id	sid	tid	token	lemma	pos
ap-1418	1	1	acta	acta	PROPN
ap-1418	1	2	polytechnica	polytechnica	PROPN
ap-1418	1	3	vol	vol	NOUN
ap-1418	1	4	.	.	PUNCT
ap-1418	2	1	51	51	NUM
ap-1418	2	2	no	no	INTJ
ap-1418	2	3	.	.	PUNCT
ap-1418	3	1	4/2011	4/2011	NUM
ap-1418	3	2	exceptional	exceptional	ADJ
ap-1418	3	3	points	point	NOUN
ap-1418	3	4	for	for	ADP
ap-1418	3	5	nonlinear	nonlinear	ADJ
ap-1418	3	6	schrödinger	schrödinger	NOUN
ap-1418	3	7	equations	equation	NOUN
ap-1418	3	8	describing	describe	VERB
ap-1418	3	9	bose	bose	NOUN
ap-1418	3	10	-	-	PUNCT
ap-1418	3	11	einstein	einstein	NOUN
ap-1418	3	12	condensates	condensate	NOUN
ap-1418	3	13	of	of	ADP
ap-1418	3	14	ultracold	ultracold	PROPN
ap-1418	3	15	atomic	atomic	PROPN
ap-1418	3	16	gases	gas	NOUN
ap-1418	3	17	g.	g.	PROPN
ap-1418	3	18	wunner	wunner	PROPN
ap-1418	3	19	,	,	PUNCT
ap-1418	3	20	h.	h.	PROPN
ap-1418	3	21	cartarius	cartarius	PROPN
ap-1418	3	22	,	,	PUNCT
ap-1418	3	23	p.	p.	NOUN
ap-1418	3	24	köberle	köberle	PROPN
ap-1418	3	25	,	,	PUNCT
ap-1418	3	26	j.	j.	PROPN
ap-1418	3	27	main	main	PROPN
ap-1418	3	28	,	,	PUNCT
ap-1418	3	29	s.	s.	PROPN
ap-1418	3	30	rau	rau	PROPN
ap-1418	3	31	abstract	abstract	PROPN
ap-1418	3	32	the	the	DET
ap-1418	3	33	coalescence	coalescence	NOUN
ap-1418	3	34	of	of	ADP
ap-1418	3	35	two	two	NUM
ap-1418	3	36	eigenfunctions	eigenfunction	NOUN
ap-1418	3	37	with	with	ADP
ap-1418	3	38	the	the	DET
ap-1418	3	39	same	same	ADJ
ap-1418	3	40	energy	energy	NOUN
ap-1418	3	41	eigenvalue	eigenvalue	NOUN
ap-1418	3	42	is	be	AUX
ap-1418	3	43	not	not	PART
ap-1418	3	44	possible	possible	ADJ
ap-1418	3	45	in	in	ADP
ap-1418	3	46	hermitian	hermitian	ADJ
ap-1418	3	47	hamiltonians	hamiltonian	NOUN
ap-1418	3	48	.	.	PUNCT
ap-1418	4	1	it	it	PRON
ap-1418	4	2	is	be	AUX
ap-1418	4	3	,	,	PUNCT
ap-1418	4	4	however	however	ADV
ap-1418	4	5	,	,	PUNCT
ap-1418	4	6	a	a	DET
ap-1418	4	7	phenomenon	phenomenon	NOUN
ap-1418	4	8	well	well	ADV
ap-1418	4	9	known	know	VERB
ap-1418	4	10	from	from	ADP
ap-1418	4	11	non	non	ADJ
ap-1418	4	12	-	-	ADJ
ap-1418	4	13	hermitian	hermitian	ADJ
ap-1418	4	14	quantum	quantum	ADJ
ap-1418	4	15	mechanics	mechanic	NOUN
ap-1418	4	16	.	.	PUNCT
ap-1418	5	1	it	it	PRON
ap-1418	5	2	can	can	AUX
ap-1418	5	3	appear	appear	VERB
ap-1418	5	4	,	,	PUNCT
ap-1418	5	5	e.g.	e.g.	ADV
ap-1418	5	6	,	,	PUNCT
ap-1418	5	7	for	for	ADP
ap-1418	5	8	resonances	resonance	NOUN
ap-1418	5	9	in	in	ADP
ap-1418	5	10	open	open	ADJ
ap-1418	5	11	systems	system	NOUN
ap-1418	5	12	,	,	PUNCT
ap-1418	5	13	with	with	ADP
ap-1418	5	14	complex	complex	ADJ
ap-1418	5	15	energy	energy	NOUN
ap-1418	5	16	eigenvalues	eigenvalue	NOUN
ap-1418	5	17	.	.	PUNCT
ap-1418	6	1	if	if	SCONJ
ap-1418	6	2	two	two	NUM
ap-1418	6	3	eigenvalues	eigenvalue	NOUN
ap-1418	6	4	of	of	ADP
ap-1418	6	5	a	a	DET
ap-1418	6	6	quantum	quantum	ADJ
ap-1418	6	7	mechanical	mechanical	ADJ
ap-1418	6	8	system	system	NOUN
ap-1418	6	9	which	which	PRON
ap-1418	6	10	depends	depend	VERB
ap-1418	6	11	on	on	ADP
ap-1418	6	12	two	two	NUM
ap-1418	6	13	or	or	CCONJ
ap-1418	6	14	more	more	ADJ
ap-1418	6	15	parameters	parameter	NOUN
ap-1418	6	16	pass	pass	VERB
ap-1418	6	17	through	through	ADP
ap-1418	6	18	such	such	DET
ap-1418	6	19	a	a	DET
ap-1418	6	20	branch	branch	NOUN
ap-1418	6	21	point	point	NOUN
ap-1418	6	22	singularity	singularity	NOUN
ap-1418	6	23	at	at	ADP
ap-1418	6	24	a	a	DET
ap-1418	6	25	critical	critical	ADJ
ap-1418	6	26	set	set	NOUN
ap-1418	6	27	of	of	ADP
ap-1418	6	28	parameters	parameter	NOUN
ap-1418	6	29	,	,	PUNCT
ap-1418	6	30	the	the	DET
ap-1418	6	31	point	point	NOUN
ap-1418	6	32	in	in	ADP
ap-1418	6	33	the	the	DET
ap-1418	6	34	parameter	parameter	NOUN
ap-1418	6	35	space	space	NOUN
ap-1418	6	36	is	be	AUX
ap-1418	6	37	called	call	VERB
ap-1418	6	38	an	an	DET
ap-1418	6	39	exceptional	exceptional	ADJ
ap-1418	6	40	point	point	NOUN
ap-1418	6	41	.	.	PUNCT
ap-1418	7	1	we	we	PRON
ap-1418	7	2	will	will	AUX
ap-1418	7	3	demonstrate	demonstrate	VERB
ap-1418	7	4	that	that	SCONJ
ap-1418	7	5	exceptional	exceptional	ADJ
ap-1418	7	6	points	point	NOUN
ap-1418	7	7	occur	occur	VERB
ap-1418	7	8	not	not	PART
ap-1418	7	9	only	only	ADV
ap-1418	7	10	for	for	ADP
ap-1418	7	11	non	non	ADJ
ap-1418	7	12	-	-	ADJ
ap-1418	7	13	hermitean	hermitean	ADJ
ap-1418	7	14	hamiltonians	hamiltonian	NOUN
ap-1418	7	15	but	but	CCONJ
ap-1418	7	16	also	also	ADV
ap-1418	7	17	in	in	ADP
ap-1418	7	18	the	the	DET
ap-1418	7	19	nonlinear	nonlinear	ADJ
ap-1418	7	20	schrödinger	schrödinger	NOUN
ap-1418	7	21	equations	equation	NOUN
ap-1418	7	22	which	which	PRON
ap-1418	7	23	describe	describe	VERB
ap-1418	7	24	bose	bose	NOUN
ap-1418	7	25	-	-	PUNCT
ap-1418	7	26	einstein	einstein	NOUN
ap-1418	7	27	condensates	condensate	NOUN
ap-1418	7	28	,	,	PUNCT
ap-1418	7	29	i.e.	i.e.	X
ap-1418	7	30	,	,	PUNCT
ap-1418	7	31	the	the	DET
ap-1418	7	32	grosspitaevskii	grosspitaevskii	ADJ
ap-1418	7	33	equation	equation	NOUN
ap-1418	7	34	for	for	ADP
ap-1418	7	35	condensates	condensate	NOUN
ap-1418	7	36	with	with	ADP
ap-1418	7	37	a	a	DET
ap-1418	7	38	short	short	ADJ
ap-1418	7	39	-	-	PUNCT
ap-1418	7	40	range	range	NOUN
ap-1418	7	41	contact	contact	NOUN
ap-1418	7	42	interaction	interaction	NOUN
ap-1418	7	43	,	,	PUNCT
ap-1418	7	44	and	and	CCONJ
ap-1418	7	45	with	with	ADP
ap-1418	7	46	additional	additional	ADJ
ap-1418	7	47	long	long	ADJ
ap-1418	7	48	-	-	PUNCT
ap-1418	7	49	range	range	NOUN
ap-1418	7	50	interactions	interaction	NOUN
ap-1418	7	51	.	.	PUNCT
ap-1418	8	1	typically	typically	ADV
ap-1418	8	2	,	,	PUNCT
ap-1418	8	3	in	in	ADP
ap-1418	8	4	these	these	DET
ap-1418	8	5	condensates	condensate	NOUN
ap-1418	8	6	the	the	DET
ap-1418	8	7	exceptional	exceptional	ADJ
ap-1418	8	8	points	point	NOUN
ap-1418	8	9	are	be	AUX
ap-1418	8	10	also	also	ADV
ap-1418	8	11	found	find	VERB
ap-1418	8	12	to	to	PART
ap-1418	8	13	be	be	AUX
ap-1418	8	14	bifurcation	bifurcation	NOUN
ap-1418	8	15	points	point	NOUN
ap-1418	8	16	in	in	ADP
ap-1418	8	17	parameter	parameter	NOUN
ap-1418	8	18	space	space	NOUN
ap-1418	8	19	.	.	PUNCT
ap-1418	9	1	for	for	ADP
ap-1418	9	2	condensates	condensate	NOUN
ap-1418	9	3	with	with	ADP
ap-1418	9	4	a	a	DET
ap-1418	9	5	gravity	gravity	NOUN
ap-1418	9	6	-	-	PUNCT
ap-1418	9	7	like	like	ADJ
ap-1418	9	8	interaction	interaction	NOUN
ap-1418	9	9	between	between	ADP
ap-1418	9	10	the	the	DET
ap-1418	9	11	atoms	atom	NOUN
ap-1418	9	12	,	,	PUNCT
ap-1418	9	13	these	these	DET
ap-1418	9	14	findings	finding	NOUN
ap-1418	9	15	can	can	AUX
ap-1418	9	16	be	be	AUX
ap-1418	9	17	confirmed	confirm	VERB
ap-1418	9	18	in	in	ADP
ap-1418	9	19	an	an	DET
ap-1418	9	20	analytical	analytical	ADJ
ap-1418	9	21	way	way	NOUN
ap-1418	9	22	.	.	PUNCT
ap-1418	10	1	1	1	NUM
ap-1418	10	2	introduction	introduction	NOUN
ap-1418	10	3	in	in	ADP
ap-1418	10	4	1924	1924	NUM
ap-1418	10	5	,	,	PUNCT
ap-1418	10	6	satyendra	satyendra	PROPN
ap-1418	10	7	nath	nath	PROPN
ap-1418	10	8	bose	bose	PROPN
ap-1418	10	9	and	and	CCONJ
ap-1418	10	10	albert	albert	PROPN
ap-1418	10	11	einstein	einstein	PROPN
ap-1418	10	12	predicted	predict	VERB
ap-1418	10	13	that	that	SCONJ
ap-1418	10	14	when	when	SCONJ
ap-1418	10	15	the	the	DET
ap-1418	10	16	thermal	thermal	ADJ
ap-1418	10	17	de	de	X
ap-1418	10	18	broglie	broglie	PROPN
ap-1418	10	19	wavelength	wavelength	NOUN
ap-1418	10	20	becomes	become	VERB
ap-1418	10	21	of	of	ADP
ap-1418	10	22	the	the	DET
ap-1418	10	23	order	order	NOUN
ap-1418	10	24	of	of	ADP
ap-1418	10	25	the	the	DET
ap-1418	10	26	interparticle	interparticle	NOUN
ap-1418	10	27	distance	distance	NOUN
ap-1418	10	28	,	,	PUNCT
ap-1418	10	29	bosons	boson	NOUN
ap-1418	10	30	begin	begin	VERB
ap-1418	10	31	to	to	PART
ap-1418	10	32	“	"	PUNCT
ap-1418	10	33	condense	condense	VERB
ap-1418	10	34	”	"	PUNCT
ap-1418	10	35	into	into	ADP
ap-1418	10	36	their	their	PRON
ap-1418	10	37	ground	ground	NOUN
ap-1418	10	38	state	state	NOUN
ap-1418	10	39	.	.	PUNCT
ap-1418	11	1	all	all	DET
ap-1418	11	2	bosons	boson	NOUN
ap-1418	11	3	have	have	VERB
ap-1418	11	4	the	the	DET
ap-1418	11	5	same	same	ADJ
ap-1418	11	6	energy	energy	NOUN
ap-1418	11	7	and	and	CCONJ
ap-1418	11	8	quantum	quantum	NOUN
ap-1418	11	9	characteristics	characteristic	NOUN
ap-1418	11	10	,	,	PUNCT
ap-1418	11	11	similar	similar	ADJ
ap-1418	11	12	to	to	ADP
ap-1418	11	13	the	the	DET
ap-1418	11	14	way	way	NOUN
ap-1418	11	15	all	all	DET
ap-1418	11	16	photons	photon	NOUN
ap-1418	11	17	in	in	ADP
ap-1418	11	18	a	a	DET
ap-1418	11	19	laser	laser	NOUN
ap-1418	11	20	share	share	VERB
ap-1418	11	21	the	the	DET
ap-1418	11	22	same	same	ADJ
ap-1418	11	23	quantum	quantum	ADJ
ap-1418	11	24	state	state	NOUN
ap-1418	11	25	.	.	PUNCT
ap-1418	12	1	superfluidity	superfluidity	NOUN
ap-1418	12	2	of	of	ADP
ap-1418	12	3	4he	4he	ADJ
ap-1418	12	4	atoms	atom	NOUN
ap-1418	12	5	below	below	ADP
ap-1418	12	6	a	a	DET
ap-1418	12	7	temperature	temperature	NOUN
ap-1418	12	8	of	of	ADP
ap-1418	12	9	approximately	approximately	ADV
ap-1418	12	10	t	t	NOUN
ap-1418	12	11	=	=	SYM
ap-1418	13	1	2.17	2.17	NUM
ap-1418	13	2	k	k	NOUN
ap-1418	13	3	was	be	AUX
ap-1418	13	4	the	the	DET
ap-1418	13	5	first	first	ADJ
ap-1418	13	6	experimental	experimental	ADJ
ap-1418	13	7	realisation	realisation	NOUN
ap-1418	13	8	in	in	ADP
ap-1418	13	9	1937	1937	NUM
ap-1418	13	10	of	of	ADP
ap-1418	13	11	such	such	DET
ap-1418	13	12	a	a	DET
ap-1418	13	13	macroscopic	macroscopic	ADJ
ap-1418	13	14	quantum	quantum	ADJ
ap-1418	13	15	state	state	NOUN
ap-1418	13	16	[	[	X
ap-1418	13	17	1	1	NUM
ap-1418	13	18	]	]	PUNCT
ap-1418	13	19	.	.	PUNCT
ap-1418	14	1	it	it	PRON
ap-1418	14	2	took	take	VERB
ap-1418	14	3	,	,	PUNCT
ap-1418	14	4	however	however	ADV
ap-1418	14	5	,	,	PUNCT
ap-1418	14	6	until	until	ADP
ap-1418	14	7	1995	1995	NUM
ap-1418	14	8	for	for	ADP
ap-1418	14	9	bose	bose	NOUN
ap-1418	14	10	-	-	PUNCT
ap-1418	14	11	einstein	einstein	NOUN
ap-1418	14	12	condensation	condensation	NOUN
ap-1418	14	13	to	to	PART
ap-1418	14	14	be	be	AUX
ap-1418	14	15	observed	observe	VERB
ap-1418	14	16	in	in	ADP
ap-1418	14	17	dilute	dilute	ADJ
ap-1418	14	18	atomic	atomic	ADJ
ap-1418	14	19	vapours	vapour	NOUN
ap-1418	14	20	of	of	ADP
ap-1418	14	21	alkali	alkali	ADJ
ap-1418	14	22	atoms	atom	NOUN
ap-1418	14	23	,	,	PUNCT
ap-1418	14	24	namely	namely	ADV
ap-1418	14	25	,	,	PUNCT
ap-1418	14	26	by	by	ADP
ap-1418	14	27	wieman	wieman	NOUN
ap-1418	14	28	et	et	PROPN
ap-1418	14	29	al	al	PROPN
ap-1418	14	30	.	.	PUNCT
ap-1418	15	1	[	[	X
ap-1418	15	2	2	2	X
ap-1418	15	3	]	]	PUNCT
ap-1418	15	4	in	in	ADP
ap-1418	15	5	87rb	87rb	PROPN
ap-1418	15	6	and	and	CCONJ
ap-1418	15	7	by	by	ADP
ap-1418	15	8	ketterle	ketterle	PROPN
ap-1418	15	9	et	et	PROPN
ap-1418	15	10	al	al	PROPN
ap-1418	15	11	.	.	PUNCT
ap-1418	16	1	[	[	X
ap-1418	16	2	3	3	X
