
ap-2092	199	10	.	.	PUNCT
ap-2092	200	1	real	real	ADJ
ap-2092	200	2	spectra	spectra	NOUN
ap-2092	200	3	in	in	ADP
ap-2092	200	4	non	non	ADJ
ap-2092	200	5	-	-	ADJ
ap-2092	200	6	hermitian	hermitian	ADJ
ap-2092	200	7	hamiltonians	hamiltonian	NOUN
ap-2092	200	8	having	have	VERB
ap-2092	200	9	pt	pt	PRON
ap-2092	200	10	symmetry	symmetry	NOUN
ap-2092	200	11	.	.	PUNCT
ap-2092	201	1	phys	phy	NOUN
ap-2092	201	2	rev	rev	VERB
ap-2092	201	3	lett	lett	PROPN
ap-2092	201	4	80:5243	80:5243	NUM
ap-2092	201	5	,	,	PUNCT
ap-2092	201	6	1998	1998	NUM
ap-2092	201	7	.	.	PUNCT
ap-2092	202	1	doi	doi	NOUN
ap-2092	202	2	:	:	PUNCT
ap-2092	202	3	10.1103	10.1103	NUM
ap-2092	202	4	/	/	SYM
ap-2092	202	5	physrevlett.80.5243	physrevlett.80.5243	NOUN
ap-2092	203	1	[	[	X
ap-2092	203	2	3	3	X
ap-2092	203	3	]	]	PUNCT
ap-2092	203	4	e.	e.	PROPN
ap-2092	203	5	p.	p.	PROPN
ap-2092	203	6	gross	gross	PROPN
ap-2092	203	7	.	.	PUNCT
ap-2092	203	8	structure	structure	NOUN
ap-2092	203	9	of	of	ADP
ap-2092	203	10	a	a	DET
ap-2092	203	11	quantized	quantize	VERB
ap-2092	203	12	vortex	vortex	NOUN
ap-2092	203	13	in	in	ADP
ap-2092	203	14	boson	boson	NOUN
ap-2092	203	15	systems	system	NOUN
ap-2092	203	16	.	.	PUNCT
ap-2092	204	1	nuovo	nuovo	PROPN
ap-2092	204	2	cimento	cimento	PROPN
ap-2092	204	3	20:454	20:454	NUM
ap-2092	204	4	,	,	PUNCT
ap-2092	204	5	1961	1961	NUM
ap-2092	204	6	.	.	PUNCT
ap-2092	205	1	doi	doi	NOUN
ap-2092	205	2	:	:	PUNCT
ap-2092	205	3	10.1007	10.1007	NUM
ap-2092	205	4	/	/	SYM
ap-2092	205	5	bf02731494	bf02731494	NOUN
ap-2092	206	1	[	[	X
ap-2092	206	2	4	4	NUM
ap-2092	206	3	]	]	PUNCT
ap-2092	206	4	l.	l.	PROPN
ap-2092	206	5	p.	p.	PROPN
ap-2092	206	6	pitaevskii	pitaevskii	PROPN
ap-2092	206	7	.	.	PUNCT
ap-2092	207	1	vortex	vortex	NOUN
ap-2092	207	2	lines	line	NOUN
ap-2092	207	3	in	in	ADP
ap-2092	207	4	an	an	DET
ap-2092	207	5	imperfect	imperfect	ADJ
ap-2092	207	6	bose	bose	NOUN
ap-2092	207	7	gas	gas	NOUN
ap-2092	207	8	.	.	PUNCT
ap-2092	208	1	sov	sov	PROPN
ap-2092	208	2	phys	phy	NOUN
ap-2092	208	3	jetp	jetp	VERB
ap-2092	208	4	13:451	13:451	NUM
ap-2092	208	5	,	,	PUNCT
ap-2092	208	6	1961	1961	NUM
ap-2092	208	7	.	.	PUNCT
ap-2092	209	1	[	[	X
ap-2092	209	2	5	5	X
ap-2092	209	3	]	]	PUNCT
ap-2092	209	4	s.	s.	PROPN
ap-2092	209	5	klaiman	klaiman	PROPN
ap-2092	209	6	,	,	PUNCT
ap-2092	209	7	et	et	PROPN
ap-2092	209	8	al	al	PROPN
ap-2092	209	9	.	.	PUNCT
ap-2092	209	10	visualization	visualization	NOUN
ap-2092	209	11	of	of	ADP
ap-2092	209	12	branch	branch	NOUN
ap-2092	209	13	points	point	NOUN
ap-2092	209	14	in	in	ADP
ap-2092	209	15	pt	pt	NOUN
ap-2092	209	16	-symmetric	-symmetric	ADJ
ap-2092	209	17	waveguides	waveguide	NOUN
ap-2092	209	18	.	.	PUNCT
ap-2092	210	1	phys	phy	NOUN
ap-2092	210	2	rev	rev	VERB
ap-2092	210	3	lett	lett	PROPN
ap-2092	210	4	101:080402	101:080402	PROPN
ap-2092	210	5	,	,	PUNCT
ap-2092	210	6	2008	2008	NUM
ap-2092	210	7	.	.	PUNCT
ap-2092	211	1	doi	doi	NOUN
ap-2092	211	2	:	:	PUNCT
ap-2092	211	3	10.1103	10.1103	NUM
ap-2092	211	4	/	/	SYM
ap-2092	211	5	physrevlett.101.080402	physrevlett.101.080402	X
ap-2092	211	6	[	[	X
ap-2092	211	7	6	6	NUM
ap-2092	211	8	]	]	PUNCT
ap-2092	211	9	a.	a.	NOUN
ap-2092	211	10	guo	guo	PROPN
ap-2092	211	11	,	,	PUNCT
ap-2092	211	12	et	et	PROPN
ap-2092	211	13	al	al	PROPN
ap-2092	211	14	.	.	PROPN
ap-2092	212	1	observation	observation	NOUN
ap-2092	212	2	of	of	ADP
ap-2092	212	3	pt	pt	PROPN
ap-2092	212	4	-symmetry	-symmetry	NOUN
ap-2092	212	5	breaking	break	VERB
ap-2092	212	6	in	in	ADP
ap-2092	212	7	complex	complex	ADJ
ap-2092	212	8	optical	optical	ADJ
ap-2092	212	9	potentials	potential	NOUN
ap-2092	212	10	.	.	PUNCT
ap-2092	213	1	phys	phy	NOUN
ap-2092	213	2	rev	rev	VERB
ap-2092	213	3	lett	lett	PROPN
ap-2092	213	4	103:093902	103:093902	NUM
ap-2092	213	5	,	,	PUNCT
ap-2092	213	6	2009	2009	NUM
ap-2092	213	7	.	.	PUNCT
ap-2092	214	1	doi	doi	NOUN
ap-2092	214	2	:	:	PUNCT
ap-2092	214	3	10.1103	10.1103	NUM
ap-2092	214	4	/	/	SYM