ap-1418	16	3	]	]	PUNCT
ap-1418	16	4	in	in	ADP
ap-1418	16	5	23na	23na	PROPN
ap-1418	16	6	(	(	PUNCT
ap-1418	16	7	in	in	ADP
ap-1418	16	8	both	both	DET
ap-1418	16	9	cases	case	NOUN
ap-1418	16	10	the	the	DET
ap-1418	16	11	number	number	NOUN
ap-1418	16	12	of	of	ADP
ap-1418	16	13	nucleons	nucleon	NOUN
ap-1418	16	14	and	and	CCONJ
ap-1418	16	15	electrons	electron	NOUN
ap-1418	16	16	add	add	VERB
ap-1418	16	17	up	up	ADP
ap-1418	16	18	to	to	ADP
ap-1418	16	19	an	an	DET
ap-1418	16	20	even	even	ADJ
ap-1418	16	21	number	number	NOUN
ap-1418	16	22	,	,	PUNCT
ap-1418	16	23	to	to	PART
ap-1418	16	24	form	form	VERB
ap-1418	16	25	a	a	DET
ap-1418	16	26	boson	boson	NOUN
ap-1418	16	27	)	)	PUNCT
ap-1418	16	28	.	.	PUNCT
ap-1418	17	1	in	in	ADP
ap-1418	17	2	these	these	DET
ap-1418	17	3	experiments	experiment	NOUN
ap-1418	17	4	,	,	PUNCT
ap-1418	17	5	advanced	advanced	ADJ
ap-1418	17	6	optical	optical	ADJ
ap-1418	17	7	techniques	technique	NOUN
ap-1418	17	8	(	(	PUNCT
ap-1418	17	9	capture	capture	VERB
ap-1418	17	10	in	in	ADP
ap-1418	17	11	a	a	DET
ap-1418	17	12	magneto	magneto	ADJ
ap-1418	17	13	-	-	PUNCT
ap-1418	17	14	optical	optical	ADJ
ap-1418	17	15	trap	trap	NOUN
ap-1418	17	16	and	and	CCONJ
ap-1418	17	17	application	application	NOUN
ap-1418	17	18	of	of	ADP
ap-1418	17	19	laser	laser	NOUN
ap-1418	17	20	cooling	cooling	NOUN
ap-1418	17	21	and	and	CCONJ
ap-1418	17	22	evaporative	evaporative	ADJ
ap-1418	17	23	cooling	cooling	NOUN
ap-1418	17	24	)	)	PUNCT
ap-1418	17	25	had	have	VERB
ap-1418	17	26	to	to	PART
ap-1418	17	27	be	be	AUX
ap-1418	17	28	employed	employ	VERB
ap-1418	17	29	to	to	PART
ap-1418	17	30	cool	cool	VERB
ap-1418	17	31	the	the	DET
ap-1418	17	32	atoms	atom	NOUN
ap-1418	17	33	to	to	ADP
ap-1418	17	34	temperatures	temperature	NOUN
ap-1418	17	35	very	very	ADV
ap-1418	17	36	near	near	ADV
ap-1418	17	37	to	to	ADP
ap-1418	17	38	absolute	absolute	ADJ
ap-1418	17	39	zero	zero	NUM
ap-1418	17	40	(	(	PUNCT
ap-1418	17	41	170	170	NUM
ap-1418	17	42	nk	nk	NOUN
ap-1418	17	43	in	in	ADP
ap-1418	17	44	the	the	DET
ap-1418	17	45	rubidium	rubidium	NOUN
ap-1418	17	46	experiment	experiment	NOUN
ap-1418	17	47	and	and	CCONJ
ap-1418	17	48	2	2	NUM
ap-1418	17	49	μk	μk	NOUN
ap-1418	17	50	in	in	ADP
ap-1418	17	51	the	the	DET
ap-1418	17	52	sodium	sodium	NOUN
ap-1418	17	53	experiment	experiment	NOUN
ap-1418	17	54	)	)	PUNCT
ap-1418	17	55	.	.	PUNCT
ap-1418	18	1	meanwhile	meanwhile	ADV
ap-1418	18	2	bose	bose	NOUN
ap-1418	18	3	-	-	PUNCT
ap-1418	18	4	einstein	einstein	NOUN
ap-1418	18	5	condensates	condensate	NOUN
ap-1418	18	6	of	of	ADP
ap-1418	18	7	many	many	ADJ
ap-1418	18	8	more	more	ADJ
ap-1418	18	9	alkaline	alkaline	NOUN
ap-1418	18	10	and	and	CCONJ
ap-1418	18	11	alkaline	alkaline	NOUN
ap-1418	18	12	earth	earth	NOUN
ap-1418	18	13	atoms	atom	NOUN
ap-1418	18	14	have	have	AUX
ap-1418	18	15	been	be	AUX
ap-1418	18	16	produced	produce	VERB
ap-1418	18	17	(	(	PUNCT
ap-1418	18	18	for	for	SCONJ
ap-1418	18	19	a	a	DET
ap-1418	18	20	review	review	NOUN
ap-1418	18	21	see	see	VERB
ap-1418	18	22	,	,	PUNCT
ap-1418	18	23	e.g.	e.g.	ADV
ap-1418	18	24	,	,	PUNCT
ap-1418	18	25	ref	ref	NOUN
ap-1418	18	26	.	.	PUNCT
ap-1418	19	1	[	[	X
ap-1418	19	2	4	4	NUM
ap-1418	19	3	]	]	NUM
ap-1418	19	4	)	)	PUNCT
ap-1418	19	5	.	.	PUNCT
ap-1418	20	1	alkalis	alkali	NOUN
ap-1418	20	2	,	,	PUNCT
ap-1418	20	3	however	however	ADV
ap-1418	20	4	,	,	PUNCT
ap-1418	20	5	are	be	AUX
ap-1418	20	6	not	not	PART
ap-1418	20	7	ideal	ideal	ADJ
ap-1418	20	8	bose	bose	NOUN
ap-1418	20	9	gases	gas	NOUN
ap-1418	20	10	:	:	PUNCT
ap-1418	20	11	at	at	ADP
ap-1418	20	12	small	small	ADJ
ap-1418	20	13	distances	distance	NOUN
ap-1418	20	14	,	,	PUNCT
ap-1418	20	15	the	the	DET
ap-1418	20	16	atoms	atom	NOUN
ap-1418	20	17	still	still	ADV
ap-1418	20	18	interact	interact	VERB
ap-1418	20	19	via	via	ADP
ap-1418	20	20	the	the	DET
ap-1418	20	21	short	short	ADJ
ap-1418	20	22	-	-	PUNCT
ap-1418	20	23	range	range	NOUN
ap-1418	20	24	van	van	PROPN
ap-1418	20	25	der	der	NOUN
ap-1418	20	26	waals	waal	NOUN
ap-1418	20	27	force	force	NOUN
ap-1418	20	28	,	,	PUNCT
ap-1418	20	29	whose	whose	DET
ap-1418	20	30	action	action	NOUN
ap-1418	20	31	can	can	AUX
ap-1418	20	32	be	be	AUX
ap-1418	20	33	simulated	simulate	VERB
ap-1418	20	34	by	by	ADP
ap-1418	20	35	a	a	DET
ap-1418	20	36	short	short	ADJ
ap-1418	20	37	-	-	PUNCT
ap-1418	20	38	range	range	NOUN
ap-1418	20	39	isotropic	isotropic	NOUN
ap-1418	20	40	s	s	PART
ap-1418	20	41	-	-	PUNCT
ap-1418	20	42	wave	wave	NOUN
ap-1418	20	43	scattering	scatter	VERB
ap-1418	20	44	contact	contact	NOUN
ap-1418	20	45	potential	potential	NOUN
ap-1418	20	46	vs(r	vs(r	NOUN
ap-1418	20	47	,	,	PUNCT
ap-1418	20	48	r′	r′	NUM
ap-1418	20	49	)	)	PUNCT
ap-1418	21	1	=	=	NOUN
ap-1418	21	2	4πah̄2	4πah̄2	X
ap-1418	21	3	m	m	VERB
ap-1418	21	4	δ(r−	δ(r−	PROPN
ap-1418	21	5	r′	r′	NUM
ap-1418	21	6	)	)	PUNCT
ap-1418	21	7	,	,	PUNCT
ap-1418	21	8	where	where	SCONJ
ap-1418	21	9	a	a	PRON
ap-1418	21	10	is	be	AUX
ap-1418	21	11	the	the	DET
ap-1418	21	12	s	s	NOUN
ap-1418	21	13	-	-	PUNCT
ap-1418	21	14	wave	wave	NOUN
ap-1418	21	15	scattering	scattering	NOUN
ap-1418	21	16	length	length	NOUN
ap-1418	21	17	.	.	PUNCT
ap-1418	22	1	the	the	DET
ap-1418	22	2	latter	latter	ADJ
ap-1418	22	3	can	can	AUX
ap-1418	22	4	be	be	AUX
ap-1418	22	5	tuned	tune	VERB
ap-1418	22	6	,	,	PUNCT
ap-1418	22	7	using	use	VERB
ap-1418	22	8	feshbach	feshbach	NOUN
ap-1418	22	9	resonances	resonance	NOUN
ap-1418	22	10	of	of	ADP
ap-1418	22	11	hyperfine	hyperfine	ADJ
ap-1418	22	12	levels	level	NOUN
ap-1418	22	13	and	and	CCONJ
ap-1418	22	14	changing	change	VERB
ap-1418	22	15	the	the	DET
ap-1418	22	16	applied	apply	VERB
ap-1418	22	17	magnetic	magnetic	ADJ
ap-1418	22	18	field	field	NOUN
ap-1418	22	19	,	,	PUNCT
ap-1418	22	20	from	from	ADP
ap-1418	22	21	positive	positive	ADJ
ap-1418	22	22	values	value	NOUN
ap-1418	22	23	(	(	PUNCT
ap-1418	22	24	repulsive	repulsive	ADJ
ap-1418	22	25	interaction	interaction	NOUN
ap-1418	22	26	)	)	PUNCT
ap-1418	22	27	to	to	ADP
ap-1418	22	28	negative	negative	ADJ
ap-1418	22	29	values	value	NOUN
ap-1418	22	30	(	(	PUNCT
ap-1418	22	31	attractive	attractive	ADJ
ap-1418	22	32	interaction	interaction	NOUN
ap-1418	22	33	)	)	PUNCT
ap-1418	22	34	,	,	PUNCT
ap-1418	22	35	until	until	SCONJ
ap-1418	22	36	the	the	DET
ap-1418	22	37	interaction	interaction	NOUN
ap-1418	22	38	becomes	become	VERB
ap-1418	22	39	so	so	ADV
ap-1418	22	40	attractive	attractive	ADJ
ap-1418	22	41	that	that	SCONJ
ap-1418	22	42	the	the	DET
ap-1418	22	43	condensates	condensate	NOUN
ap-1418	22	44	collapse	collapse	NOUN
ap-1418	22	45	.	.	PUNCT
ap-1418	23	1	in	in	ADP
ap-1418	23	2	this	this	DET
ap-1418	23	3	paper	paper	NOUN
ap-1418	23	4	we	we	PRON
ap-1418	23	5	will	will	AUX
ap-1418	23	6	be	be	AUX
ap-1418	23	7	concerned	concern	VERB
ap-1418	23	8	with	with	ADP
ap-1418	23	9	boseeinstein	boseeinstein	NOUN
ap-1418	23	10	condensates	condensate	NOUN
ap-1418	23	11	where	where	SCONJ
ap-1418	23	12	an	an	DET
ap-1418	23	13	additional	additional	ADJ
ap-1418	23	14	long	long	ADJ
ap-1418	23	15	-	-	PUNCT
ap-1418	23	16	range	range	NOUN
ap-1418	23	17	atom	atom	NOUN
ap-1418	23	18	-	-	PUNCT
ap-1418	23	19	atom	atom	NOUN
ap-1418	23	20	interaction	interaction	NOUN
ap-1418	23	21	is	be	AUX
ap-1418	23	22	active	active	ADJ
ap-1418	23	23	.	.	PUNCT
ap-1418	24	1	an	an	DET
ap-1418	24	2	example	example	NOUN
ap-1418	24	3	is	be	AUX
ap-1418	24	4	boseeinstein	boseeinstein	NOUN
ap-1418	24	5	condensation	condensation	NOUN
ap-1418	24	6	of	of	ADP
ap-1418	24	7	52cr	52cr	ADJ
ap-1418	24	8	atoms	atom	NOUN
ap-1418	24	9	(	(	PUNCT
ap-1418	24	10	griesmeier	griesmeier	NOUN
ap-1418	24	11	et	et	PROPN
ap-1418	24	12	al	al	PROPN
ap-1418	24	13	.	.	PUNCT
ap-1418	25	1	[	[	X
ap-1418	25	2	5	5	NUM
ap-1418	25	3	]	]	PUNCT
ap-1418	25	4	,	,	PUNCT
ap-1418	25	5	koch	koch	PROPN
ap-1418	25	6	et	et	PROPN
ap-1418	25	7	al	al	PROPN
ap-1418	25	8	.	.	PUNCT
ap-1418	26	1	[	[	X
ap-1418	26	2	6	6	NUM
ap-1418	26	3	]	]	PUNCT
ap-1418	26	4	)	)	PUNCT
ap-1418	26	5	,	,	PUNCT
ap-1418	26	6	with	with	ADP
ap-1418	26	7	a	a	DET
ap-1418	26	8	large	large	ADJ
ap-1418	26	9	magnetic	magnetic	ADJ
ap-1418	26	10	moment	moment	NOUN
ap-1418	26	11	of	of	ADP
ap-1418	26	12	μ	μ	PROPN
ap-1418	26	13	=	=	SYM
ap-1418	26	14	6μb	6μb	NOUN
ap-1418	26	15	,	,	PUNCT
ap-1418	26	16	so	so	SCONJ
ap-1418	26	17	that	that	SCONJ
ap-1418	26	18	the	the	DET
ap-1418	26	19	atoms	atom	NOUN
ap-1418	26	20	interact	interact	VERB
ap-1418	26	21	via	via	ADP
ap-1418	26	22	the	the	DET
ap-1418	26	23	dipole	dipole	NOUN
ap-1418	26	24	-	-	PUNCT
ap-1418	26	25	dipole	dipole	NOUN
ap-1418	26	26	interaction	interaction	NOUN
ap-1418	26	27	over	over	ADP
ap-1418	26	28	large	large	ADJ
ap-1418	26	29	distances	distance	NOUN
ap-1418	26	30	.	.	PUNCT
ap-1418	27	1	in	in	ADP
ap-1418	27	2	these	these	DET
ap-1418	27	3	condensates	condensate	NOUN
ap-1418	27	4	the	the	DET
ap-1418	27	5	possibility	possibility	NOUN
ap-1418	27	6	of	of	ADP
ap-1418	27	7	tuning	tune	VERB
ap-1418	27	8	the	the	DET
ap-1418	27	9	relative	relative	ADJ
ap-1418	27	10	strengths	strength	NOUN
ap-1418	27	11	of	of	ADP
ap-1418	27	12	the	the	DET
ap-1418	27	13	short	short	ADJ
ap-1418	27	14	-	-	PUNCT
ap-1418	27	15	range	range	NOUN
ap-1418	27	16	interaction	interaction	NOUN
ap-1418	27	17	and	and	CCONJ
ap-1418	27	18	the	the	DET
ap-1418	27	19	long	long	ADJ
ap-1418	27	20	-	-	PUNCT
ap-1418	27	21	range	range	NOUN
ap-1418	27	22	interaction	interaction	NOUN
ap-1418	27	23	has	have	AUX
ap-1418	27	24	opened	open	VERB
ap-1418	27	25	the	the	DET
ap-1418	27	26	way	way	NOUN
ap-1418	27	27	to	to	ADP
ap-1418	27	28	a	a	DET
ap-1418	27	29	variety	variety	NOUN
ap-1418	27	30	of	of	ADP
ap-1418	27	31	new	new	ADJ
ap-1418	27	32	phenomena	phenomenon	NOUN
ap-1418	27	33	(	(	PUNCT
ap-1418	27	34	see	see	VERB
ap-1418	27	35	,	,	PUNCT
ap-1418	27	36	e.g.	e.g.	ADV
ap-1418	27	37	,	,	PUNCT
ap-1418	27	38	the	the	DET
ap-1418	27	39	review	review	NOUN
ap-1418	27	40	article	article	NOUN
ap-1418	27	41	by	by	ADP
ap-1418	27	42	lahaye	lahaye	NOUN
ap-1418	27	43	et	et	PROPN
ap-1418	27	44	al	al	PROPN
ap-1418	27	45	.	.	PUNCT
ap-1418	28	1	[	[	X
ap-1418	28	2	7	7	NUM
ap-1418	28	3	]	]	NUM
ap-1418	28	4	)	)	PUNCT
ap-1418	28	5	.	.	PUNCT
ap-1418	29	1	furthermore	furthermore	ADV
ap-1418	29	2	,	,	PUNCT
ap-1418	29	3	the	the	DET
ap-1418	29	4	stability	stability	NOUN
ap-1418	29	5	of	of	ADP
ap-1418	29	6	these	these	DET
ap-1418	29	7	condensates	condensate	NOUN
ap-1418	29	8	depends	depend	VERB
ap-1418	29	9	strongly	strongly	ADV
ap-1418	29	10	on	on	ADP
ap-1418	29	11	the	the	DET
ap-1418	29	12	trap	trap	NOUN
ap-1418	29	13	geometry	geometry	NOUN
ap-1418	29	14	.	.	PUNCT
ap-1418	30	1	the	the	DET
ap-1418	30	2	atoms	atom	NOUN
ap-1418	30	3	are	be	AUX
ap-1418	30	4	aligned	align	VERB
ap-1418	30	5	by	by	ADP
ap-1418	30	6	an	an	DET
ap-1418	30	7	external	external	ADJ
ap-1418	30	8	magnetic	magnetic	ADJ
ap-1418	30	9	field	field	NOUN
ap-1418	30	10	in	in	ADP
ap-1418	30	11	the	the	DET
ap-1418	30	12	z	z	NOUN
ap-1418	30	13	direction	direction	NOUN
ap-1418	30	14	.	.	PUNCT
ap-1418	31	1	if	if	SCONJ
ap-1418	31	2	the	the	DET
ap-1418	31	3	confinement	confinement	NOUN
ap-1418	31	4	in	in	ADP
ap-1418	31	5	the	the	DET
ap-1418	31	6	z	z	NOUN
ap-1418	31	7	direction	direction	NOUN
ap-1418	31	8	is	be	AUX
ap-1418	31	9	stronger	strong	ADJ
ap-1418	31	10	than	than	ADP
ap-1418	31	11	perpendicular	perpendicular	ADJ
ap-1418	31	12	to	to	ADP
ap-1418	31	13	it	it	PRON
ap-1418	31	14	(	(	PUNCT
ap-1418	31	15	if	if	SCONJ
ap-1418	31	16	the	the	DET
ap-1418	31	17	aspect	aspect	NOUN
ap-1418	31	18	ratio	ratio	NOUN
ap-1418	31	19	λ	λ	PROPN
ap-1418	31	20	of	of	ADP
ap-1418	31	21	the	the	DET
ap-1418	31	22	trapping	trap	VERB
ap-1418	31	23	frequencies	frequency	NOUN
ap-1418	31	24	ωz	ωz	ADP
ap-1418	31	25	/	/	SYM
ap-1418	31	26	ω	ω	NUM
ap-1418	31	27	�	�	PROPN
ap-1418	31	28	is	be	AUX
ap-1418	31	29	greater	great	ADJ
ap-1418	31	30	than	than	ADP
ap-1418	31	31	one	one	NUM
ap-1418	31	32	)	)	PUNCT
ap-1418	31	33	,	,	PUNCT
ap-1418	31	34	the	the	DET
ap-1418	31	35	condensate	condensate	NOUN
ap-1418	31	36	assumes	assume	VERB
ap-1418	31	37	an	an	DET
ap-1418	31	38	oblate	oblate	ADJ
ap-1418	31	39	shape	shape	NOUN
ap-1418	31	40	and	and	CCONJ
ap-1418	31	41	the	the	DET
ap-1418	31	42	dipole	dipole	NOUN
ap-1418	31	43	-	-	PUNCT
ap-1418	31	44	dipole	dipole	NOUN
ap-1418	31	45	interaction	interaction	NOUN
ap-1418	31	46	acts	act	VERB
ap-1418	31	47	predominantly	predominantly	ADV
ap-1418	31	48	repulsive	repulsive	ADJ
ap-1418	31	49	,	,	PUNCT
ap-1418	31	50	while	while	SCONJ
ap-1418	31	51	for	for	ADP
ap-1418	31	52	λ	λ	PROPN
ap-1418	31	53	<	<	X
ap-1418	31	54	1	1	NUM
ap-1418	31	55	the	the	DET
ap-1418	31	56	shape	shape	NOUN
ap-1418	31	57	is	be	AUX
ap-1418	31	58	prolate	prolate	ADJ
ap-1418	31	59	,	,	PUNCT
ap-1418	31	60	the	the	DET
ap-1418	31	61	atoms	atom	NOUN
ap-1418	31	62	are	be	AUX
ap-1418	31	63	arranged	arrange	VERB
ap-1418	31	64	in	in	ADP
ap-1418	31	65	the	the	DET
ap-1418	31	66	favoured	favour	VERB
ap-1418	31	67	head	head	NOUN
ap-1418	31	68	-	-	PUNCT
ap-1418	31	69	to	to	ADP
ap-1418	31	70	-	-	PUNCT
ap-1418	31	71	tail	tail	NOUN
ap-1418	31	72	configuration	configuration	NOUN
ap-1418	31	73	,	,	PUNCT
ap-1418	31	74	and	and	CCONJ
ap-1418	31	75	the	the	DET
ap-1418	31	76	interaction	interaction	NOUN
ap-1418	31	77	acts	act	VERB
ap-1418	31	78	attractive	attractive	ADJ
ap-1418	31	79	.	.	PUNCT
ap-1418	32	1	as	as	ADP
ap-1418	32	2	an	an	DET
ap-1418	32	3	alternative	alternative	ADJ
ap-1418	32	4	system	system	NOUN
ap-1418	32	5	,	,	PUNCT
ap-1418	32	6	o’dell	o’dell	ADV
ap-1418	32	7	et	et	NOUN
ap-1418	32	8	al	al	PROPN
ap-1418	32	9	.	.	PUNCT
ap-1418	33	1	[	[	X
ap-1418	33	2	8	8	NUM
ap-1418	33	3	]	]	PUNCT
ap-1418	33	4	have	have	AUX
ap-1418	33	5	proposed	propose	VERB
ap-1418	33	6	bose	bose	NOUN
ap-1418	33	7	-	-	PUNCT
ap-1418	33	8	einstein	einstein	NOUN
ap-1418	33	9	condensation	condensation	NOUN
ap-1418	33	10	of	of	ADP
ap-1418	33	11	neutral	neutral	ADJ
ap-1418	33	12	atoms	atom	NOUN
ap-1418	33	13	with	with	ADP
ap-1418	33	14	an	an	DET
ap-1418	33	15	electromagnetically	electromagnetically	ADV
ap-1418	33	16	induced	induce	VERB
ap-1418	33	17	attractive	attractive	ADJ
ap-1418	33	18	long	long	ADJ
ap-1418	33	19	-	-	PUNCT
ap-1418	33	20	range	range	NOUN
ap-1418	33	21	1	1	NUM
ap-1418	33	22	/	/	SYM
ap-1418	33	23	r	r	NOUN
ap-1418	33	24	interaction	interaction	NOUN
ap-1418	33	25	.	.	PUNCT
ap-1418	34	1	in	in	ADP
ap-1418	34	2	their	their	PRON
ap-1418	34	3	proposal	proposal	NOUN
ap-1418	34	4	,	,	PUNCT
ap-1418	34	5	6	6	NUM
ap-1418	34	6	“	"	PUNCT
ap-1418	34	7	triads	triad	NOUN
ap-1418	34	8	”	"	PUNCT
ap-1418	34	9	of	of	ADP
ap-1418	34	10	intense	intense	ADJ
ap-1418	34	11	off	off	ADJ
ap-1418	34	12	-	-	PUNCT
ap-1418	34	13	resonant	resonant	NOUN
ap-1418	34	14	laser	laser	NOUN
ap-1418	34	15	beams	beam	NOUN
ap-1418	34	16	average	average	VERB
ap-1418	34	17	out	out	ADP
ap-1418	34	18	1	1	NUM
ap-1418	34	19	/	/	SYM
ap-1418	34	20	r3	r3	NOUN
ap-1418	34	21	interactions	interaction	NOUN
ap-1418	34	22	in	in	ADP
ap-1418	34	23	the	the	DET
ap-1418	34	24	near	near	ADJ
ap-1418	34	25	-	-	PUNCT
ap-1418	34	26	zone	zone	NOUN
ap-1418	34	27	limit	limit	NOUN
ap-1418	34	28	of	of	ADP
ap-1418	34	29	the	the	DET
ap-1418	34	30	retarded	retarded	ADJ
ap-1418	34	31	dipole	dipole	NOUN
ap-1418	34	32	-	-	PUNCT
ap-1418	34	33	dipole	dipole	NOUN
ap-1418	34	34	interaction	interaction	NOUN
ap-1418	34	35	of	of	ADP
ap-1418	34	36	the	the	DET
ap-1418	34	37	atoms	atom	NOUN
ap-1418	34	38	produced	produce	VERB
ap-1418	34	39	by	by	ADP
ap-1418	34	40	the	the	DET
ap-1418	34	41	irradiation	irradiation	NOUN
ap-1418	34	42	,	,	PUNCT
ap-1418	34	43	while	while	SCONJ
ap-1418	34	44	the	the	DET
ap-1418	34	45	weaker	weak	ADJ
ap-1418	34	46	1	1	NUM
ap-1418	34	47	/	/	SYM
ap-1418	34	48	r	r	NOUN
ap-1418	34	49	95	95	NUM
ap-1418	34	50	acta	acta	PROPN
ap-1418	34	51	polytechnica	polytechnica	PROPN
ap-1418	34	52	vol	vol	NOUN
ap-1418	34	53	.	.	PUNCT
ap-1418	35	1	51	51	NUM
ap-1418	35	2	no	no	INTJ
ap-1418	35	3	.	.	PUNCT
ap-1418	36	1	4/2011	4/2011	NUM
ap-1418	36	2	interaction	interaction	NOUN
ap-1418	36	3	is	be	AUX
ap-1418	36	4	retained	retain	VERB
ap-1418	36	5	.	.	PUNCT
ap-1418	37	1	the	the	DET
ap-1418	37	2	novel	novel	ADJ
ap-1418	37	3	feature	feature	NOUN
ap-1418	37	4	of	of	ADP
ap-1418	37	5	these	these	DET
ap-1418	37	6	condensates	condensate	NOUN
ap-1418	37	7	is	be	AUX
ap-1418	37	8	that	that	SCONJ
ap-1418	37	9	the	the	DET
ap-1418	37	10	atoms	atom	NOUN
ap-1418	37	11	can	can	AUX
ap-1418	37	12	be	be	AUX
ap-1418	37	13	self	self	NOUN
ap-1418	37	14	-	-	PUNCT
ap-1418	37	15	trapped	trap	VERB
ap-1418	37	16	,	,	PUNCT
ap-1418	37	17	without	without	ADP
ap-1418	37	18	an	an	DET
ap-1418	37	19	external	external	ADJ
ap-1418	37	20	trap	trap	NOUN
ap-1418	37	21	.	.	PUNCT
ap-1418	38	1	on	on	ADP
ap-1418	38	2	the	the	DET
ap-1418	38	3	theoretical	theoretical	ADJ
ap-1418	38	4	side	side	NOUN
ap-1418	38	5	,	,	PUNCT
ap-1418	38	6	the	the	DET
ap-1418	38	7	advantage	advantage	NOUN
ap-1418	38	8	is	be	AUX
ap-1418	38	9	that	that	SCONJ
ap-1418	38	10	for	for	SCONJ
ap-1418	38	11	self	self	NOUN
ap-1418	38	12	-	-	PUNCT
ap-1418	38	13	trapping	trap	VERB
ap-1418	38	14	analytical	analytical	ADJ
ap-1418	38	15	variational	variational	ADJ
ap-1418	38	16	calculations	calculation	NOUN
ap-1418	38	17	are	be	AUX
ap-1418	38	18	possible	possible	ADJ
ap-1418	38	19	,	,	PUNCT
ap-1418	38	20	which	which	PRON
ap-1418	38	21	can	can	AUX
ap-1418	38	22	serve	serve	VERB
ap-1418	38	23	as	as	ADP
ap-1418	38	24	a	a	DET
ap-1418	38	25	guide	guide	NOUN
ap-1418	38	26	for	for	ADP
ap-1418	38	27	investigations	investigation	NOUN
ap-1418	38	28	of	of	ADP
ap-1418	38	29	more	more	ADJ
ap-1418	38	30	complex	complex	ADJ
ap-1418	38	31	situations	situation	NOUN
ap-1418	38	32	and	and	CCONJ
ap-1418	38	33	condensates	condensate	NOUN
ap-1418	38	34	with	with	ADP
ap-1418	38	35	other	other	ADJ
ap-1418	38	36	interatomic	interatomic	ADJ
ap-1418	38	37	interactions	interaction	NOUN
ap-1418	38	38	.	.	PUNCT
ap-1418	39	1	a	a	DET
ap-1418	39	2	theoretical	theoretical	ADJ
ap-1418	39	3	description	description	NOUN
ap-1418	39	4	of	of	ADP
ap-1418	39	5	condensates	condensate	NOUN
ap-1418	39	6	of	of	ADP
ap-1418	39	7	weakly	weakly	ADJ
ap-1418	39	8	interacting	interacting	ADJ
ap-1418	39	9	bosons	boson	NOUN
ap-1418	39	10	at	at	ADP
ap-1418	39	11	ultracold	ultracold	ADJ
ap-1418	39	12	temperatures	temperature	NOUN
ap-1418	39	13	can	can	AUX
ap-1418	39	14	be	be	AUX
ap-1418	39	15	performed	perform	VERB
ap-1418	39	16	within	within	ADP
ap-1418	39	17	a	a	DET
ap-1418	39	18	mean	mean	ADJ
ap-1418	39	19	-	-	PUNCT
ap-1418	39	20	field	field	NOUN
ap-1418	39	21	picture	picture	NOUN
ap-1418	39	22	by	by	ADP
ap-1418	39	23	the	the	DET
ap-1418	39	24	grosspitaevskii	grosspitaevskii	ADJ
ap-1418	39	25	equation	equation	NOUN
ap-1418	39	26	.	.	PUNCT
ap-1418	40	1	this	this	DET
ap-1418	40	2	equation	equation	NOUN
ap-1418	40	3	can	can	AUX
ap-1418	40	4	be	be	AUX
ap-1418	40	5	considered	consider	VERB
ap-1418	40	6	as	as	ADP
ap-1418	40	7	the	the	DET
ap-1418	40	8	hartree	hartree	ADJ
ap-1418	40	9	equation	equation	NOUN
ap-1418	40	10	for	for	ADP
ap-1418	40	11	the	the	DET
ap-1418	40	12	single	single	ADJ
ap-1418	40	13	particle	particle	NOUN
ap-1418	40	14	orbital	orbital	ADJ
ap-1418	40	15	ψ(r	ψ(r	NOUN
ap-1418	40	16	)	)	PUNCT
ap-1418	40	17	which	which	PRON
ap-1418	40	18	all	all	DET
ap-1418	40	19	atoms	atom	NOUN
ap-1418	40	20	occupy	occupy	VERB
ap-1418	40	21	.	.	PUNCT
ap-1418	41	1	it	it	PRON
ap-1418	41	2	is	be	AUX
ap-1418	41	3	a	a	DET
ap-1418	41	4	nonlinear	nonlinear	ADJ
ap-1418	41	5	schrödinger	schrödinger	NOUN
ap-1418	41	6	equation	equation	NOUN
ap-1418	41	7	,	,	PUNCT
ap-1418	41	8	and	and	CCONJ
ap-1418	41	9	therefore	therefore	ADV
ap-1418	41	10	phenomena	phenomena	VERB
ap-1418	41	11	not	not	PART
ap-1418	41	12	present	present	ADJ
ap-1418	41	13	in	in	ADP
ap-1418	41	14	linear	linear	ADJ
ap-1418	41	15	quantum	quantum	ADJ
ap-1418	41	16	mechnics	mechnic	NOUN
ap-1418	41	17	appear	appear	VERB
ap-1418	41	18	.	.	PUNCT
ap-1418	42	1	for	for	ADP
ap-1418	42	2	example	example	NOUN
ap-1418	42	3	,	,	PUNCT
ap-1418	42	4	the	the	DET
ap-1418	42	5	superposition	superposition	NOUN
ap-1418	42	6	principle	principle	NOUN
ap-1418	42	7	is	be	AUX
ap-1418	42	8	no	no	ADV
ap-1418	42	9	longer	long	ADV
ap-1418	42	10	applicable	applicable	ADJ
ap-1418	42	11	to	to	ADP
ap-1418	42	12	the	the	DET
ap-1418	42	13	equation	equation	NOUN
ap-1418	42	14	.	.	PUNCT
ap-1418	43	1	for	for	ADP
ap-1418	43	2	bose	bose	NOUN
ap-1418	43	3	-	-	PUNCT
ap-1418	43	4	einstein	einstein	NOUN
ap-1418	43	5	condensates	condensate	NOUN
ap-1418	43	6	with	with	ADP
ap-1418	43	7	gravity	gravity	NOUN
ap-1418	43	8	-	-	PUNCT
ap-1418	43	9	like	like	ADJ
ap-1418	43	10	long	long	ADJ
ap-1418	43	11	-	-	PUNCT
ap-1418	43	12	range	range	NOUN
ap-1418	43	13	interaction	interaction	NOUN
ap-1418	43	14	vu(r	vu(r	NOUN
ap-1418	43	15	,	,	PUNCT
ap-1418	43	16	r	r	NOUN
ap-1418	43	17	′	′	NOUN
ap-1418	43	18	)	)	PUNCT
ap-1418	43	19	=	=	SYM
ap-1418	44	1	−u/|r−	−u/|r−	ADJ
ap-1418	44	2	r	r	NOUN
ap-1418	44	3	′|	′|	NUM
ap-1418	44	4	(	(	PUNCT
ap-1418	44	5	“	"	PUNCT
ap-1418	44	6	monopolar	monopolar	ADJ
ap-1418	44	7	condensates	condensate	NOUN
ap-1418	44	8	”	"	PUNCT
ap-1418	44	9	,	,	PUNCT
ap-1418	44	10	u	u	PRON
ap-1418	44	11	describes	describe	VERB
ap-1418	44	12	the	the	DET
ap-1418	44	13	strength	strength	NOUN