ap-2092	214	5	physrevlett.103.093902	physrevlett.103.093902	X
ap-2092	215	1	[	[	X
ap-2092	215	2	7	7	X
ap-2092	215	3	]	]	X
ap-2092	215	4	c.	c.	PROPN
ap-2092	215	5	e.	e.	PROPN
ap-2092	215	6	rüter	rüter	PROPN
ap-2092	215	7	,	,	PUNCT
ap-2092	215	8	et	et	PROPN
ap-2092	215	9	al	al	PROPN
ap-2092	215	10	.	.	PUNCT
ap-2092	215	11	observation	observation	NOUN
ap-2092	215	12	of	of	ADP
ap-2092	215	13	parity	parity	NOUN
ap-2092	215	14	-	-	PUNCT
ap-2092	215	15	time	time	NOUN
ap-2092	215	16	symmetry	symmetry	NOUN
ap-2092	215	17	in	in	ADP
ap-2092	215	18	optics	optic	NOUN
ap-2092	215	19	.	.	PUNCT
ap-2092	216	1	nat	nat	PROPN
ap-2092	216	2	phys	phy	NOUN
ap-2092	216	3	6:192	6:192	NOUN
ap-2092	216	4	,	,	PUNCT
ap-2092	216	5	2010	2010	NUM
ap-2092	216	6	.	.	PUNCT
ap-2092	217	1	doi	doi	NOUN
ap-2092	217	2	:	:	PUNCT
ap-2092	217	3	10.1038	10.1038	NUM
ap-2092	217	4	/	/	SYM
ap-2092	217	5	nphys1515	nphys1515	PROPN
ap-2092	218	1	[	[	X
ap-2092	218	2	8	8	X
ap-2092	218	3	]	]	X
ap-2092	218	4	h.	h.	NOUN
ap-2092	218	5	cartarius	cartarius	PROPN
ap-2092	218	6	,	,	PUNCT
ap-2092	218	7	et	et	PROPN
ap-2092	218	8	al	al	PROPN
ap-2092	218	9	.	.	PROPN
ap-2092	218	10	model	model	NOUN
ap-2092	218	11	of	of	ADP
ap-2092	218	12	a	a	DET
ap-2092	218	13	pt	pt	NOUN
ap-2092	218	14	-symmetric	-symmetric	NOUN
ap-2092	218	15	bose	bose	NOUN
ap-2092	218	16	-	-	PUNCT
ap-2092	218	17	einstein	einstein	NOUN
ap-2092	218	18	condensate	condensate	NOUN
ap-2092	218	19	in	in	ADP
ap-2092	218	20	a	a	DET
ap-2092	218	21	δ	δ	NOUN
ap-2092	218	22	-	-	PUNCT
ap-2092	218	23	function	function	NOUN
ap-2092	218	24	double	double	ADJ
ap-2092	218	25	-	-	PUNCT
ap-2092	218	26	well	well	NOUN
ap-2092	218	27	potential	potential	NOUN
ap-2092	218	28	.	.	PUNCT
ap-2092	219	1	phys	phy	NOUN
ap-2092	219	2	rev	rev	VERB
ap-2092	219	3	a	a	DET
ap-2092	219	4	86:013612	86:013612	NUM
ap-2092	219	5	,	,	PUNCT
ap-2092	219	6	2012	2012	NUM
ap-2092	219	7	.	.	PUNCT
ap-2092	220	1	doi	doi	NOUN
ap-2092	220	2	:	:	PUNCT
ap-2092	220	3	10.1103	10.1103	NUM
ap-2092	220	4	/	/	SYM
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ap-2092	221	1	[	[	X
ap-2092	221	2	9	9	NUM
ap-2092	221	3	]	]	X
ap-2092	221	4	h.	h.	NOUN
ap-2092	221	5	cartarius	cartarius	PROPN
ap-2092	221	6	,	,	PUNCT
ap-2092	221	7	et	et	PROPN
ap-2092	221	8	al	al	PROPN
ap-2092	221	9	.	.	PROPN
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ap-2092	222	2	schrödinger	schrödinger	ADJ
ap-2092	222	3	equation	equation	NOUN
ap-2092	222	4	for	for	ADP
ap-2092	222	5	a	a	DET
ap-2092	222	6	pt	pt	NOUN
ap-2092	222	7	-symmetric	-symmetric	ADJ
ap-2092	222	8	delta	delta	NOUN
ap-2092	222	9	-	-	PUNCT
ap-2092	222	10	function	function	NOUN
ap-2092	222	11	double	double	ADJ
ap-2092	222	12	well	well	ADV
ap-2092	222	13	.	.	PUNCT
ap-2092	223	1	j	j	PROPN
ap-2092	223	2	phys	phy	NOUN
ap-2092	223	3	a	a	DET
ap-2092	223	4	45:444008	45:444008	NOUN
ap-2092	223	5	,	,	PUNCT
ap-2092	223	6	2012	2012	NUM
ap-2092	223	7	.	.	PUNCT
ap-2092	224	1	doi	doi	NOUN
ap-2092	224	2	:	:	PUNCT
ap-2092	224	3	10.1088/1751	10.1088/1751	NUM
ap-2092	224	4	-	-	PUNCT
ap-2092	224	5	8113/45/44/444008	8113/45/44/444008	PROPN
ap-2092	225	1	[	[	X
ap-2092	225	2	10	10	NUM
ap-2092	225	3	]	]	X
ap-2092	225	4	w.	w.	PROPN
ap-2092	225	5	d.	d.	PROPN
ap-2092	225	6	heiss	heiss	PROPN
ap-2092	225	7	,	,	PUNCT
ap-2092	225	8	et	et	PROPN
ap-2092	225	9	al	al	PROPN
ap-2092	225	10	.	.	PUNCT
ap-2092	226	1	spectral	spectral	ADJ
ap-2092	226	2	singularities	singularity	NOUN
ap-2092	226	3	in	in	ADP
ap-2092	226	4	pt	pt	X
ap-2092	226	5	-symmetric	-symmetric	ADJ
ap-2092	226	6	bose	bose	NOUN
ap-2092	226	7	-	-	PUNCT
ap-2092	226	8	einstein	einstein	NOUN
ap-2092	226	9	condensates	condensate	NOUN
ap-2092	226	10	.	.	PUNCT
ap-2092	227	1	j	j	PROPN
ap-2092	227	2	phys	phy	NOUN
ap-2092	227	3	a	a	DET
ap-2092	227	4	46:275307	46:275307	NUM
ap-2092	227	5	,	,	PUNCT
ap-2092	227	6	2013	2013	NUM
ap-2092	227	7	.	.	PUNCT
ap-2092	228	1	doi	doi	NOUN