ap-1418	44	14	of	of	ADP
ap-1418	44	15	the	the	DET
ap-1418	44	16	interaction	interaction	NOUN
ap-1418	44	17	)	)	PUNCT
ap-1418	44	18	the	the	DET
ap-1418	44	19	gross	gross	ADJ
ap-1418	44	20	-	-	PUNCT
ap-1418	44	21	pitaevskii	pitaevskii	ADJ
ap-1418	44	22	equation	equation	NOUN
ap-1418	44	23	reads	read	VERB
ap-1418	44	24	{	{	PUNCT
ap-1418	44	25	−δ	−δ	ADJ
ap-1418	44	26	+	+	CCONJ
ap-1418	44	27	γ2r2	γ2r2	X
ap-1418	44	28	+	+	CCONJ
ap-1418	44	29	n8π	n8π	X
ap-1418	44	30	a	a	DET
ap-1418	44	31	au	au	ADJ
ap-1418	44	32	|ψ(r)|2	|ψ(r)|2	NUM
ap-1418	44	33	−	−	PROPN
ap-1418	44	34	(	(	PUNCT
ap-1418	44	35	1	1	NUM
ap-1418	44	36	)	)	PUNCT
ap-1418	44	37	2n	2n	NUM
ap-1418	44	38	∫	∫	PROPN
ap-1418	44	39	|ψ(r′)|2	|ψ(r′)|2	PROPN
ap-1418	44	40	|r−	|r−	PROPN
ap-1418	44	41	r′|	r′|	VERB
ap-1418	44	42	d3r′	d3r′	NOUN
ap-1418	44	43	}	}	PUNCT
ap-1418	44	44	ψ(r	ψ(r	PROPN
ap-1418	44	45	)	)	PUNCT
ap-1418	44	46	=	=	SYM
ap-1418	44	47	ih̄	ih̄	NOUN
ap-1418	44	48	∂ψ(r	∂ψ(r	PROPN
ap-1418	44	49	)	)	PUNCT
ap-1418	44	50	∂t	∂t	PROPN
ap-1418	44	51	.	.	PUNCT
ap-1418	45	1	here	here	ADV
ap-1418	45	2	γ	γ	X
ap-1418	45	3	=	=	SYM
ap-1418	45	4	h̄ω0	h̄ω0	PROPN
ap-1418	45	5	/	/	SYM
ap-1418	45	6	eu	eu	PROPN
ap-1418	45	7	is	be	AUX
ap-1418	45	8	the	the	DET
ap-1418	45	9	trapping	trap	VERB
ap-1418	45	10	frequency	frequency	NOUN
ap-1418	45	11	measured	measure	VERB
ap-1418	45	12	in	in	ADP
ap-1418	45	13	the	the	DET
ap-1418	45	14	time	time	NOUN
ap-1418	45	15	scale	scale	NOUN
ap-1418	45	16	given	give	VERB
ap-1418	45	17	by	by	ADP
ap-1418	45	18	the	the	DET
ap-1418	45	19	“	"	PUNCT
ap-1418	45	20	rydberg	rydberg	PROPN
ap-1418	45	21	”	"	PUNCT
ap-1418	45	22	energy	energy	NOUN
ap-1418	45	23	eu	eu	PROPN
ap-1418	45	24	associated	associate	VERB
ap-1418	45	25	with	with	ADP
ap-1418	45	26	the	the	DET
ap-1418	45	27	strength	strength	NOUN
ap-1418	45	28	of	of	ADP
ap-1418	45	29	the	the	DET
ap-1418	45	30	1	1	NUM
ap-1418	45	31	/	/	SYM
ap-1418	45	32	r	r	NOUN
ap-1418	45	33	interaction	interaction	NOUN
ap-1418	45	34	,	,	PUNCT
ap-1418	45	35	n	n	X
ap-1418	45	36	is	be	AUX
ap-1418	45	37	the	the	DET
ap-1418	45	38	particle	particle	NOUN
ap-1418	45	39	number	number	NOUN
ap-1418	45	40	,	,	PUNCT
ap-1418	45	41	and	and	CCONJ
ap-1418	45	42	a	a	DET
ap-1418	45	43	/	/	SYM
ap-1418	45	44	au	au	X
ap-1418	45	45	the	the	DET
ap-1418	45	46	scattering	scatter	VERB
ap-1418	45	47	length	length	NOUN
ap-1418	45	48	in	in	ADP
ap-1418	45	49	units	unit	NOUN
ap-1418	45	50	of	of	ADP
ap-1418	45	51	the	the	DET
ap-1418	45	52	“	"	PUNCT
ap-1418	45	53	bohr	bohr	PROPN
ap-1418	45	54	”	"	PUNCT
ap-1418	45	55	radius	radius	NOUN
ap-1418	45	56	au	au	PROPN
ap-1418	45	57	.	.	PUNCT
ap-1418	46	1	it	it	PRON
ap-1418	46	2	can	can	AUX
ap-1418	46	3	be	be	AUX
ap-1418	46	4	shown	show	VERB
ap-1418	46	5	[	[	PUNCT
ap-1418	46	6	9	9	X
ap-1418	46	7	]	]	PUNCT
ap-1418	46	8	that	that	SCONJ
ap-1418	46	9	the	the	DET
ap-1418	46	10	equation	equation	NOUN
ap-1418	46	11	effectively	effectively	ADV
ap-1418	46	12	depends	depend	VERB
ap-1418	46	13	only	only	ADV
ap-1418	46	14	on	on	ADP
ap-1418	46	15	two	two	NUM
ap-1418	46	16	physical	physical	ADJ
ap-1418	46	17	parameters	parameter	NOUN
ap-1418	46	18	,	,	PUNCT
ap-1418	46	19	viz	viz	PROPN
ap-1418	46	20	.	.	PUNCT
ap-1418	47	1	the	the	DET
ap-1418	47	2	particle	particle	NOUN
ap-1418	47	3	number	number	NOUN
ap-1418	47	4	scaled	scale	VERB
ap-1418	47	5	quantities	quantity	NOUN
ap-1418	47	6	n2a	n2a	NOUN
ap-1418	47	7	/	/	SYM
ap-1418	47	8	au	au	X
ap-1418	47	9	and	and	CCONJ
ap-1418	47	10	γ	γ	X
ap-1418	47	11	/	/	SYM
ap-1418	47	12	n2	n2	NOUN
ap-1418	47	13	.	.	PUNCT
ap-1418	48	1	for	for	ADP
ap-1418	48	2	condensates	condensate	NOUN
ap-1418	48	3	with	with	ADP
ap-1418	48	4	dipole	dipole	NOUN
ap-1418	48	5	-	-	PUNCT
ap-1418	48	6	dipole	dipole	NOUN
ap-1418	48	7	interactions	interaction	NOUN
ap-1418	48	8	(	(	PUNCT
ap-1418	48	9	“	"	PUNCT
ap-1418	48	10	dipolar	dipolar	ADJ
ap-1418	48	11	condensates	condensate	NOUN
ap-1418	48	12	”	"	PUNCT
ap-1418	48	13	)	)	PUNCT
ap-1418	48	14	in	in	ADP
ap-1418	48	15	which	which	PRON
ap-1418	48	16	the	the	DET
ap-1418	48	17	atoms	atom	NOUN
ap-1418	48	18	are	be	AUX
ap-1418	48	19	spinpolarized	spinpolarize	VERB
ap-1418	48	20	in	in	ADP
ap-1418	48	21	the	the	DET
ap-1418	48	22	z	z	NOUN
ap-1418	48	23	direction	direction	NOUN
ap-1418	48	24	,	,	PUNCT
ap-1418	48	25	the	the	DET
ap-1418	48	26	gross	gross	ADJ
ap-1418	48	27	-	-	PUNCT
ap-1418	48	28	pitaevskii	pitaevskii	ADJ
ap-1418	48	29	equation	equation	NOUN
ap-1418	48	30	reads	read	VERB
ap-1418	48	31	{	{	PUNCT
ap-1418	48	32	−	−	PROPN
ap-1418	48	33	δ	δ	PROPN
ap-1418	48	34	+	+	CCONJ
ap-1418	48	35	γ2ρρ2	γ2ρρ2	NOUN
ap-1418	48	36	+	+	CCONJ
ap-1418	48	37	γ2zz2	γ2zz2	ADV
ap-1418	48	38	+	+	CCONJ
ap-1418	48	39	n8π	n8π	PROPN
ap-1418	48	40	a	a	DET
ap-1418	48	41	ad	ad	NOUN
ap-1418	48	42	|ψ(r)|2	|ψ(r)|2	NOUN
ap-1418	48	43	+	+	CCONJ
ap-1418	48	44	n	n	NUM
ap-1418	48	45	∫	∫	PROPN
ap-1418	48	46	|ψ(r	|ψ(r	PROPN
ap-1418	48	47	′)|2	′)|2	PROPN
ap-1418	48	48	(	(	PUNCT
ap-1418	48	49	1	1	NUM
ap-1418	48	50	−	−	NUM
ap-1418	48	51	3	3	NUM
ap-1418	48	52	cos2	cos2	PROPN
ap-1418	48	53	ϑ′	ϑ′	ADV
ap-1418	48	54	)	)	PUNCT
ap-1418	48	55	|r−	|r−	NOUN
ap-1418	48	56	r	r	NOUN
ap-1418	48	57	′|3	′|3	NOUN
ap-1418	48	58	d3r	d3r	ADJ
ap-1418	48	59	′	′	NUM
ap-1418	48	60	}	}	PUNCT
ap-1418	48	61	ψ(r	ψ(r	PROPN
ap-1418	48	62	)	)	PUNCT
ap-1418	48	63	=	=	PUNCT
ap-1418	48	64	(	(	PUNCT
ap-1418	48	65	2	2	NUM
ap-1418	48	66	)	)	PUNCT
ap-1418	48	67	ih̄	ih̄	NOUN
ap-1418	48	68	∂ψ(r	∂ψ(r	PROPN
ap-1418	48	69	)	)	PUNCT
ap-1418	49	1	∂t	∂t	PROPN
ap-1418	49	2	,	,	PUNCT
ap-1418	49	3	where	where	SCONJ
ap-1418	49	4	we	we	PRON
ap-1418	49	5	have	have	AUX
ap-1418	49	6	used	use	VERB
ap-1418	49	7	as	as	ADP
ap-1418	49	8	units	unit	NOUN
ap-1418	49	9	of	of	ADP
ap-1418	49	10	length	length	NOUN
ap-1418	49	11	,	,	PUNCT
ap-1418	49	12	energy	energy	NOUN
ap-1418	49	13	,	,	PUNCT
ap-1418	49	14	and	and	CCONJ
ap-1418	49	15	frequency	frequency	VERB
ap-1418	49	16	the	the	DET
ap-1418	49	17	quantities	quantity	NOUN
ap-1418	49	18	ad	ad	NOUN
ap-1418	49	19	=	=	SYM
ap-1418	49	20	μ0μ	μ0μ	PROPN
ap-1418	49	21	2m/(2πh̄2	2m/(2πh̄2	NUM
ap-1418	49	22	)	)	PUNCT
ap-1418	49	23	(	(	PUNCT
ap-1418	49	24	μ	μ	PROPN
ap-1418	49	25	is	be	AUX
ap-1418	49	26	the	the	DET
ap-1418	49	27	magnetic	magnetic	ADJ
ap-1418	49	28	moment	moment	NOUN
ap-1418	49	29	)	)	PUNCT
ap-1418	49	30	,	,	PUNCT
ap-1418	49	31	ed	ed	PROPN
ap-1418	49	32	=	=	SYM
ap-1418	49	33	h̄2/(2ma2d	h̄2/(2ma2d	PROPN
ap-1418	49	34	)	)	PUNCT
ap-1418	49	35	,	,	PUNCT
ap-1418	49	36	and	and	CCONJ
ap-1418	49	37	ωd	ωd	X
ap-1418	49	38	=	=	NOUN
ap-1418	49	39	ed	ed	NOUN
ap-1418	49	40	/	/	SYM
ap-1418	49	41	h̄	h̄	NOUN
ap-1418	49	42	,	,	PUNCT
ap-1418	49	43	respectively	respectively	ADV
ap-1418	49	44	.	.	PUNCT
ap-1418	50	1	again	again	ADV
ap-1418	50	2	it	it	PRON
ap-1418	50	3	can	can	AUX
ap-1418	50	4	be	be	AUX
ap-1418	50	5	shown	show	VERB
ap-1418	50	6	[	[	PUNCT
ap-1418	50	7	10	10	NUM
ap-1418	50	8	]	]	PUNCT
ap-1418	50	9	that	that	SCONJ
ap-1418	50	10	the	the	DET
ap-1418	50	11	equation	equation	NOUN
ap-1418	50	12	only	only	ADV
ap-1418	50	13	depends	depend	VERB
ap-1418	50	14	on	on	ADP
ap-1418	50	15	the	the	DET
ap-1418	50	16	three	three	NUM
ap-1418	50	17	scaled	scaled	ADJ
ap-1418	50	18	parameters	parameter	NOUN
ap-1418	50	19	n2γ̄	n2γ̄	NOUN
ap-1418	50	20	,	,	PUNCT
ap-1418	50	21	λ	λ	PROPN
ap-1418	50	22	,	,	PUNCT
ap-1418	50	23	a	a	DET
ap-1418	50	24	/	/	SYM
ap-1418	50	25	ad	ad	NOUN
ap-1418	50	26	(	(	PUNCT
ap-1418	50	27	or	or	CCONJ
ap-1418	50	28	alternatively	alternatively	ADV
ap-1418	50	29	n2γ̄	n2γ̄	PRON
ap-1418	50	30	=	=	PRON
ap-1418	50	31	γ2/3ρ	γ2/3ρ	NOUN
ap-1418	50	32	γ1/3z	γ1/3z	ADJ
ap-1418	50	33	,	,	PUNCT
ap-1418	50	34	λ	λ	X
ap-1418	50	35	=	=	PRON
ap-1418	50	36	γz	γz	PROPN
ap-1418	50	37	/	/	SYM
ap-1418	50	38	γρ	γρ	NOUN
ap-1418	50	39	)	)	PUNCT
ap-1418	50	40	.	.	PUNCT
ap-1418	51	1	equations	equation	NOUN
ap-1418	51	2	(	(	PUNCT
ap-1418	51	3	1	1	NUM
ap-1418	51	4	)	)	PUNCT
ap-1418	51	5	and	and	CCONJ
ap-1418	51	6	(	(	PUNCT
ap-1418	51	7	2	2	X
ap-1418	51	8	)	)	PUNCT
ap-1418	51	9	are	be	AUX
ap-1418	51	10	the	the	DET
ap-1418	51	11	starting	starting	NOUN
ap-1418	51	12	point	point	NOUN
ap-1418	51	13	for	for	ADP
ap-1418	51	14	the	the	DET
ap-1418	51	15	investigations	investigation	NOUN
ap-1418	51	16	below	below	ADV
ap-1418	51	17	.	.	PUNCT
ap-1418	52	1	2	2	NUM
ap-1418	52	2	monopolar	monopolar	NOUN
ap-1418	52	3	condensates	condensate	VERB
ap-1418	52	4	2.1	2.1	NUM
ap-1418	52	5	variational	variational	ADJ
ap-1418	52	6	results	result	NOUN
ap-1418	52	7	to	to	PART
ap-1418	52	8	find	find	VERB
ap-1418	52	9	stationary	stationary	ADJ
ap-1418	52	10	solutions	solution	NOUN
ap-1418	52	11	of	of	ADP
ap-1418	52	12	the	the	DET
ap-1418	52	13	gross	gross	ADJ
ap-1418	52	14	-	-	PUNCT
ap-1418	52	15	pitaevskii	pitaevskii	ADJ
ap-1418	52	16	equation	equation	NOUN
ap-1418	52	17	(	(	PUNCT
ap-1418	52	18	1	1	X
ap-1418	52	19	)	)	PUNCT
ap-1418	52	20	we	we	PRON
ap-1418	52	21	can	can	AUX
ap-1418	52	22	enter	enter	VERB
ap-1418	52	23	into	into	ADP
ap-1418	52	24	the	the	DET
ap-1418	52	25	corresponding	corresponding	ADJ
ap-1418	52	26	mean	mean	ADJ
ap-1418	52	27	-	-	PUNCT
ap-1418	52	28	field	field	NOUN
ap-1418	52	29	energy	energy	NOUN
ap-1418	52	30	functional	functional	ADJ
ap-1418	52	31	e[ψ	e[ψ	NOUN
ap-1418	52	32	]	]	PUNCT
ap-1418	52	33	=	=	SYM
ap-1418	52	34	n	n	NUM
ap-1418	52	35	∫	∫	PROPN
ap-1418	52	36	d3r	d3r	PROPN
ap-1418	52	37	ψ∗(r	ψ∗(r	PROPN
ap-1418	52	38	)	)	PUNCT
ap-1418	52	39	(	(	PUNCT
ap-1418	52	40	−δr	−δr	PROPN
ap-1418	52	41	+	+	CCONJ
ap-1418	52	42	γ2r2	γ2r2	X
ap-1418	52	43	+	+	NUM
ap-1418	52	44	4πn	4πn	ADJ
ap-1418	52	45	a	a	DET
ap-1418	52	46	au	au	ADJ
ap-1418	52	47	|ψ(r)|2	|ψ(r)|2	NUM
ap-1418	52	48	−	−	NUM
ap-1418	52	49	n	n	PRON
ap-1418	52	50	∫	∫	PROPN
ap-1418	52	51	d3r′	d3r′	PROPN
ap-1418	52	52	|ψ(r′)|2	|ψ(r′)|2	PROPN
ap-1418	52	53	|r−	|r−	NOUN
ap-1418	52	54	r′|	r′|	NOUN
ap-1418	52	55	)	)	PUNCT
ap-1418	52	56	ψ(r	ψ(r	PROPN
ap-1418	52	57	)	)	PUNCT
ap-1418	52	58	with	with	ADP
ap-1418	52	59	the	the	DET
ap-1418	52	60	gaussian	gaussian	ADJ
ap-1418	52	61	variational	variational	ADJ
ap-1418	52	62	ansatz	ansatz	ADJ
ap-1418	52	63	ψ(r	ψ(r	NOUN
ap-1418	52	64	)	)	PUNCT
ap-1418	52	65	=	=	PUNCT
ap-1418	52	66	a	a	DET
ap-1418	52	67	exp	exp	NOUN
ap-1418	52	68	(	(	PUNCT
ap-1418	52	69	−k2r2/2	−k2r2/2	PROPN
ap-1418	52	70	)	)	PUNCT
ap-1418	52	71	,	,	PUNCT
ap-1418	52	72	with	with	ADP
ap-1418	52	73	a	a	DET
ap-1418	52	74	=	=	X
ap-1418	52	75	(	(	PUNCT
ap-1418	52	76	k/	k/	NOUN
ap-1418	52	77	√	√	PROPN
ap-1418	52	78	π	π	PROPN
ap-1418	52	79	)	)	PUNCT
ap-1418	52	80	3/2	3/2	NUM
ap-1418	52	81	.	.	PUNCT
ap-1418	53	1	all	all	DET