ap-2092	228	2	:	:	PUNCT
ap-2092	228	3	10.1088/1751	10.1088/1751	NUM
ap-2092	228	4	-	-	SYM
ap-2092	228	5	8113/46/27/275307	8113/46/27/275307	NUM
ap-2092	228	6	137	137	NUM
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ap-2092	228	8	http://dx.doi.org/10.1007/bf02731494	http://dx.doi.org/10.1007/bf02731494	NOUN
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ap-2092	228	10	http://dx.doi.org/10.1103/physrevlett.103.093902	http://dx.doi.org/10.1103/physrevlett.103.093902	VERB
ap-2092	228	11	http://dx.doi.org/10.1038/nphys1515	http://dx.doi.org/10.1038/nphys1515	PROPN
ap-2092	228	12	http://dx.doi.org/10.1103/physreva.86.013612	http://dx.doi.org/10.1103/physreva.86.013612	PROPN
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ap-2092	228	16	löhle	löhle	PROPN
ap-2092	228	17	,	,	PUNCT
ap-2092	228	18	h.	h.	PROPN
ap-2092	228	19	cartarius	cartarius	PROPN
ap-2092	228	20	,	,	PUNCT
ap-2092	228	21	d.	d.	PROPN
ap-2092	228	22	haag	haag	PROPN
ap-2092	229	1	et	et	PROPN
ap-2092	229	2	al	al	PROPN
ap-2092	229	3	.	.	PROPN
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ap-2092	230	1	[	[	X
ap-2092	230	2	11	11	NUM
ap-2092	230	3	]	]	PUNCT
ap-2092	230	4	d.	d.	PROPN
ap-2092	230	5	dast	dast	PROPN
ap-2092	230	6	,	,	PUNCT
ap-2092	230	7	et	et	PROPN
ap-2092	230	8	al	al	PROPN
ap-2092	230	9	.	.	PUNCT
ap-2092	231	1	a	a	DET
ap-2092	231	2	bose	bose	NOUN
ap-2092	231	3	-	-	PUNCT
ap-2092	231	4	einstein	einstein	NOUN
ap-2092	231	5	condensate	condensate	NOUN
ap-2092	231	6	in	in	ADP
ap-2092	231	7	a	a	DET
ap-2092	231	8	pt	pt	NOUN
ap-2092	231	9	symmetric	symmetric	ADJ
ap-2092	231	10	double	double	ADJ
ap-2092	231	11	well	well	ADV
ap-2092	231	12	.	.	PUNCT
ap-2092	232	1	fortschr	fortschr	PROPN
ap-2092	232	2	physik	physik	PROPN
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ap-2092	232	4	,	,	PUNCT
ap-2092	232	5	2013	2013	NUM
ap-2092	232	6	.	.	PUNCT
ap-2092	233	1	doi	doi	NOUN
ap-2092	233	2	:	:	PUNCT
ap-2092	234	1	10.1002	10.1002	NUM
ap-2092	234	2	/	/	SYM
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ap-2092	234	4	[	[	X
ap-2092	234	5	12	12	NUM
ap-2092	234	6	]	]	X
ap-2092	234	7	d.	d.	PROPN
ap-2092	234	8	dast	dast	PROPN
ap-2092	234	9	,	,	PUNCT
ap-2092	234	10	et	et	PROPN
ap-2092	235	1	al	al	PROPN
ap-2092	235	2	.	.	PUNCT
ap-2092	235	3	eigenvalue	eigenvalue	PROPN
ap-2092	235	4	structure	structure	NOUN
ap-2092	235	5	of	of	ADP
ap-2092	235	6	a	a	DET
ap-2092	235	7	bose	bose	NOUN
ap-2092	235	8	-	-	PUNCT
ap-2092	235	9	einstein	einstein	NOUN
ap-2092	235	10	condensate	condensate	NOUN
ap-2092	235	11	in	in	ADP
ap-2092	235	12	a	a	DET
ap-2092	235	13	pt	pt	NOUN
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ap-2092	235	16	well	well	ADV
ap-2092	235	17	.	.	PUNCT
ap-2092	236	1	j	j	PROPN
ap-2092	236	2	phys	phy	NOUN
ap-2092	236	3	a	a	DET
ap-2092	236	4	46:375301	46:375301	NOUN
ap-2092	236	5	,	,	PUNCT
ap-2092	236	6	2013	2013	NUM
ap-2092	236	7	.	.	PUNCT
ap-2092	237	1	doi	doi	NOUN
ap-2092	237	2	:	:	PUNCT
ap-2092	237	3	10.1088/1751	10.1088/1751	NUM
ap-2092	237	4	-	-	PUNCT
ap-2092	237	5	8113/46/37/375301	8113/46/37/375301	PROPN
ap-2092	238	1	[	[	X
ap-2092	238	2	13	13	NUM
ap-2092	238	3	]	]	X
ap-2092	238	4	h.	h.	PROPN
ap-2092	238	5	cartarius	cartarius	PROPN
ap-2092	238	6	,	,	PUNCT
ap-2092	238	7	et	et	PROPN
ap-2092	238	8	al	al	PROPN
ap-2092	238	9	.	.	PROPN
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ap-2092	238	11	and	and	CCONJ
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ap-2092	238	13	solutions	solution	NOUN
ap-2092	238	14	of	of	ADP
ap-2092	238	15	the	the	DET
ap-2092	238	16	gross	gross	ADJ
ap-2092	238	17	-	-	PUNCT
ap-2092	238	18	pitaevskii	pitaevskii	ADJ
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ap-2092	238	20	for	for	ADP
ap-2092	238	21	a	a	DET
ap-2092	238	22	bose	bose	NOUN
ap-2092	238	23	-	-	PUNCT
ap-2092	238	24	einstein	einstein	NOUN
ap-2092	238	25	condensate	condensate	NOUN
ap-2092	238	26	in	in	ADP