ap-1418	53	2	integrals	integral	NOUN
ap-1418	53	3	,	,	PUNCT
ap-1418	53	4	including	include	VERB
ap-1418	53	5	the	the	DET
ap-1418	53	6	gravity	gravity	NOUN
ap-1418	53	7	-	-	PUNCT
ap-1418	53	8	like	like	ADJ
ap-1418	53	9	interaction	interaction	NOUN
ap-1418	53	10	integral	integral	ADJ
ap-1418	53	11	,	,	PUNCT
ap-1418	53	12	can	can	AUX
ap-1418	53	13	be	be	AUX
ap-1418	53	14	evaluated	evaluate	VERB
ap-1418	53	15	analytically	analytically	ADV
ap-1418	53	16	.	.	PUNCT
ap-1418	54	1	requiring	require	VERB
ap-1418	54	2	(	(	PUNCT
ap-1418	54	3	3	3	NUM
ap-1418	54	4	)	)	PUNCT
ap-1418	54	5	to	to	PART
ap-1418	54	6	become	become	VERB
ap-1418	54	7	stationary	stationary	ADJ
ap-1418	54	8	with	with	ADP
ap-1418	54	9	respect	respect	NOUN
ap-1418	54	10	to	to	ADP
ap-1418	54	11	variation	variation	NOUN
ap-1418	54	12	of	of	ADP
ap-1418	54	13	the	the	DET
ap-1418	54	14	width	width	NOUN
ap-1418	54	15	leads	lead	VERB
ap-1418	54	16	to	to	ADP
ap-1418	54	17	a	a	DET
ap-1418	54	18	quintic	quintic	ADJ
ap-1418	54	19	equation	equation	NOUN
ap-1418	54	20	for	for	ADP
ap-1418	54	21	k	k	PROPN
ap-1418	54	22	,	,	PUNCT
ap-1418	54	23	which	which	PRON
ap-1418	54	24	,	,	PUNCT
ap-1418	54	25	however	however	ADV
ap-1418	54	26	,	,	PUNCT
ap-1418	54	27	reduces	reduce	VERB
ap-1418	54	28	to	to	ADP
ap-1418	54	29	a	a	DET
ap-1418	54	30	simple	simple	ADJ
ap-1418	54	31	quadratic	quadratic	ADJ
ap-1418	54	32	equation	equation	NOUN
ap-1418	54	33	in	in	ADP
ap-1418	54	34	the	the	DET
ap-1418	54	35	special	special	ADJ
ap-1418	54	36	case	case	NOUN
ap-1418	54	37	γ	γ	X
ap-1418	54	38	=	=	SYM
ap-1418	54	39	0	0	NUM
ap-1418	54	40	,	,	PUNCT
ap-1418	54	41	i.e.	i.e.	X
ap-1418	54	42	,	,	PUNCT
ap-1418	54	43	for	for	ADP
ap-1418	54	44	a	a	DET
ap-1418	54	45	self	self	NOUN
ap-1418	54	46	-	-	PUNCT
ap-1418	54	47	trapping	trap	VERB
ap-1418	54	48	condensate	condensate	NOUN
ap-1418	54	49	.	.	PUNCT
ap-1418	55	1	the	the	DET
ap-1418	55	2	two	two	NUM
ap-1418	55	3	solutions	solution	NOUN
ap-1418	55	4	read	read	VERB
ap-1418	55	5	[	[	X
ap-1418	55	6	11	11	NUM
ap-1418	55	7	,	,	PUNCT
ap-1418	55	8	13	13	NUM
ap-1418	55	9	]	]	PUNCT
ap-1418	55	10	k±	k±	PROPN
ap-1418	56	1	=	=	SYM
ap-1418	57	1	1	1	NUM
ap-1418	57	2	2	2	NUM
ap-1418	57	3	√	√	NUM
ap-1418	57	4	π	π	PROPN
ap-1418	57	5	2	2	NUM
ap-1418	57	6	1	1	NUM
ap-1418	57	7	n	n	NOUN
ap-1418	57	8	a	a	DET
ap-1418	57	9	au	au	X
ap-1418	57	10	(	(	PUNCT
ap-1418	57	11	±	±	NOUN
ap-1418	57	12	√	√	ADV
ap-1418	57	13	1	1	NUM
ap-1418	57	14	+	+	CCONJ
ap-1418	57	15	8	8	NUM
ap-1418	57	16	3π	3π	NUM
ap-1418	57	17	n2	n2	NOUN
ap-1418	57	18	a	a	DET
ap-1418	57	19	au	au	ADJ
ap-1418	57	20	−	−	PROPN
ap-1418	57	21	1	1	NUM
ap-1418	57	22	)	)	PUNCT
ap-1418	57	23	,	,	PUNCT
ap-1418	57	24	(	(	PUNCT
ap-1418	57	25	3	3	X
ap-1418	57	26	)	)	PUNCT
ap-1418	57	27	where	where	SCONJ
ap-1418	57	28	the	the	DET
ap-1418	57	29	plus	plus	ADJ
ap-1418	57	30	sign	sign	NOUN
ap-1418	57	31	corresponds	correspond	VERB
ap-1418	57	32	to	to	ADP
ap-1418	57	33	a	a	DET
ap-1418	57	34	local	local	ADJ
ap-1418	57	35	minimum	minimum	NOUN
ap-1418	57	36	(	(	PUNCT
ap-1418	57	37	stable	stable	ADJ
ap-1418	57	38	ground	ground	NOUN
ap-1418	57	39	state	state	NOUN
ap-1418	57	40	of	of	ADP
ap-1418	57	41	the	the	DET
ap-1418	57	42	condensate	condensate	NOUN
ap-1418	57	43	)	)	PUNCT
ap-1418	57	44	and	and	CCONJ
ap-1418	57	45	the	the	DET
ap-1418	57	46	minus	minus	NOUN
ap-1418	57	47	sign	sign	NOUN
ap-1418	57	48	to	to	ADP
ap-1418	57	49	a	a	DET
ap-1418	57	50	local	local	ADJ
ap-1418	57	51	maximum	maximum	NOUN
ap-1418	57	52	(	(	PUNCT
ap-1418	57	53	collectively	collectively	ADV
ap-1418	57	54	excited	excited	ADJ
ap-1418	57	55	state	state	NOUN
ap-1418	57	56	of	of	ADP
ap-1418	57	57	the	the	DET
ap-1418	57	58	condensate	condensate	NOUN
ap-1418	57	59	)	)	PUNCT
ap-1418	57	60	of	of	ADP
ap-1418	57	61	the	the	DET
ap-1418	57	62	energy	energy	NOUN
ap-1418	57	63	.	.	PUNCT
ap-1418	58	1	from	from	ADP
ap-1418	58	2	(	(	PUNCT
ap-1418	58	3	3	3	X
ap-1418	58	4	)	)	PUNCT
ap-1418	58	5	it	it	PRON
ap-1418	58	6	can	can	AUX
ap-1418	58	7	be	be	AUX
ap-1418	58	8	seen	see	VERB
ap-1418	58	9	that	that	SCONJ
ap-1418	58	10	these	these	DET
ap-1418	58	11	solutions	solution	NOUN
ap-1418	58	12	only	only	ADV
ap-1418	58	13	exist	exist	VERB
ap-1418	58	14	for	for	ADP
ap-1418	58	15	n2a	n2a	PROPN
ap-1418	58	16	/	/	SYM
ap-1418	58	17	au	au	X
ap-1418	58	18	≥	≥	X
ap-1418	58	19	−3π/8	−3π/8	NUM
ap-1418	58	20	.	.	PUNCT
ap-1418	59	1	accurate	accurate	PROPN
ap-1418	59	2	numerical	numerical	ADJ
ap-1418	59	3	stationary	stationary	ADJ
ap-1418	59	4	solutions	solution	NOUN
ap-1418	59	5	of	of	ADP
ap-1418	59	6	(	(	PUNCT
ap-1418	59	7	1	1	X
ap-1418	59	8	)	)	PUNCT
ap-1418	59	9	can	can	AUX
ap-1418	59	10	be	be	AUX
ap-1418	59	11	determined	determine	VERB
ap-1418	59	12	by	by	ADP
ap-1418	59	13	direct	direct	ADJ
ap-1418	59	14	outward	outward	ADJ
ap-1418	59	15	integration	integration	NOUN
ap-1418	59	16	starting	start	VERB
ap-1418	59	17	with	with	ADP
ap-1418	59	18	suitable	suitable	ADJ
ap-1418	59	19	initial	initial	ADJ
ap-1418	59	20	conditions	condition	NOUN
ap-1418	59	21	at	at	ADP
ap-1418	59	22	r	r	NOUN
ap-1418	59	23	=	=	SYM
ap-1418	59	24	0	0	PUNCT
ap-1418	60	1	[	[	X
ap-1418	60	2	9	9	NUM
ap-1418	60	3	]	]	PUNCT
ap-1418	60	4	.	.	PUNCT
ap-1418	61	1	figure	figure	NOUN
ap-1418	61	2	1	1	NUM
ap-1418	61	3	compares	compare	VERB
ap-1418	61	4	the	the	DET
ap-1418	61	5	variational	variational	ADJ
ap-1418	61	6	and	and	CCONJ
ap-1418	61	7	numerically	numerically	ADV
ap-1418	61	8	exact	exact	ADJ
ap-1418	61	9	results	result	NOUN
ap-1418	61	10	for	for	ADP
ap-1418	61	11	the	the	DET
ap-1418	61	12	mean	mean	ADJ
ap-1418	61	13	-	-	PUNCT
ap-1418	61	14	field	field	NOUN
ap-1418	61	15	energy	energy	NOUN
ap-1418	61	16	and	and	CCONJ
ap-1418	61	17	the	the	DET
ap-1418	61	18	chemical	chemical	NOUN
ap-1418	61	19	potential	potential	NOUN
ap-1418	61	20	.	.	PUNCT
ap-1418	62	1	it	it	PRON
ap-1418	62	2	can	can	AUX
ap-1418	62	3	be	be	AUX
ap-1418	62	4	seen	see	VERB
ap-1418	62	5	that	that	SCONJ
ap-1418	62	6	the	the	DET
ap-1418	62	7	simple	simple	ADJ
ap-1418	62	8	gaussian	gaussian	NOUN
ap-1418	62	9	ansatz	ansatz	VERB
ap-1418	62	10	qualitatively	qualitatively	ADV
ap-1418	62	11	well	well	ADV
ap-1418	62	12	describes	describe	VERB
ap-1418	62	13	the	the	DET
ap-1418	62	14	overall	overall	ADJ
ap-1418	62	15	behaviour	behaviour	NOUN
ap-1418	62	16	:	:	PUNCT
ap-1418	62	17	both	both	PRON
ap-1418	62	18	in	in	ADP
ap-1418	62	19	the	the	DET
ap-1418	62	20	variational	variational	ADJ
ap-1418	62	21	calculations	calculation	NOUN
ap-1418	62	22	and	and	CCONJ
ap-1418	62	23	in	in	ADP
ap-1418	62	24	the	the	DET
ap-1418	62	25	numerical	numerical	ADJ
ap-1418	62	26	calculations	calculation	NOUN
ap-1418	62	27	two	two	NUM
ap-1418	62	28	solutions	solution	NOUN
ap-1418	62	29	are	be	AUX
ap-1418	62	30	born	bear	VERB
ap-1418	62	31	in	in	ADP
ap-1418	62	32	a	a	DET
ap-1418	62	33	tangent	tangent	ADJ
ap-1418	62	34	bifurcation	bifurcation	NOUN
ap-1418	62	35	at	at	ADP
ap-1418	62	36	a	a	DET
ap-1418	62	37	critical	critical	ADJ
ap-1418	62	38	negative	negative	ADJ
ap-1418	62	39	value	value	NOUN
ap-1418	62	40	of	of	ADP
ap-1418	62	41	the	the	DET
ap-1418	62	42	scattering	scattering	NOUN
ap-1418	62	43	strength	strength	NOUN
ap-1418	62	44	,	,	PUNCT
ap-1418	62	45	with	with	ADP
ap-1418	62	46	the	the	DET
ap-1418	62	47	value	value	NOUN
ap-1418	62	48	being	be	AUX
ap-1418	62	49	only	only	ADV
ap-1418	62	50	slightly	slightly	ADV
ap-1418	62	51	underestimated	underestimate	VERB
ap-1418	62	52	by	by	ADP
ap-1418	62	53	the	the	DET
ap-1418	62	54	gaussian	gaussian	ADJ
ap-1418	62	55	ansatz	ansatz	ADJ
ap-1418	62	56	(	(	PUNCT
ap-1418	62	57	n2a	n2a	VERB
ap-1418	62	58	/	/	SYM
ap-1418	62	59	au	au	NOUN
ap-1418	62	60	=	=	PUNCT
ap-1418	62	61	−3π/8	−3π/8	NOUN
ap-1418	63	1	=	=	NOUN
ap-1418	63	2	−1.178	−1.178	NOUN
ap-1418	63	3	0	0	PUNCT
ap-1418	63	4	variationally	variationally	ADV
ap-1418	63	5	,	,	PUNCT
ap-1418	63	6	and	and	CCONJ
ap-1418	63	7	−1.025	−1.025	ADJ
ap-1418	63	8	1	1	NUM
ap-1418	63	9	numerically	numerically	ADV
ap-1418	63	10	)	)	PUNCT
ap-1418	63	11	.	.	PUNCT
ap-1418	64	1	we	we	PRON
ap-1418	64	2	note	note	VERB
ap-1418	64	3	that	that	SCONJ
ap-1418	64	4	similar	similar	ADJ
ap-1418	64	5	tangent	tangent	NOUN
ap-1418	64	6	bifurcation	bifurcation	NOUN
ap-1418	64	7	behaviour	behaviour	NOUN
ap-1418	64	8	is	be	AUX
ap-1418	64	9	also	also	ADV
ap-1418	64	10	present	present	ADJ
ap-1418	64	11	for	for	ADP
ap-1418	64	12	non	non	ADJ
ap-1418	64	13	-	-	ADJ
ap-1418	64	14	vanishing	vanishing	ADJ
ap-1418	64	15	trapping	trap	VERB
ap-1418	64	16	potentials	potential	NOUN
ap-1418	64	17	[	[	X
ap-1418	64	18	9	9	NUM
ap-1418	64	19	]	]	PUNCT
ap-1418	64	20	.	.	PUNCT
ap-1418	65	1	at	at	ADP
ap-1418	65	2	the	the	DET
ap-1418	65	3	bifurcation	bifurcation	NOUN
ap-1418	65	4	point	point	NOUN
ap-1418	65	5	,	,	PUNCT
ap-1418	65	6	the	the	DET
ap-1418	65	7	energies	energy	NOUN
ap-1418	65	8	and	and	CCONJ
ap-1418	65	9	the	the	DET
ap-1418	65	10	wave	wave	NOUN
ap-1418	65	11	functions	function	NOUN
ap-1418	65	12	ψk+	ψk+	VERB
ap-1418	65	13	and	and	CCONJ
ap-1418	65	14	ψk−	ψk−	NOUN
ap-1418	65	15	are	be	AUX
ap-1418	65	16	identical	identical	ADJ
ap-1418	65	17	,	,	PUNCT
ap-1418	65	18	which	which	PRON
ap-1418	65	19	is	be	AUX
ap-1418	65	20	characteristic	characteristic	ADJ
ap-1418	65	21	of	of	ADP
ap-1418	65	22	exceptional	exceptional	ADJ
ap-1418	65	23	points	point	NOUN
ap-1418	65	24	known	know	VERB
ap-1418	65	25	to	to	PART
ap-1418	65	26	appear	appear	VERB
ap-1418	65	27	in	in	ADP
ap-1418	65	28	non	non	ADJ
ap-1418	65	29	-	-	ADJ
ap-1418	65	30	hermitian	hermitian	ADJ
ap-1418	65	31	quantum	quantum	ADJ
ap-1418	65	32	mechanics	mechanic	NOUN
ap-1418	65	33	.	.	PUNCT
ap-1418	66	1	to	to	PART
ap-1418	66	2	confirm	confirm	VERB
ap-1418	66	3	that	that	SCONJ
ap-1418	66	4	the	the	DET
ap-1418	66	5	bifurcation	bifurcation	NOUN
ap-1418	66	6	point	point	NOUN
ap-1418	66	7	is	be	AUX
ap-1418	66	8	an	an	DET
ap-1418	66	9	exceptional	exceptional	ADJ
ap-1418	66	10	point	point	NOUN
ap-1418	66	11	,	,	PUNCT
ap-1418	66	12	we	we	PRON
ap-1418	66	13	have	have	VERB
ap-1418	66	14	to	to	PART
ap-1418	66	15	perform	perform	VERB
ap-1418	66	16	a	a	DET
ap-1418	66	17	circle	circle	NOUN
ap-1418	66	18	around	around	ADP
ap-1418	66	19	the	the	DET
ap-1418	66	20	bifurcation	bifurcation	NOUN
ap-1418	66	21	point	point	NOUN
ap-1418	66	22	.	.	PUNCT
ap-1418	67	1	if	if	SCONJ
ap-1418	67	2	the	the	DET
ap-1418	67	3	two	two	NUM
ap-1418	67	4	eigenvalues	eigenvalue	VERB
ap-1418	67	5	permute	permute	NOUN
ap-1418	67	6	after	after	ADP
ap-1418	67	7	traversing	traverse	VERB
ap-1418	67	8	the	the	DET
ap-1418	67	9	full	full	ADJ
ap-1418	67	10	circle	circle	NOUN
ap-1418	67	11	,	,	PUNCT