ap-2092	238	27	a	a	DET
ap-2092	238	28	pt	pt	NOUN
ap-2092	238	29	symmetric	symmetric	ADJ
ap-2092	238	30	double	double	ADJ
ap-2092	238	31	well	well	ADV
ap-2092	238	32	.	.	PUNCT
ap-2092	239	1	acta	acta	PROPN
ap-2092	239	2	polytechnica	polytechnica	PROPN
ap-2092	239	3	53(3):259–267	53(3):259–267	PROPN
ap-2092	239	4	,	,	PUNCT
ap-2092	239	5	2013	2013	NUM
ap-2092	239	6	.	.	PUNCT
ap-2092	240	1	[	[	X
ap-2092	240	2	14	14	NUM
ap-2092	240	3	]	]	X
ap-2092	240	4	e.	e.	PROPN
ap-2092	240	5	m.	m.	PROPN
ap-2092	240	6	graefe	graefe	PROPN
ap-2092	240	7	,	,	PUNCT
ap-2092	240	8	et	et	PROPN
ap-2092	240	9	al	al	PROPN
ap-2092	240	10	.	.	PUNCT
ap-2092	241	1	a	a	DET
ap-2092	241	2	non	non	ADJ
ap-2092	241	3	-	-	ADJ
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ap-2092	241	5	pt	pt	PROPN
ap-2092	241	6	symmetric	symmetric	PROPN
ap-2092	241	7	bose	bose	PROPN
ap-2092	241	8	-	-	PUNCT
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ap-2092	241	11	:	:	PUNCT
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ap-2092	241	13	rings	ring	NOUN
ap-2092	241	14	from	from	ADP
ap-2092	241	15	unfolding	unfold	VERB
ap-2092	241	16	higher	high	ADJ
ap-2092	241	17	-	-	PUNCT
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ap-2092	241	20	points	point	NOUN
ap-2092	241	21	.	.	PUNCT
ap-2092	242	1	j	j	PROPN
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ap-2092	242	3	a	a	DET
ap-2092	242	4	41:255206	41:255206	NUM
ap-2092	242	5	,	,	PUNCT
ap-2092	242	6	2008	2008	NUM
ap-2092	242	7	.	.	PUNCT
ap-2092	243	1	doi	doi	NOUN
ap-2092	243	2	:	:	PUNCT
ap-2092	243	3	10.1088/1751	10.1088/1751	NUM
ap-2092	243	4	-	-	SYM
ap-2092	243	5	8113/41/25/255206	8113/41/25/255206	PROPN
ap-2092	243	6	[	[	X
ap-2092	243	7	15	15	NUM
ap-2092	243	8	]	]	X
ap-2092	243	9	e.	e.	PROPN
ap-2092	243	10	m.	m.	PROPN
ap-2092	243	11	graefe	graefe	PROPN
ap-2092	243	12	,	,	PUNCT
ap-2092	243	13	et	et	PROPN
ap-2092	243	14	al	al	PROPN
ap-2092	243	15	.	.	PUNCT
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ap-2092	244	2	-	-	PUNCT
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ap-2092	244	5	of	of	ADP
ap-2092	244	6	a	a	DET
ap-2092	244	7	non	non	ADJ
ap-2092	244	8	-	-	ADJ
ap-2092	244	9	hermitian	hermitian	ADJ
ap-2092	244	10	bose	bose	PROPN
ap-2092	244	11	-	-	PUNCT
ap-2092	244	12	hubbard	hubbard	NOUN
ap-2092	244	13	dimer	dimer	NOUN
ap-2092	244	14	.	.	PUNCT
ap-2092	245	1	phys	phy	NOUN
ap-2092	245	2	rev	rev	VERB
ap-2092	245	3	lett	lett	PROPN
ap-2092	245	4	101:150408	101:150408	NUM
ap-2092	245	5	,	,	PUNCT
ap-2092	245	6	2008	2008	NUM
ap-2092	245	7	.	.	PUNCT
ap-2092	246	1	doi	doi	NOUN
ap-2092	246	2	:	:	PUNCT
ap-2092	246	3	10.1103	10.1103	NUM
ap-2092	246	4	/	/	SYM
ap-2092	246	5	physrevlett.101.150408	physrevlett.101.150408	NOUN
ap-2092	247	1	[	[	X
ap-2092	247	2	16	16	NUM
ap-2092	247	3	]	]	X
ap-2092	247	4	e.	e.	PROPN
ap-2092	247	5	m.	m.	PROPN
ap-2092	247	6	graefe	graefe	PROPN
ap-2092	247	7	,	,	PUNCT
ap-2092	247	8	et	et	PROPN
ap-2092	247	9	al	al	PROPN
ap-2092	247	10	.	.	PUNCT
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ap-2092	247	12	-	-	ADJ
ap-2092	247	13	classical	classical	ADJ
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ap-2092	247	16	a	a	DET
ap-2092	247	17	non	non	ADJ
ap-2092	247	18	-	-	ADJ
ap-2092	247	19	hermitian	hermitian	ADJ
ap-2092	247	20	bose	bose	PROPN
ap-2092	247	21	-	-	PUNCT
ap-2092	247	22	hubbard	hubbard	NOUN
ap-2092	247	23	dimer	dimer	NOUN
ap-2092	247	24	.	.	PUNCT
ap-2092	248	1	phys	phy	NOUN
ap-2092	248	2	rev	rev	VERB
ap-2092	248	3	a	a	DET
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ap-2092	248	5	,	,	PUNCT
ap-2092	248	6	2010	2010	NUM
ap-2092	248	7	.	.	PUNCT
ap-2092	249	1	doi	doi	NOUN
ap-2092	249	2	:	:	PUNCT
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ap-2092	249	4	/	/	SYM
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ap-2092	249	8	]	]	X
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ap-2092	250	5	pt	pt	NOUN
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ap-2092	250	7	two	two	NUM
ap-2092	250	8	-	-	PUNCT
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ap-2092	250	11	-	-	PUNCT
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ap-2092	250	14	.	.	PUNCT
ap-2092	251	1	j	j	PROPN
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ap-2092	251	3	a	a	DET
ap-2092	251	4	45:444015	45:444015	PROPN
ap-2092	251	5	,	,	PUNCT
ap-2092	251	6	2012	2012	NUM
ap-2092	251	7	.	.	PUNCT
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ap-2092	252	2	:	:	PUNCT
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ap-2092	252	4	-	-	SYM
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ap-2092	252	6	[	[	X
ap-2092	252	7	18	18	NUM
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ap-2092	254	1	phys	phy	NOUN
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ap-2092	254	5	,	,	PUNCT
ap-2092	254	6	2010	2010	NUM
ap-2092	254	7	.	.	PUNCT
ap-2092	255	1	doi	doi	NOUN
ap-2092	255	2	:	:	PUNCT
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ap-2092	255	4	/	/	SYM
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ap-2092	256	3	]	]	PUNCT
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ap-2092	256	5	h.	h.	PROPN
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ap-2092	256	8	et	et	PROPN
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ap-2092	257	2	solitons	soliton	NOUN
ap-2092	257	3	in	in	ADP
ap-2092	257	4	pt	pt	PRON
ap-2092	257	5	periodic	periodic	ADJ
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ap-2092	257	7	.	.	PUNCT
ap-2092	258	1	phys	phy	NOUN
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ap-2092	258	7	.	.	PUNCT
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ap-2092	259	2	:	:	PUNCT
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ap-2092	259	4	/	/	SYM
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ap-2092	259	6	[	[	X
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ap-2092	259	8	]	]	PUNCT
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ap-2092	260	5	solitons	soliton	NOUN
ap-2092	260	6	,	,	PUNCT
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ap-2092	260	12	schrödinger	schrödinger	ADJ
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ap-2092	261	7	.	.	PUNCT
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ap-2092	264	5	v.	v.	PROPN
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ap-2092	266	6	2010	2010	NUM
ap-2092	266	7	.	.	PUNCT
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ap-2092	268	3	]	]	PUNCT
ap-2092	268	4	r.	r.	PROPN
ap-2092	268	5	driben	driben	PROPN
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ap-2092	268	7	et	et	PROPN
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ap-2092	268	9	.	.	PROPN
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ap-2092	268	13	in	in	ADP
ap-2092	268	14	parity	parity	NOUN
ap-2092	268	15	-	-	PUNCT
ap-2092	268	16	time	time	NOUN
ap-2092	268	17	-	-	PUNCT
ap-2092	268	18	symmetric	symmetric	ADJ
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ap-2092	268	20	.	.	PUNCT
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ap-2092	269	3	36:4323–4325	36:4323–4325	NUM
ap-2092	269	4	,	,	PUNCT
ap-2092	269	5	2011	2011	NUM
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ap-2092	270	2	:	:	PUNCT
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ap-2092	271	2	23	23	NUM
ap-2092	271	3	]	]	PUNCT
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ap-2092	271	5	k.	k.	PROPN
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ap-2092	271	13	pt	pt	NOUN
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ap-2092	271	16	lattices	lattice	NOUN
ap-2092	271	17	.	.	PUNCT
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ap-2092	272	3	a	a	DET
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ap-2092	272	5	,	,	PUNCT
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ap-2092	274	3	]	]	X