ap-1418	67	12	we	we	PRON
ap-1418	67	13	have	have	VERB
ap-1418	67	14	an	an	DET
ap-1418	67	15	exceptional	exceptional	ADJ
ap-1418	67	16	point	point	NOUN
ap-1418	67	17	.	.	PUNCT
ap-1418	68	1	this	this	PRON
ap-1418	68	2	requires	require	VERB
ap-1418	68	3	a	a	DET
ap-1418	68	4	two	two	NUM
ap-1418	68	5	-	-	PUNCT
ap-1418	68	6	dimensional	dimensional	ADJ
ap-1418	68	7	parameter	parameter	NOUN
ap-1418	68	8	space	space	NOUN
ap-1418	68	9	and	and	CCONJ
ap-1418	68	10	thus	thus	ADV
ap-1418	68	11	96	96	NUM
ap-1418	68	12	acta	acta	PROPN
ap-1418	68	13	polytechnica	polytechnica	PROPN
ap-1418	68	14	vol	vol	NOUN
ap-1418	68	15	.	.	PUNCT
ap-1418	69	1	51	51	NUM
ap-1418	69	2	no	no	NOUN
ap-1418	69	3	.	.	PUNCT
ap-1418	70	1	4/2011	4/2011	NUM
ap-1418	70	2	fig	fig	NOUN
ap-1418	70	3	.	.	PUNCT
ap-1418	71	1	1	1	NUM
ap-1418	71	2	:	:	PUNCT
ap-1418	71	3	comparison	comparison	NOUN
ap-1418	71	4	of	of	ADP
ap-1418	71	5	variational	variational	ADJ
ap-1418	71	6	and	and	CCONJ
ap-1418	71	7	numerically	numerically	ADV
ap-1418	71	8	accurate	accurate	ADJ
ap-1418	71	9	results	result	NOUN
ap-1418	71	10	for	for	ADP
ap-1418	71	11	the	the	DET
ap-1418	71	12	mean	mean	ADJ
ap-1418	71	13	-	-	PUNCT
ap-1418	71	14	field	field	NOUN
ap-1418	71	15	energy	energy	NOUN
ap-1418	71	16	(	(	PUNCT
ap-1418	71	17	left	left	ADJ
ap-1418	71	18	)	)	PUNCT
ap-1418	71	19	and	and	CCONJ
ap-1418	71	20	chemical	chemical	NOUN
ap-1418	71	21	potential	potential	NOUN
ap-1418	71	22	(	(	PUNCT
ap-1418	71	23	right	right	NOUN
ap-1418	71	24	)	)	PUNCT
ap-1418	71	25	of	of	ADP
ap-1418	71	26	a	a	DET
ap-1418	71	27	self	self	NOUN
ap-1418	71	28	-	-	PUNCT
ap-1418	71	29	trapped	trap	VERB
ap-1418	71	30	monopolar	monopolar	NOUN
ap-1418	71	31	condensate	condensate	NOUN
ap-1418	71	32	as	as	ADP
ap-1418	71	33	a	a	DET
ap-1418	71	34	function	function	NOUN
ap-1418	71	35	of	of	ADP
ap-1418	71	36	the	the	DET
ap-1418	71	37	particle	particle	NOUN
ap-1418	71	38	number	number	NOUN
ap-1418	71	39	scaled	scale	VERB
ap-1418	71	40	scattering	scattering	NOUN
ap-1418	71	41	length	length	NOUN
ap-1418	71	42	fig	fig	NOUN
ap-1418	71	43	.	.	PUNCT
ap-1418	72	1	2	2	NUM
ap-1418	72	2	:	:	PUNCT
ap-1418	72	3	paths	path	NOUN
ap-1418	72	4	of	of	ADP
ap-1418	72	5	the	the	DET
ap-1418	72	6	real	real	ADJ
ap-1418	72	7	and	and	CCONJ
ap-1418	72	8	imaginary	imaginary	ADJ
ap-1418	72	9	parts	part	NOUN
ap-1418	72	10	of	of	ADP
ap-1418	72	11	the	the	DET
ap-1418	72	12	mean	mean	ADJ
ap-1418	72	13	-	-	PUNCT
ap-1418	72	14	field	field	NOUN
ap-1418	72	15	energy	energy	NOUN
ap-1418	72	16	and	and	CCONJ
ap-1418	72	17	the	the	DET
ap-1418	72	18	chemical	chemical	NOUN
ap-1418	72	19	potential	potential	NOUN
ap-1418	72	20	in	in	ADP
ap-1418	72	21	the	the	DET
ap-1418	72	22	variational	variational	ADJ
ap-1418	72	23	calculation	calculation	NOUN
ap-1418	72	24	with	with	ADP
ap-1418	72	25	a	a	DET
ap-1418	72	26	gaussian	gaussian	ADJ
ap-1418	72	27	-	-	PUNCT
ap-1418	72	28	type	type	NOUN
ap-1418	72	29	orbital	orbital	NOUN
ap-1418	72	30	for	for	ADP
ap-1418	72	31	self	self	NOUN
ap-1418	72	32	-	-	PUNCT
ap-1418	72	33	trapped	trap	VERB
ap-1418	72	34	monopolar	monopolar	NOUN
ap-1418	72	35	condensates	condensate	NOUN
ap-1418	72	36	if	if	SCONJ
ap-1418	72	37	a	a	DET
ap-1418	72	38	circle	circle	NOUN
ap-1418	72	39	of	of	ADP
ap-1418	72	40	radius	radius	NOUN
ap-1418	72	41	10−8	10−8	PROPN
ap-1418	72	42	is	be	AUX
ap-1418	72	43	traversed	traverse	VERB
ap-1418	72	44	around	around	ADP
ap-1418	72	45	the	the	DET
ap-1418	72	46	bifurcation	bifurcation	NOUN
ap-1418	72	47	point	point	NOUN
ap-1418	72	48	n2a	n2a	PROPN
ap-1418	72	49	/	/	SYM
ap-1418	72	50	au	au	NOUN
ap-1418	72	51	=	=	VERB
ap-1418	72	52	−3π/8	−3π/8	VERB
ap-1418	72	53	an	an	DET
ap-1418	72	54	extension	extension	NOUN
ap-1418	72	55	of	of	ADP
ap-1418	72	56	the	the	DET
ap-1418	72	57	scattering	scatter	VERB
ap-1418	72	58	length	length	NOUN
ap-1418	72	59	to	to	ADP
ap-1418	72	60	complex	complex	ADJ
ap-1418	72	61	values	value	NOUN
ap-1418	72	62	[	[	X
ap-1418	72	63	11	11	NUM
ap-1418	72	64	,	,	PUNCT
ap-1418	72	65	13	13	NUM
ap-1418	72	66	]	]	PUNCT
ap-1418	72	67	.	.	PUNCT
ap-1418	73	1	we	we	PRON
ap-1418	73	2	demonstrate	demonstrate	VERB
ap-1418	73	3	this	this	PRON
ap-1418	73	4	first	first	ADJ
ap-1418	73	5	for	for	SCONJ
ap-1418	73	6	the	the	DET
ap-1418	73	7	analytical	analytical	ADJ
ap-1418	73	8	solution	solution	NOUN
ap-1418	73	9	obtained	obtain	VERB
ap-1418	73	10	with	with	ADP
ap-1418	73	11	the	the	DET
ap-1418	73	12	gaussian	gaussian	NOUN
ap-1418	73	13	ansatz	ansatz	ADV
ap-1418	73	14	for	for	ADP
ap-1418	73	15	selftrapping	selftrappe	VERB
ap-1418	73	16	condensates	condensate	NOUN
ap-1418	73	17	.	.	PUNCT
ap-1418	74	1	figure	figure	NOUN
ap-1418	74	2	2	2	NUM
ap-1418	74	3	shows	show	VERB
ap-1418	74	4	the	the	DET
ap-1418	74	5	resulting	result	VERB
ap-1418	74	6	paths	path	NOUN
ap-1418	74	7	of	of	ADP
ap-1418	74	8	the	the	DET
ap-1418	74	9	values	value	NOUN
ap-1418	74	10	of	of	ADP
ap-1418	74	11	the	the	DET
ap-1418	74	12	mean	mean	ADJ
ap-1418	74	13	-	-	PUNCT
ap-1418	74	14	field	field	NOUN
ap-1418	74	15	energy	energy	NOUN
ap-1418	74	16	and	and	CCONJ
ap-1418	74	17	the	the	DET
ap-1418	74	18	chemical	chemical	NOUN
ap-1418	74	19	potential	potential	NOUN
ap-1418	74	20	in	in	ADP
ap-1418	74	21	the	the	DET
ap-1418	74	22	complex	complex	ADJ
ap-1418	74	23	plane	plane	NOUN
ap-1418	74	24	if	if	SCONJ
ap-1418	74	25	a	a	DET
ap-1418	74	26	small	small	ADJ
ap-1418	74	27	circle	circle	NOUN
ap-1418	74	28	reiϕ	reiϕ	NOUN
ap-1418	74	29	,	,	PUNCT
ap-1418	74	30	ϕ	ϕ	NOUN
ap-1418	74	31	=	=	NOUN
ap-1418	74	32	0	0	PROPN
ap-1418	74	33	.	.	PUNCT
ap-1418	74	34	.	.	PUNCT
ap-1418	74	35	.	.	PUNCT
ap-1418	75	1	2π	2π	NOUN
ap-1418	75	2	,	,	PUNCT
ap-1418	75	3	with	with	ADP
ap-1418	75	4	radius	radius	NOUN
ap-1418	75	5	r	r	NOUN
ap-1418	75	6	=	=	PUNCT
ap-1418	75	7	10−8	10−8	NUM
ap-1418	75	8	is	be	AUX
ap-1418	75	9	performed	perform	VERB
ap-1418	75	10	around	around	ADP
ap-1418	75	11	the	the	DET
ap-1418	75	12	critical	critical	ADJ
ap-1418	75	13	scattering	scattering	NOUN
ap-1418	75	14	length	length	NOUN
ap-1418	75	15	n2a	n2a	NOUN
ap-1418	75	16	/	/	SYM
ap-1418	75	17	au	au	NOUN
ap-1418	75	18	=	=	VERB
ap-1418	75	19	−3π/8	−3π/8	PROPN
ap-1418	75	20	.	.	PUNCT
ap-1418	76	1	a	a	DET
ap-1418	76	2	surprising	surprising	ADJ
ap-1418	76	3	result	result	NOUN
ap-1418	76	4	is	be	AUX
ap-1418	76	5	that	that	SCONJ
ap-1418	76	6	while	while	SCONJ
ap-1418	76	7	for	for	ADP
ap-1418	76	8	the	the	DET
ap-1418	76	9	chemical	chemical	NOUN
ap-1418	76	10	potential	potential	NOUN
ap-1418	76	11	a	a	DET
ap-1418	76	12	clear	clear	ADJ
ap-1418	76	13	permutation	permutation	NOUN
ap-1418	76	14	of	of	ADP
ap-1418	76	15	the	the	DET
ap-1418	76	16	two	two	NUM
ap-1418	76	17	solutions	solution	NOUN
ap-1418	76	18	is	be	AUX
ap-1418	76	19	visible	visible	ADJ
ap-1418	76	20	,	,	PUNCT
ap-1418	76	21	after	after	ADP
ap-1418	76	22	a	a	DET
ap-1418	76	23	full	full	ADJ
ap-1418	76	24	circle	circle	NOUN
ap-1418	76	25	the	the	DET
ap-1418	76	26	two	two	NUM
ap-1418	76	27	mean	mean	ADJ
ap-1418	76	28	-	-	PUNCT
ap-1418	76	29	field	field	NOUN
ap-1418	76	30	energy	energy	NOUN
ap-1418	76	31	values	value	NOUN
ap-1418	76	32	do	do	AUX
ap-1418	76	33	not	not	PART
ap-1418	76	34	permute	permute	VERB
ap-1418	76	35	.	.	PUNCT
ap-1418	77	1	this	this	PRON
ap-1418	77	2	can	can	AUX
ap-1418	77	3	be	be	AUX
ap-1418	77	4	explained	explain	VERB
ap-1418	77	5	by	by	ADP
ap-1418	77	6	looking	look	VERB
ap-1418	77	7	at	at	ADP
ap-1418	77	8	the	the	DET
ap-1418	77	9	analytical	analytical	ADJ
ap-1418	77	10	fractional	fractional	ADJ
ap-1418	77	11	power	power	NOUN
ap-1418	77	12	series	series	PROPN
ap-1418	77	13	expansion	expansion	NOUN
ap-1418	77	14	of	of	ADP
ap-1418	77	15	the	the	DET
ap-1418	77	16	mean	mean	ADJ
ap-1418	77	17	-	-	PUNCT
ap-1418	77	18	field	field	NOUN
ap-1418	77	19	energy	energy	NOUN
ap-1418	77	20	around	around	ADP
ap-1418	77	21	the	the	DET
ap-1418	77	22	critical	critical	ADJ
ap-1418	77	23	value	value	NOUN
ap-1418	77	24	[	[	X
ap-1418	77	25	11	11	NUM
ap-1418	77	26	]	]	PUNCT
ap-1418	77	27	ẽ±(ϕ	ẽ±(ϕ	ADV
ap-1418	77	28	)	)	PUNCT
ap-1418	78	1	=	=	SYM
ap-1418	78	2	−	−	PROPN
ap-1418	78	3	4	4	NUM
ap-1418	78	4	9π	9π	NOUN
ap-1418	78	5	+	+	CCONJ
ap-1418	78	6	0	0	NUM
ap-1418	78	7	·	·	PUNCT
ap-1418	78	8	√	√	PUNCT
ap-1418	79	1	reiϕ/2	reiϕ/2	NOUN
ap-1418	79	2	+	+	CCONJ
ap-1418	79	3	32	32	NUM
ap-1418	79	4	27π2	27π2	NUM
ap-1418	79	5	·	·	PUNCT
ap-1418	79	6	√	√	NUM
ap-1418	80	1	r	r	NOUN
ap-1418	80	2	2	2	NUM
ap-1418	80	3	eiϕ	eiϕ	NOUN
ap-1418	80	4	±	±	NOUN
ap-1418	80	5	(	(	PUNCT
ap-1418	80	6	4	4	NUM
ap-1418	80	7	9π	9π	NOUN
ap-1418	80	8	−	−	PROPN
ap-1418	80	9	32	32	NUM
ap-1418	80	10	9π2	9π2	NUM
ap-1418	80	11	)	)	PUNCT
ap-1418	80	12	·	·	PUNCT
ap-1418	81	1	√	√	NUM
ap-1418	82	1	r	r	NOUN
ap-1418	82	2	3	3	NUM
ap-1418	82	3	e(3/2)iϕ	e(3/2)iϕ	PROPN
ap-1418	82	4	+	+	NUM
ap-1418	82	5	o	o	X
ap-1418	82	6	(	(	PUNCT
ap-1418	82	7	√	√	NOUN
ap-1418	82	8	r	r	NOUN
ap-1418	82	9	4	4	NUM
ap-1418	82	10	)	)	PUNCT
ap-1418	82	11	.	.	PUNCT
ap-1418	83	1	evidently	evidently	ADV
ap-1418	83	2	the	the	DET
ap-1418	83	3	first	first	ADJ
ap-1418	83	4	-	-	PUNCT
ap-1418	83	5	order	order	NOUN
ap-1418	83	6	term	term	NOUN
ap-1418	83	7	with	with	ADP
ap-1418	83	8	the	the	DET
ap-1418	83	9	phase	phase	NOUN
ap-1418	83	10	factor	factor	NOUN
ap-1418	83	11	eiϕ/2	eiϕ/2	PROPN
ap-1418	83	12	vanishes	vanish	VERB
ap-1418	83	13	,	,	PUNCT
ap-1418	83	14	the	the	DET
ap-1418	83	15	lowest	low	ADJ
ap-1418	83	16	non	non	ADJ
ap-1418	83	17	-	-	ADJ
ap-1418	83	18	vanishing	vanishing	ADJ
ap-1418	83	19	order	order	NOUN
ap-1418	83	20	has	have	VERB
ap-1418	83	21	the	the	DET
ap-1418	83	22	phase	phase	NOUN
ap-1418	83	23	factor	factor	NOUN
ap-1418	83	24	eiϕ	eiϕ	PROPN
ap-1418	83	25	,	,	PUNCT
ap-1418	83	26	which	which	PRON
ap-1418	83	27	does	do	AUX
ap-1418	83	28	not	not	PART
ap-1418	83	29	lead	lead	VERB
ap-1418	83	30	to	to	ADP
ap-1418	83	31	a	a	DET
ap-1418	83	32	permutation	permutation	NOUN
ap-1418	83	33	of	of	ADP
ap-1418	83	34	the	the	DET
ap-1418	83	35	energies	energy	NOUN
ap-1418	83	36	,	,	PUNCT
ap-1418	83	37	and	and	CCONJ
ap-1418	83	38	it	it	PRON
ap-1418	83	39	is	be	AUX
ap-1418	83	40	only	only	ADV
ap-1418	83	41	the	the	DET
ap-1418	83	42	third	third	ADJ
ap-1418	83	43	-	-	PUNCT
ap-1418	83	44	order	order	NOUN
ap-1418	83	45	term	term	NOUN
ap-1418	83	46	which	which	PRON
ap-1418	83	47	can	can	AUX
ap-1418	83	48	yield	yield	VERB
ap-1418	83	49	the	the	DET
ap-1418	83	50	permutation	permutation	NOUN
ap-1418	83	51	.	.	PUNCT
ap-1418	84	1	by	by	ADP
ap-1418	84	2	contrast	contrast	NOUN
ap-1418	84	3	,	,	PUNCT
ap-1418	84	4	in	in	ADP
ap-1418	84	5	the	the	DET
ap-1418	84	6	fractional	fractional	ADJ
ap-1418	84	7	power	power	NOUN