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ap-2092	274	9	al	al	PROPN
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ap-2092	274	14	in	in	ADP
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ap-2092	275	3	a	a	DET
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ap-2092	275	7	.	.	PUNCT
ap-2092	276	1	doi	doi	NOUN
ap-2092	276	2	:	:	PUNCT
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ap-2092	276	4	/	/	SYM
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ap-2092	277	2	25	25	NUM
ap-2092	277	3	]	]	PUNCT
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ap-2092	277	9	al	al	PROPN
ap-2092	277	10	.	.	PROPN
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ap-2092	278	4	pt	pt	PROPN
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ap-2092	280	2	:	:	PUNCT
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ap-2092	280	10	g.	g.	PROPN
ap-2092	280	11	makris	makris	PROPN
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ap-2092	280	13	et	et	PROPN
ap-2092	281	1	al	al	PROPN
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ap-2092	281	3	pt	pt	PROPN
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ap-2092	281	5	optical	optical	ADJ
ap-2092	281	6	lattices	lattice	NOUN
ap-2092	281	7	.	.	PUNCT
ap-2092	282	1	phys	phy	NOUN
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ap-2092	282	3	a	a	DET
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ap-2092	282	5	,	,	PUNCT
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ap-2092	282	7	.	.	PUNCT
ap-2092	283	1	doi	doi	NOUN
ap-2092	283	2	:	:	PUNCT
ap-2092	283	3	10.1103	10.1103	NUM
ap-2092	283	4	/	/	SYM
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ap-2092	283	6	[	[	X
ap-2092	283	7	27	27	NUM
ap-2092	283	8	]	]	PUNCT
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ap-2092	284	4	pt	pt	NOUN
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ap-2092	284	9	a	a	DET
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ap-2092	284	11	slab	slab	NOUN
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ap-2092	284	13	.	.	PUNCT
ap-2092	285	1	j	j	PROPN
ap-2092	285	2	phys	phy	NOUN
ap-2092	285	3	a	a	PRON
ap-2092	285	4	38	38	NUM
ap-2092	285	5	:	:	PUNCT
ap-2092	285	6	l171	l171	PROPN
ap-2092	285	7	,	,	PUNCT
ap-2092	285	8	2005	2005	NUM
ap-2092	285	9	.	.	PUNCT
ap-2092	286	1	doi	doi	NOUN
ap-2092	286	2	:	:	PUNCT
ap-2092	286	3	10.1088/0305	10.1088/0305	NUM
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ap-2092	286	6	/	/	SYM
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ap-2092	287	1	[	[	X
ap-2092	287	2	28	28	NUM
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ap-2092	287	4	r.	r.	PROPN
ap-2092	287	5	el	el	PROPN
ap-2092	287	6	-	-	PROPN
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ap-2092	287	9	et	et	PROPN
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ap-2092	287	16	pt	pt	NOUN
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ap-2092	289	1	doi	doi	NOUN
ap-2092	289	2	:	:	PUNCT
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ap-2092	289	4	/	/	SYM
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ap-2092	290	7	et	et	PROPN
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ap-2092	291	8	pt	pt	PROPN
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ap-2092	293	8	-	-	PUNCT
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ap-2092	295	2	-	-	PUNCT
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ap-2092	295	4	potential	potential	NOUN
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ap-2092	296	1	j	j	PROPN
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ap-2092	296	4	39:13495	39:13495	NUM
ap-2092	296	5	,	,	PUNCT
ap-2092	296	6	2006	2006	NUM
ap-2092	296	7	.	.	PUNCT
ap-2092	297	1	doi	doi	NOUN
ap-2092	297	2	:	:	PUNCT
ap-2092	297	3	10.1088/0305	10.1088/0305	NUM
ap-2092	297	4	-	-	SYM
ap-2092	297	5	4470/39/43/008	4470/39/43/008	PROPN
ap-2092	297	6	[	[	X
ap-2092	297	7	31	31	NUM
ap-2092	297	8	]	]	PUNCT
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ap-2092	297	13	al	al	PROPN
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ap-2092	298	8	two	two	NUM
ap-2092	298	9	-	-	PUNCT
ap-2092	298	10	parameter	parameter	NOUN
ap-2092	298	11	family	family	NOUN
ap-2092	298	12	of	of	ADP
ap-2092	298	13	complex	complex	ADJ
ap-2092	298	14	point	point	NOUN
ap-2092	298	15	interactions	interaction	NOUN
ap-2092	298	16	.	.	PUNCT
ap-2092	299	1	j	j	PROPN
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ap-2092	299	3	a	a	DET
ap-2092	299	4	42:125303	42:125303	NUM
ap-2092	299	5	,	,	PUNCT
ap-2092	299	6	2009	2009	NUM
ap-2092	299	7	.	.	PUNCT
ap-2092	300	1	doi	doi	NOUN
ap-2092	300	2	:	:	PUNCT
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ap-2092	300	4	-	-	PUNCT
ap-2092	300	5	8113/42/12/125303	8113/42/12/125303	PROPN
ap-2092	300	6	[	[	X
ap-2092	300	7	32	32	NUM
ap-2092	300	8	]	]	PUNCT
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ap-2092	301	14	scattering	scattering	ADJ
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ap-2092	301	16	with	with	ADP
ap-2092	301	17	point	point	NOUN
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ap-2092	302	1	j	j	PROPN
ap-2092	302	2	phys	phy	NOUN
ap-2092	302	3	a	a	DET
ap-2092	302	4	43:145301	43:145301	NUM
ap-2092	302	5	,	,	PUNCT
ap-2092	302	6	2010	2010	NUM
ap-2092	302	7	.	.	PUNCT
ap-2092	303	1	doi	doi	NOUN
ap-2092	303	2	:	:	PUNCT
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ap-2092	303	4	-	-	PUNCT
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ap-2092	303	6	[	[	X
ap-2092	303	7	33	33	NUM
ap-2092	303	8	]	]	PUNCT
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ap-2092	303	10	f.	f.	PROPN
ap-2092	303	11	jones	jones	PROPN
ap-2092	303	12	.	.	PROPN
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ap-2092	304	2	between	between	ADP
ap-2092	304	3	hermitian	hermitian	PROPN
ap-2092	304	4	and	and	CCONJ
ap-2092	304	5	nonhermitian	nonhermitian	ADJ
ap-2092	304	6	hamiltonians	hamiltonian	NOUN
ap-2092	304	7	in	in	ADP
ap-2092	304	8	a	a	DET
ap-2092	304	9	model	model	NOUN
ap-2092	304	10	calculation	calculation	NOUN
ap-2092	304	11	.	.	PUNCT
ap-2092	305	1	phys	phy	NOUN
ap-2092	305	2	rev	rev	VERB
ap-2092	305	3	d	d	PROPN
ap-2092	305	4	78:065032	78:065032	NUM
ap-2092	305	5	,	,	PUNCT
ap-2092	305	6	2008	2008	NUM
ap-2092	305	7	.	.	PUNCT
ap-2092	306	1	doi	doi	NOUN
ap-2092	306	2	:	:	PUNCT
ap-2092	306	3	10.1103	10.1103	NUM
ap-2092	306	4	/	/	SYM
ap-2092	306	5	physrevd.78.065032	physrevd.78.065032	NOUN
ap-2092	306	6	[	[	X
ap-2092	306	7	34	34	NUM
ap-2092	306	8	]	]	X
ap-2092	306	9	m.	m.	NOUN
ap-2092	306	10	kreibich	kreibich	PROPN
ap-2092	306	11	,	,	PUNCT
ap-2092	306	12	et	et	PROPN
ap-2092	306	13	al	al	PROPN
ap-2092	306	14	.	.	PROPN
ap-2092	307	1	hermitian	hermitian	PROPN
ap-2092	307	2	four	four	NUM
ap-2092	307	3	-	-	PUNCT
ap-2092	307	4	well	well	NOUN
ap-2092	307	5	potential	potential	NOUN
ap-2092	307	6	as	as	ADP
ap-2092	307	7	a	a	DET
ap-2092	307	8	realization	realization	NOUN
ap-2092	307	9	of	of	ADP
ap-2092	307	10	a	a	DET
ap-2092	307	11	pt	pt	NOUN
ap-2092	307	12	-symmetric	-symmetric	ADJ
ap-2092	307	13	system	system	NOUN
ap-2092	307	14	.	.	PUNCT
ap-2092	308	1	phys	phy	NOUN
ap-2092	308	2	rev	rev	VERB
ap-2092	308	3	a	a	DET
ap-2092	308	4	87:051601(r	87:051601(r	NOUN
ap-2092	308	5	)	)	PUNCT
ap-2092	308	6	,	,	PUNCT
ap-2092	308	7	2013	2013	NUM
ap-2092	308	8	.	.	PUNCT
ap-2092	309	1	doi	doi	NOUN
ap-2092	309	2	:	:	PUNCT
ap-2092	309	3	10.1103	10.1103	NUM
ap-2092	309	4	/	/	SYM
ap-2092	309	5	physreva.87.051601	physreva.87.051601	NOUN
ap-2092	309	6	138	138	NUM
ap-2092	309	7	http://dx.doi.org/10.1002/prop.201200080	http://dx.doi.org/10.1002/prop.201200080	NOUN
ap-2092	309	8	http://dx.doi.org/10.1088/1751-8113/46/37/375301	http://dx.doi.org/10.1088/1751-8113/46/37/375301	X
ap-2092	309	9	http://dx.doi.org/10.1088/1751-8113/41/25/255206	http://dx.doi.org/10.1088/1751-8113/41/25/255206	X