ap-1418	84	8	series	series	PROPN
ap-1418	84	9	expansion	expansion	NOUN
ap-1418	84	10	of	of	ADP
ap-1418	84	11	the	the	DET
ap-1418	84	12	chemical	chemical	NOUN
ap-1418	84	13	potential	potential	NOUN
ap-1418	84	14	μ̃±(ϕ	μ̃±(ϕ	NUM
ap-1418	84	15	)	)	PUNCT
ap-1418	84	16	=	=	SYM
ap-1418	84	17	−	−	PROPN
ap-1418	84	18	20	20	NUM
ap-1418	84	19	9π	9π	NUM
ap-1418	84	20	±	±	NUM
ap-1418	84	21	8	8	NUM
ap-1418	84	22	3π	3π	NOUN
ap-1418	84	23	·	·	PUNCT
ap-1418	84	24	√	√	NUM
ap-1418	84	25	reiϕ/2	reiϕ/2	NUM
ap-1418	84	26	−	−	PROPN
ap-1418	84	27	(	(	PUNCT
ap-1418	84	28	4	4	NUM
ap-1418	84	29	3π	3π	NOUN
ap-1418	84	30	+	+	CCONJ
ap-1418	84	31	128	128	NUM
ap-1418	84	32	27π2	27π2	NUM
ap-1418	84	33	)	)	PUNCT
ap-1418	84	34	·	·	PUNCT
ap-1418	84	35	√	√	NUM
ap-1418	84	36	r	r	NOUN
ap-1418	84	37	2	2	NUM
ap-1418	84	38	eiϕ	eiϕ	NOUN
ap-1418	84	39	±	±	NOUN
ap-1418	84	40	(	(	PUNCT
ap-1418	84	41	8	8	NUM
ap-1418	84	42	9π	9π	NOUN
ap-1418	84	43	−	−	PROPN
ap-1418	84	44	64	64	NUM
ap-1418	84	45	9π2	9π2	NUM
ap-1418	84	46	)	)	PUNCT
ap-1418	84	47	·	·	PUNCT
ap-1418	85	1	√	√	NUM
ap-1418	86	1	r	r	NOUN
ap-1418	86	2	3	3	NUM
ap-1418	86	3	e(3/2)iϕ	e(3/2)iϕ	PROPN
ap-1418	86	4	+	+	NUM
ap-1418	86	5	o	o	X
ap-1418	86	6	(	(	PUNCT
ap-1418	86	7	√	√	NOUN
ap-1418	86	8	r	r	NOUN
ap-1418	86	9	4	4	NUM
ap-1418	86	10	)	)	PUNCT
ap-1418	86	11	the	the	DET
ap-1418	86	12	first	first	ADJ
ap-1418	86	13	-	-	PUNCT
ap-1418	86	14	order	order	NOUN
ap-1418	86	15	term	term	NOUN
ap-1418	86	16	does	do	AUX
ap-1418	86	17	not	not	PART
ap-1418	86	18	vanish	vanish	VERB
ap-1418	86	19	and	and	CCONJ
ap-1418	86	20	leads	lead	VERB
ap-1418	86	21	to	to	ADP
ap-1418	86	22	a	a	DET
ap-1418	86	23	permutation	permutation	NOUN
ap-1418	86	24	of	of	ADP
ap-1418	86	25	the	the	DET
ap-1418	86	26	chemical	chemical	ADJ
ap-1418	86	27	potential	potential	ADJ
ap-1418	86	28	values	value	NOUN
ap-1418	86	29	.	.	PUNCT
ap-1418	87	1	thus	thus	ADV
ap-1418	87	2	the	the	DET
ap-1418	87	3	permutation	permutation	NOUN
ap-1418	87	4	of	of	ADP
ap-1418	87	5	the	the	DET
ap-1418	87	6	eigenvalues	eigenvalue	NOUN
ap-1418	87	7	appears	appear	VERB
ap-1418	87	8	for	for	ADP
ap-1418	87	9	a	a	DET
ap-1418	87	10	small	small	ADJ
ap-1418	87	11	radius	radius	NOUN
ap-1418	87	12	,	,	PUNCT
ap-1418	87	13	in	in	ADP
ap-1418	87	14	the	the	DET
ap-1418	87	15	same	same	ADJ
ap-1418	87	16	way	way	NOUN
ap-1418	87	17	that	that	PRON
ap-1418	87	18	it	it	PRON
ap-1418	87	19	occurs	occur	VERB
ap-1418	87	20	for	for	ADP
ap-1418	87	21	exceptional	exceptional	ADJ
ap-1418	87	22	points	point	NOUN
ap-1418	87	23	in	in	ADP
ap-1418	87	24	simple	simple	ADJ
ap-1418	87	25	non	non	ADJ
ap-1418	87	26	-	-	ADJ
ap-1418	87	27	hermitian	hermitian	ADJ
ap-1418	87	28	linear	linear	PROPN
ap-1418	87	29	model	model	NOUN
ap-1418	87	30	systems	system	NOUN
ap-1418	87	31	.	.	PUNCT
ap-1418	88	1	97	97	NUM
ap-1418	88	2	acta	acta	PROPN
ap-1418	88	3	polytechnica	polytechnica	PROPN
ap-1418	88	4	vol	vol	NOUN
ap-1418	88	5	.	.	PUNCT
ap-1418	89	1	51	51	NUM
ap-1418	89	2	no	no	NOUN
ap-1418	89	3	.	.	PUNCT
ap-1418	90	1	4/2011	4/2011	NUM
ap-1418	90	2	fig	fig	NOUN
ap-1418	90	3	.	.	PUNCT
ap-1418	91	1	3	3	NUM
ap-1418	91	2	:	:	PUNCT
ap-1418	91	3	same	same	ADJ
ap-1418	91	4	as	as	ADP
ap-1418	91	5	figure	figure	NOUN
ap-1418	91	6	2	2	NUM
ap-1418	91	7	,	,	PUNCT
ap-1418	91	8	but	but	CCONJ
ap-1418	91	9	for	for	ADP
ap-1418	91	10	a	a	DET
ap-1418	91	11	larger	large	ADJ
ap-1418	91	12	radius	radius	NOUN
ap-1418	91	13	of	of	ADP
ap-1418	91	14	r	r	NOUN
ap-1418	91	15	=	=	SYM
ap-1418	91	16	10−3	10−3	NUM
ap-1418	91	17	fig	fig	NOUN
ap-1418	91	18	.	.	PUNCT
ap-1418	92	1	4	4	NUM
ap-1418	92	2	:	:	PUNCT
ap-1418	92	3	same	same	ADJ
ap-1418	92	4	as	as	ADP
ap-1418	92	5	figure	figure	NOUN
ap-1418	92	6	2	2	NUM
ap-1418	92	7	,	,	PUNCT
ap-1418	92	8	but	but	CCONJ
ap-1418	92	9	for	for	ADP
ap-1418	92	10	a	a	DET
ap-1418	92	11	still	still	ADV
ap-1418	92	12	larger	large	ADJ
ap-1418	92	13	radius	radius	NOUN
ap-1418	92	14	of	of	ADP
ap-1418	92	15	r	r	NOUN
ap-1418	92	16	=	=	SYM
ap-1418	92	17	10−1	10−1	NUM
ap-1418	92	18	for	for	ADP
ap-1418	92	19	increasing	increase	VERB
ap-1418	92	20	radius	radius	NOUN
ap-1418	92	21	,	,	PUNCT
ap-1418	92	22	the	the	DET
ap-1418	92	23	higher	high	ADJ
ap-1418	92	24	-	-	PUNCT
ap-1418	92	25	order	order	NOUN
ap-1418	92	26	terms	term	NOUN
ap-1418	92	27	in	in	ADP
ap-1418	92	28	the	the	DET
ap-1418	92	29	expansions	expansion	NOUN
ap-1418	92	30	become	become	VERB
ap-1418	92	31	more	more	ADV
ap-1418	92	32	and	and	CCONJ
ap-1418	92	33	more	more	ADV
ap-1418	92	34	important	important	ADJ
ap-1418	92	35	,	,	PUNCT
ap-1418	92	36	and	and	CCONJ
ap-1418	92	37	the	the	DET
ap-1418	92	38	permutation	permutation	NOUN
ap-1418	92	39	of	of	ADP
ap-1418	92	40	the	the	DET
ap-1418	92	41	mean	mean	ADJ
ap-1418	92	42	-	-	PUNCT
ap-1418	92	43	field	field	NOUN
ap-1418	92	44	energy	energy	NOUN
ap-1418	92	45	values	value	NOUN
ap-1418	92	46	after	after	SCONJ
ap-1418	92	47	a	a	DET
ap-1418	92	48	full	full	ADJ
ap-1418	92	49	circle	circle	NOUN
ap-1418	92	50	becomes	become	VERB
ap-1418	92	51	recognizable	recognizable	ADJ
ap-1418	92	52	,	,	PUNCT
ap-1418	92	53	as	as	SCONJ
ap-1418	92	54	can	can	AUX
ap-1418	92	55	be	be	AUX
ap-1418	92	56	seen	see	VERB
ap-1418	92	57	in	in	ADP
ap-1418	92	58	figure	figure	NOUN
ap-1418	92	59	3	3	NUM
ap-1418	92	60	.	.	PUNCT
ap-1418	93	1	the	the	DET
ap-1418	93	2	permutation	permutation	NOUN
ap-1418	93	3	behaviour	behaviour	NOUN
ap-1418	93	4	of	of	ADP
ap-1418	93	5	the	the	DET
ap-1418	93	6	chemical	chemical	ADJ
ap-1418	93	7	potential	potential	ADJ
ap-1418	93	8	solutions	solution	NOUN
ap-1418	93	9	is	be	AUX
ap-1418	93	10	not	not	PART
ap-1418	93	11	altered	alter	VERB
ap-1418	93	12	,	,	PUNCT
ap-1418	93	13	as	as	SCONJ
ap-1418	93	14	is	be	AUX
ap-1418	93	15	expected	expect	VERB
ap-1418	93	16	from	from	ADP
ap-1418	93	17	the	the	DET
ap-1418	93	18	expansion	expansion	NOUN
ap-1418	93	19	.	.	PUNCT
ap-1418	94	1	for	for	ADP
ap-1418	94	2	the	the	DET
ap-1418	94	3	case	case	NOUN
ap-1418	94	4	of	of	ADP
ap-1418	94	5	an	an	DET
ap-1418	94	6	ever	ever	ADV
ap-1418	94	7	increasing	increase	VERB
ap-1418	94	8	radius	radius	NOUN
ap-1418	94	9	of	of	ADP
ap-1418	94	10	r	r	NOUN
ap-1418	94	11	=	=	SYM
ap-1418	94	12	10−1	10−1	NUM
ap-1418	94	13	,	,	PUNCT
ap-1418	94	14	shown	show	VERB
ap-1418	94	15	in	in	ADP
ap-1418	94	16	figure	figure	NOUN
ap-1418	94	17	4	4	NUM
ap-1418	94	18	,	,	PUNCT
ap-1418	94	19	the	the	DET
ap-1418	94	20	higher	high	ADJ
ap-1418	94	21	-	-	PUNCT
ap-1418	94	22	order	order	NOUN
ap-1418	94	23	terms	term	NOUN
ap-1418	94	24	lead	lead	VERB
ap-1418	94	25	to	to	ADP
ap-1418	94	26	a	a	DET
ap-1418	94	27	deformation	deformation	NOUN
ap-1418	94	28	of	of	ADP
ap-1418	94	29	the	the	DET
ap-1418	94	30	circle	circle	NOUN
ap-1418	94	31	of	of	ADP
ap-1418	94	32	the	the	DET
ap-1418	94	33	mean	mean	ADJ
ap-1418	94	34	-	-	PUNCT
ap-1418	94	35	field	field	NOUN
ap-1418	94	36	energy	energy	NOUN
ap-1418	94	37	(	(	PUNCT
ap-1418	94	38	as	as	ADP
ap-1418	94	39	in	in	ADP
ap-1418	94	40	linear	linear	PROPN
ap-1418	94	41	model	model	NOUN
ap-1418	94	42	systems	system	NOUN
ap-1418	94	43	)	)	PUNCT
ap-1418	94	44	.	.	PUNCT
ap-1418	95	1	the	the	DET
ap-1418	95	2	shape	shape	NOUN
ap-1418	95	3	of	of	ADP
ap-1418	95	4	the	the	DET
ap-1418	95	5	chemical	chemical	ADJ
ap-1418	95	6	potential	potential	ADJ
ap-1418	95	7	circle	circle	NOUN
ap-1418	95	8	does	do	AUX
ap-1418	95	9	not	not	PART
ap-1418	95	10	change	change	VERB
ap-1418	95	11	,	,	PUNCT
ap-1418	95	12	but	but	CCONJ
ap-1418	95	13	the	the	DET
ap-1418	95	14	spacing	spacing	NOUN
ap-1418	95	15	between	between	ADP
ap-1418	95	16	the	the	DET
ap-1418	95	17	points	point	NOUN
ap-1418	95	18	is	be	AUX
ap-1418	95	19	no	no	PRON
ap-1418	95	20	longer	long	ADV
ap-1418	95	21	uniform	uniform	ADJ
ap-1418	95	22	.	.	PUNCT
ap-1418	96	1	for	for	SCONJ
ap-1418	96	2	the	the	DET
ap-1418	96	3	gaussian	gaussian	PROPN
ap-1418	96	4	ansatz	ansatz	NOUN
ap-1418	96	5	,	,	PUNCT
ap-1418	96	6	analytical	analytical	ADJ
ap-1418	96	7	expansions	expansion	NOUN
ap-1418	96	8	can	can	AUX
ap-1418	96	9	also	also	ADV
ap-1418	96	10	be	be	AUX
ap-1418	96	11	performed	perform	VERB
ap-1418	96	12	for	for	ADP
ap-1418	96	13	circles	circle	NOUN
ap-1418	96	14	around	around	ADP
ap-1418	96	15	the	the	DET
ap-1418	96	16	bifurcation	bifurcation	NOUN
ap-1418	96	17	point	point	NOUN
ap-1418	96	18	with	with	ADP
ap-1418	96	19	large	large	ADJ
ap-1418	96	20	radii	radius	NOUN
ap-1418	96	21	,	,	PUNCT
ap-1418	96	22	r	r	NOUN
ap-1418	96	23	�	�	PROPN
ap-1418	96	24	1	1	NUM
ap-1418	96	25	.	.	PUNCT
ap-1418	97	1	the	the	DET
ap-1418	97	2	expression	expression	NOUN
ap-1418	97	3	for	for	ADP
ap-1418	97	4	the	the	DET
ap-1418	97	5	mean	mean	ADJ
ap-1418	97	6	-	-	PUNCT
ap-1418	97	7	field	field	NOUN
ap-1418	97	8	energy	energy	NOUN
ap-1418	97	9	reads	read	NOUN
ap-1418	97	10	[	[	X
ap-1418	97	11	11	11	NUM
ap-1418	97	12	]	]	PUNCT
ap-1418	97	13	ẽ±(ϕ	ẽ±(ϕ	NUM
ap-1418	97	14	)	)	PUNCT
ap-1418	97	15	=	=	SYM
ap-1418	97	16	±	±	NOUN
ap-1418	97	17	(	(	PUNCT
ap-1418	97	18	π	π	PROPN
ap-1418	97	19	16	16	NUM
ap-1418	97	20	−	−	NOUN
ap-1418	97	21	1	1	NUM
ap-1418	97	22	2	2	NUM
ap-1418	97	23	)	)	PUNCT
ap-1418	97	24	·	·	PUNCT
ap-1418	98	1	e−iϕ/2	e−iϕ/2	NOUN
ap-1418	98	2	√	√	NUM
ap-1418	98	3	r	r	NOUN
ap-1418	98	4	+	+	NOUN
ap-1418	98	5	1	1	NUM
ap-1418	98	6	2	2	NUM
ap-1418	98	7	·	·	PUNCT
ap-1418	98	8	e−iϕ	e−iϕ	NOUN
ap-1418	98	9	√	√	ADP
ap-1418	98	10	r	r	NOUN
ap-1418	98	11	2	2	NUM
ap-1418	98	12	±	±	NOUN
ap-1418	98	13	(	(	PUNCT
ap-1418	98	14	3π2	3π2	NUM
ap-1418	98	15	64	64	NUM
ap-1418	98	16	−	−	NOUN
ap-1418	98	17	3π	3π	NOUN
ap-1418	98	18	8	8	NUM
ap-1418	98	19	)	)	PUNCT
ap-1418	98	20	·	·	PUNCT
ap-1418	98	21	e−(3/2)iϕ	e−(3/2)iϕ	VERB
ap-1418	98	22	√	√	NUM
ap-1418	98	23	r	r	NOUN
ap-1418	98	24	3	3	NUM
ap-1418	98	25	+	+	CCONJ
ap-1418	98	26	o	o	NOUN
ap-1418	98	27	(	(	PUNCT
ap-1418	98	28	1	1	NUM
ap-1418	98	29	√	√	NOUN
ap-1418	98	30	r	r	NOUN
ap-1418	98	31	4	4	NUM
ap-1418	98	32	)	)	PUNCT
ap-1418	98	33	while	while	SCONJ
ap-1418	98	34	for	for	ADP
ap-1418	98	35	the	the	DET
ap-1418	98	36	chemical	chemical	NOUN
ap-1418	98	37	potential	potential	NOUN
ap-1418	98	38	we	we	PRON
ap-1418	98	39	obtain	obtain	VERB
ap-1418	98	40	μ̃±(ϕ	μ̃±(ϕ	NUM
ap-1418	98	41	)	)	PUNCT
ap-1418	98	42	=	=	SYM
ap-1418	98	43	±	±	NOUN
ap-1418	98	44	(	(	PUNCT
ap-1418	98	45	π	π	PROPN
ap-1418	98	46	8	8	NUM
ap-1418	98	47	−	−	NOUN
ap-1418	98	48	1	1	NUM
ap-1418	98	49	)	)	PUNCT
ap-1418	98	50	·	·	PUNCT
ap-1418	99	1	e−iϕ/2	e−iϕ/2	NOUN
ap-1418	99	2	√	√	NUM
ap-1418	99	3	r	r	NOUN
ap-1418	99	4	+	+	CCONJ
ap-1418	99	5	(	(	PUNCT
ap-1418	99	6	1	1	NUM
ap-1418	99	7	−	−	PROPN
ap-1418	99	8	3π	3π	NOUN
ap-1418	99	9	16	16	NUM
ap-1418	99	10	)	)	PUNCT
ap-1418	99	11	·	·	PUNCT