ap-2092	309	10	http://dx.doi.org/10.1103/physrevlett.101.150408	http://dx.doi.org/10.1103/physrevlett.101.150408	PROPN
ap-2092	310	1	http://dx.doi.org/10.1103/physreva.82.013629	http://dx.doi.org/10.1103/physreva.82.013629	ADV
ap-2092	310	2	http://dx.doi.org/10.1088/1751-8113/45/44/444015	http://dx.doi.org/10.1088/1751-8113/45/44/444015	NUM
ap-2092	311	1	http://dx.doi.org/10.1103/physreva.82.043803	http://dx.doi.org/10.1103/physreva.82.043803	PROPN
ap-2092	311	2	http://dx.doi.org/10.1103/physrevlett.100.030402	http://dx.doi.org/10.1103/physrevlett.100.030402	NOUN
ap-2092	311	3	http://dx.doi.org/10.1103/physreve.82.056606	http://dx.doi.org/10.1103/physreve.82.056606	PROPN
ap-2092	311	4	http://dx.doi.org/10.1103/physreva.81.013625	http://dx.doi.org/10.1103/physreva.81.013625	PROPN
ap-2092	311	5	http://dx.doi.org/10.1364/ol.36.004323	http://dx.doi.org/10.1364/ol.36.004323	NOUN
ap-2092	311	6	http://dx.doi.org/10.1103/physreva.83.041805	http://dx.doi.org/10.1103/physreva.83.041805	PROPN
ap-2092	311	7	http://dx.doi.org/10.1103/physreva.87.013816	http://dx.doi.org/10.1103/physreva.87.013816	PROPN
ap-2092	311	8	http://dx.doi.org/10.1103/physrevlett.100.103904	http://dx.doi.org/10.1103/physrevlett.100.103904	VERB
ap-2092	311	9	http://dx.doi.org/10.1103/physreva.81.063807	http://dx.doi.org/10.1103/physreva.81.063807	PROPN
ap-2092	311	10	http://dx.doi.org/10.1088/0305-4470/38/9/l03	http://dx.doi.org/10.1088/0305-4470/38/9/l03	ADJ
ap-2092	311	11	http://dx.doi.org/10.1364/ol.32.002632	http://dx.doi.org/10.1364/ol.32.002632	ADJ
ap-2092	311	12	http://dx.doi.org/10.1007/s10582-005-0115-x	http://dx.doi.org/10.1007/s10582-005-0115-x	NOUN
ap-2092	311	13	http://dx.doi.org/10.1088/0305-4470/39/43/008	http://dx.doi.org/10.1088/0305-4470/39/43/008	NOUN
ap-2092	312	1	http://dx.doi.org/10.1088/1751-8113/42/12/125303	http://dx.doi.org/10.1088/1751-8113/42/12/125303	X
ap-2092	312	2	http://dx.doi.org/10.1088/1751-8113/43/14/145301	http://dx.doi.org/10.1088/1751-8113/43/14/145301	PROPN
ap-2092	313	1	http://dx.doi.org/10.1103/physrevd.78.065032	http://dx.doi.org/10.1103/physrevd.78.065032	PROPN
ap-2092	313	2	http://dx.doi.org/10.1103/physreva.87.051601	http://dx.doi.org/10.1103/physreva.87.051601	PROPN
ap-2092	313	3	acta	acta	PROPN
ap-2092	313	4	polytechnica	polytechnica	PROPN
ap-2092	313	5	54(2):133–138	54(2):133–138	PROPN
ap-2092	313	6	,	,	PUNCT
ap-2092	313	7	2014	2014	NUM
ap-2092	313	8	1	1	NUM
ap-2092	313	9	introduction	introduction	NOUN
ap-2092	313	10	2	2	NUM
ap-2092	313	11	bose	bose	NOUN
ap-2092	313	12	-	-	PUNCT
ap-2092	313	13	einstein	einstein	NOUN
ap-2092	313	14	condensates	condensate	NOUN
ap-2092	313	15	in	in	ADP
ap-2092	313	16	the	the	DET
ap-2092	313	17	pt	pt	PROPN
ap-2092	313	18	symmetric	symmetric	PROPN
ap-2092	313	19	doubletrap	doubletrap	PROPN
ap-2092	313	20	3	3	NUM
ap-2092	313	21	stability	stability	NOUN
ap-2092	313	22	analysis	analysis	NOUN
ap-2092	313	23	of	of	ADP
ap-2092	313	24	the	the	DET
ap-2092	313	25	ground	ground	NOUN
ap-2092	313	26	state	state	NOUN
ap-2092	313	27	3.1	3.1	NUM
ap-2092	313	28	stability	stability	NOUN
ap-2092	313	29	in	in	ADP
ap-2092	313	30	the	the	DET
ap-2092	313	31	vicinity	vicinity	NOUN
ap-2092	313	32	of	of	ADP
ap-2092	313	33	the	the	DET
ap-2092	313	34	bifurcation	bifurcation	NOUN
ap-2092	313	35	3.2	3.2	NUM
ap-2092	313	36	norm	norm	NOUN
ap-2092	313	37	-	-	PUNCT
ap-2092	313	38	independent	independent	ADJ
ap-2092	313	39	variant	variant	NOUN
ap-2092	313	40	of	of	ADP
ap-2092	313	41	the	the	DET
ap-2092	313	42	gross	gross	ADJ
ap-2092	313	43	-	-	PUNCT
ap-2092	313	44	pitaevskii	pitaevskii	ADJ
ap-2092	313	45	equation	equation	NOUN
ap-2092	313	46	3.3	3.3	NUM
ap-2092	313	47	discussion	discussion	NOUN
ap-2092	313	48	4	4	NUM
ap-2092	313	49	conclusions	conclusion	NOUN
ap-2092	313	50	acknowledgements	acknowledgement	NOUN
ap-2092	313	51	references	reference	NOUN