ap-1418	100	1	e−iϕ	e−iϕ	NOUN
ap-1418	100	2	√	√	ADP
ap-1418	100	3	r	r	NOUN
ap-1418	100	4	2	2	NUM
ap-1418	100	5	±	±	NOUN
ap-1418	100	6	(	(	PUNCT
ap-1418	100	7	3π2	3π2	NUM
ap-1418	100	8	32	32	NUM
ap-1418	100	9	−	−	PROPN
ap-1418	100	10	3π	3π	NOUN
ap-1418	100	11	8	8	NUM
ap-1418	100	12	)	)	PUNCT
ap-1418	100	13	·	·	PUNCT
ap-1418	100	14	e−(3/2)iϕ	e−(3/2)iϕ	VERB
ap-1418	100	15	√	√	NUM
ap-1418	100	16	r	r	NOUN
ap-1418	100	17	3	3	NUM
ap-1418	100	18	+	+	CCONJ
ap-1418	100	19	o	o	NOUN
ap-1418	100	20	(	(	PUNCT
ap-1418	100	21	1	1	NUM
ap-1418	100	22	√	√	NOUN
ap-1418	100	23	r	r	NOUN
ap-1418	100	24	4	4	NUM
ap-1418	100	25	)	)	PUNCT
ap-1418	100	26	.	.	PUNCT
ap-1418	101	1	from	from	ADP
ap-1418	101	2	the	the	DET
ap-1418	101	3	expressions	expression	NOUN
ap-1418	101	4	it	it	PRON
ap-1418	101	5	is	be	AUX
ap-1418	101	6	evident	evident	ADJ
ap-1418	101	7	that	that	SCONJ
ap-1418	101	8	a	a	DET
ap-1418	101	9	clear	clear	ADJ
ap-1418	101	10	semicircle	semicircle	NOUN
ap-1418	101	11	structure	structure	NOUN
ap-1418	101	12	should	should	AUX
ap-1418	101	13	appear	appear	VERB
ap-1418	101	14	for	for	ADP
ap-1418	101	15	large	large	ADJ
ap-1418	101	16	radii	radius	NOUN
ap-1418	101	17	,	,	PUNCT
ap-1418	101	18	as	as	SCONJ
ap-1418	101	19	can	can	AUX
ap-1418	101	20	be	be	AUX
ap-1418	101	21	seen	see	VERB
ap-1418	101	22	in	in	ADP
ap-1418	101	23	figure	figure	NOUN
ap-1418	101	24	5	5	NUM
ap-1418	101	25	for	for	ADP
ap-1418	101	26	r	r	NOUN
ap-1418	101	27	=	=	SYM
ap-1418	101	28	108	108	NUM
ap-1418	101	29	.	.	PUNCT
ap-1418	102	1	2.2	2.2	NUM
ap-1418	102	2	numerical	numerical	ADJ
ap-1418	102	3	analysis	analysis	NOUN
ap-1418	102	4	of	of	ADP
ap-1418	102	5	the	the	DET
ap-1418	102	6	bifurcation	bifurcation	NOUN
ap-1418	102	7	point	point	NOUN
ap-1418	102	8	for	for	ADP
ap-1418	102	9	self	self	NOUN
ap-1418	102	10	-	-	PUNCT
ap-1418	102	11	trapped	trap	VERB
ap-1418	102	12	condensates	condensate	NOUN
ap-1418	102	13	for	for	ADP
ap-1418	102	14	accurate	accurate	ADJ
ap-1418	102	15	numerical	numerical	ADJ
ap-1418	102	16	solutions	solution	NOUN
ap-1418	102	17	of	of	ADP
ap-1418	102	18	the	the	DET
ap-1418	102	19	grosspitaevskii	grosspitaevskii	ADJ
ap-1418	102	20	equation	equation	NOUN
ap-1418	102	21	a	a	DET
ap-1418	102	22	similar	similar	ADJ
ap-1418	102	23	investigation	investigation	NOUN
ap-1418	102	24	of	of	ADP
ap-1418	102	25	the	the	DET
ap-1418	102	26	exceptional	exceptional	ADJ
ap-1418	102	27	point	point	NOUN
ap-1418	102	28	behaviour	behaviour	NOUN
ap-1418	102	29	can	can	AUX
ap-1418	102	30	be	be	AUX
ap-1418	102	31	carried	carry	VERB
ap-1418	102	32	out	out	ADP
ap-1418	102	33	.	.	PUNCT
ap-1418	103	1	the	the	DET
ap-1418	103	2	task	task	NOUN
ap-1418	103	3	again	again	ADV
ap-1418	103	4	is	be	AUX
ap-1418	103	5	to	to	PART
ap-1418	103	6	perform	perform	VERB
ap-1418	103	7	a	a	DET
ap-1418	103	8	circle	circle	NOUN
ap-1418	103	9	in	in	ADP
ap-1418	103	10	the	the	DET
ap-1418	103	11	complex	complex	ADJ
ap-1418	103	12	scattering	scattering	NOUN
ap-1418	103	13	length	length	NOUN
ap-1418	103	14	plane	plane	NOUN
ap-1418	103	15	around	around	ADP
ap-1418	103	16	the	the	DET
ap-1418	103	17	numerically	numerically	ADV
ap-1418	103	18	accurate	accurate	ADJ
ap-1418	103	19	bifurcation	bifurcation	NOUN
ap-1418	103	20	point	point	NOUN
ap-1418	103	21	at	at	ADP
ap-1418	103	22	n2a	n2a	PROPN
ap-1418	103	23	/	/	SYM
ap-1418	103	24	au	au	NOUN
ap-1418	103	25	=	=	VERB
ap-1418	103	26	−1.025	−1.025	NOUN
ap-1418	103	27	1	1	NUM
ap-1418	103	28	and	and	CCONJ
ap-1418	103	29	to	to	PART
ap-1418	103	30	numerically	numerically	ADV
ap-1418	103	31	solve	solve	VERB
ap-1418	103	32	the	the	DET
ap-1418	103	33	equation	equation	NOUN
ap-1418	103	34	for	for	ADP
ap-1418	103	35	each	each	DET
ap-1418	103	36	complex	complex	ADJ
ap-1418	103	37	scattering	scattering	NOUN
ap-1418	103	38	length	length	NOUN
ap-1418	103	39	on	on	ADP
ap-1418	103	40	the	the	DET
ap-1418	103	41	circle	circle	NOUN
ap-1418	103	42	.	.	PUNCT
ap-1418	104	1	this	this	DET
ap-1418	104	2	yields	yield	VERB
ap-1418	104	3	not	not	PART
ap-1418	104	4	only	only	ADV
ap-1418	104	5	complex	complex	ADJ
ap-1418	104	6	values	value	NOUN
ap-1418	104	7	for	for	ADP
ap-1418	104	8	the	the	DET
ap-1418	104	9	chemical	chemical	NOUN
ap-1418	104	10	potential	potential	NOUN
ap-1418	104	11	and	and	CCONJ
ap-1418	104	12	the	the	DET
ap-1418	104	13	mean	mean	ADJ
ap-1418	104	14	-	-	PUNCT
ap-1418	104	15	field	field	NOUN
ap-1418	104	16	energy	energy	NOUN
ap-1418	104	17	but	but	CCONJ
ap-1418	104	18	also	also	ADV
ap-1418	104	19	complex	complex	ADJ
ap-1418	104	20	wave	wave	NOUN
ap-1418	104	21	functions	function	NOUN
ap-1418	104	22	.	.	PUNCT
ap-1418	105	1	98	98	NUM
ap-1418	105	2	acta	acta	PROPN
ap-1418	105	3	polytechnica	polytechnica	PROPN
ap-1418	105	4	vol	vol	NOUN
ap-1418	105	5	.	.	PUNCT
ap-1418	106	1	51	51	NUM
ap-1418	106	2	no	no	NOUN
ap-1418	106	3	.	.	PUNCT
ap-1418	107	1	4/2011	4/2011	NUM
ap-1418	107	2	fig	fig	NOUN
ap-1418	107	3	.	.	PUNCT
ap-1418	108	1	5	5	NUM
ap-1418	108	2	:	:	PUNCT
ap-1418	108	3	same	same	ADJ
ap-1418	108	4	as	as	ADP
ap-1418	108	5	figure	figure	NOUN
ap-1418	108	6	2	2	NUM
ap-1418	108	7	,	,	PUNCT
ap-1418	108	8	but	but	CCONJ
ap-1418	108	9	for	for	ADP
ap-1418	108	10	the	the	DET
ap-1418	108	11	very	very	ADV
ap-1418	108	12	large	large	ADJ
ap-1418	108	13	radius	radius	NOUN
ap-1418	108	14	r	r	NOUN
ap-1418	108	15	=	=	SYM
ap-1418	108	16	108	108	NUM
ap-1418	108	17	fig	fig	NOUN
ap-1418	108	18	.	.	PUNCT
ap-1418	109	1	6	6	NUM
ap-1418	109	2	:	:	PUNCT
ap-1418	109	3	comparison	comparison	NOUN
ap-1418	109	4	of	of	ADP
ap-1418	109	5	variational	variational	ADJ
ap-1418	109	6	and	and	CCONJ
ap-1418	109	7	numerically	numerically	ADV
ap-1418	109	8	accurate	accurate	ADJ
ap-1418	109	9	results	result	NOUN
ap-1418	109	10	proving	prove	VERB
ap-1418	109	11	the	the	DET
ap-1418	109	12	branch	branch	NOUN
ap-1418	109	13	point	point	NOUN
ap-1418	109	14	singularity	singularity	NOUN
ap-1418	109	15	at	at	ADP
ap-1418	109	16	the	the	DET
ap-1418	109	17	bifurcation	bifurcation	NOUN
ap-1418	109	18	point	point	NOUN
ap-1418	109	19	of	of	ADP
ap-1418	109	20	the	the	DET
ap-1418	109	21	gross	gross	ADJ
ap-1418	109	22	-	-	PUNCT
ap-1418	109	23	pitaevskii	pitaevskii	ADJ
ap-1418	109	24	equation	equation	NOUN
ap-1418	109	25	for	for	ADP
ap-1418	109	26	self	self	NOUN
ap-1418	109	27	-	-	PUNCT
ap-1418	109	28	trapped	trap	VERB
ap-1418	109	29	bose	bose	NOUN
ap-1418	109	30	-	-	PUNCT
ap-1418	109	31	einstein	einstein	NOUN
ap-1418	109	32	condensates	condensate	NOUN
ap-1418	109	33	with	with	ADP
ap-1418	109	34	an	an	DET
ap-1418	109	35	attractive	attractive	ADJ
ap-1418	109	36	1	1	NUM
ap-1418	109	37	/	/	SYM
ap-1418	109	38	r	r	NOUN
ap-1418	109	39	long	long	ADJ
ap-1418	109	40	-	-	PUNCT
ap-1418	109	41	range	range	NOUN
ap-1418	109	42	interaction	interaction	NOUN
ap-1418	109	43	.	.	PUNCT
ap-1418	110	1	panels	panel	NOUN
ap-1418	110	2	(	(	PUNCT
ap-1418	110	3	a	a	X
ap-1418	110	4	)	)	PUNCT
ap-1418	110	5	and	and	CCONJ
ap-1418	110	6	(	(	PUNCT
ap-1418	110	7	b	b	X
ap-1418	110	8	)	)	PUNCT
ap-1418	110	9	show	show	VERB
ap-1418	110	10	the	the	DET
ap-1418	110	11	circles	circle	NOUN
ap-1418	110	12	of	of	ADP
ap-1418	110	13	radius	radius	NOUN
ap-1418	110	14	r	r	NOUN
ap-1418	110	15	=	=	SYM
ap-1418	110	16	10−3	10−3	NUM
ap-1418	110	17	in	in	ADP
ap-1418	110	18	the	the	DET
ap-1418	110	19	complex	complex	ADJ
ap-1418	110	20	scattering	scattering	NOUN
ap-1418	110	21	length	length	NOUN
ap-1418	110	22	plane	plane	NOUN
ap-1418	110	23	around	around	ADP
ap-1418	110	24	the	the	DET
ap-1418	110	25	critical	critical	ADJ
ap-1418	110	26	values	value	NOUN
ap-1418	110	27	,	,	PUNCT
ap-1418	110	28	(	(	PUNCT
ap-1418	110	29	c	c	X
ap-1418	110	30	)	)	PUNCT
ap-1418	110	31	and	and	CCONJ
ap-1418	110	32	(	(	PUNCT
ap-1418	110	33	d	d	X
ap-1418	110	34	)	)	PUNCT
ap-1418	110	35	the	the	DET
ap-1418	110	36	reactions	reaction	NOUN
ap-1418	110	37	of	of	ADP
ap-1418	110	38	the	the	DET
ap-1418	110	39	chemical	chemical	ADJ
ap-1418	110	40	potential	potential	ADJ
ap-1418	110	41	values	value	NOUN
ap-1418	110	42	as	as	SCONJ
ap-1418	110	43	the	the	DET
ap-1418	110	44	circles	circle	NOUN
ap-1418	110	45	are	be	AUX
ap-1418	110	46	traversed	traverse	VERB
ap-1418	110	47	,	,	PUNCT
ap-1418	110	48	(	(	PUNCT
ap-1418	110	49	e	e	NOUN
ap-1418	110	50	)	)	PUNCT
ap-1418	110	51	and	and	CCONJ
ap-1418	110	52	(	(	PUNCT
ap-1418	110	53	f	f	X
ap-1418	110	54	)	)	PUNCT
ap-1418	110	55	those	those	PRON
ap-1418	110	56	of	of	ADP
ap-1418	110	57	the	the	DET
ap-1418	110	58	mean	mean	ADJ
ap-1418	110	59	-	-	PUNCT
ap-1418	110	60	field	field	NOUN
ap-1418	110	61	energies	energy	NOUN
ap-1418	110	62	(	(	PUNCT
ap-1418	110	63	variational	variational	ADJ
ap-1418	110	64	results	result	NOUN
ap-1418	110	65	:	:	PUNCT
ap-1418	110	66	left	left	ADJ
ap-1418	110	67	column	column	NOUN
ap-1418	110	68	,	,	PUNCT
ap-1418	110	69	accurate	accurate	ADJ
ap-1418	110	70	numerical	numerical	ADJ
ap-1418	110	71	results	result	NOUN
ap-1418	110	72	:	:	PUNCT
ap-1418	110	73	right	right	ADJ
ap-1418	110	74	column	column	NOUN
ap-1418	110	75	)	)	PUNCT
ap-1418	110	76	.	.	PUNCT
ap-1418	111	1	(	(	PUNCT
ap-1418	111	2	adapted	adapt	VERB
ap-1418	111	3	from	from	ADP
ap-1418	111	4	[	[	X
ap-1418	111	5	11	11	NUM
ap-1418	111	6	]	]	SYM
ap-1418	111	7	)	)	PUNCT
ap-1418	111	8	99	99	NUM
ap-1418	111	9	acta	acta	PROPN
ap-1418	111	10	polytechnica	polytechnica	PROPN
ap-1418	111	11	vol	vol	NOUN
ap-1418	111	12	.	.	PUNCT
ap-1418	112	1	51	51	NUM
ap-1418	112	2	no	no	INTJ
ap-1418	112	3	.	.	PUNCT
ap-1418	113	1	4/2011	4/2011	NUM
ap-1418	114	1	the	the	DET
ap-1418	114	2	problem	problem	NOUN
ap-1418	114	3	is	be	AUX
ap-1418	114	4	that	that	SCONJ
ap-1418	114	5	the	the	DET
ap-1418	114	6	gross	gross	ADJ
ap-1418	114	7	-	-	PUNCT
ap-1418	114	8	pitaevskii	pitaevskii	ADJ
ap-1418	114	9	equation	equation	NOUN
ap-1418	114	10	contains	contain	VERB
ap-1418	114	11	the	the	DET
ap-1418	114	12	square	square	ADJ
ap-1418	114	13	modulus	modulus	NOUN
ap-1418	114	14	of	of	ADP
ap-1418	114	15	the	the	DET
ap-1418	114	16	wave	wave	NOUN
ap-1418	114	17	function	function	NOUN
ap-1418	114	18	ψ	ψ	NOUN
ap-1418	114	19	and	and	CCONJ
ap-1418	114	20	is	be	AUX
ap-1418	114	21	therefore	therefore	ADV
ap-1418	114	22	a	a	DET
ap-1418	114	23	non	non	ADJ
ap-1418	114	24	-	-	ADJ
ap-1418	114	25	analytic	analytic	ADJ
ap-1418	114	26	function	function	NOUN
ap-1418	114	27	of	of	ADP
ap-1418	114	28	ψ	ψ	PROPN
ap-1418	114	29	.	.	PUNCT
ap-1418	115	1	we	we	PRON
ap-1418	115	2	use	use	VERB
ap-1418	115	3	the	the	DET
ap-1418	115	4	following	follow	VERB
ap-1418	115	5	procedure	procedure	NOUN
ap-1418	115	6	for	for	ADP
ap-1418	115	7	complex	complex	ADJ
ap-1418	115	8	wave	wave	NOUN
ap-1418	115	9	functions	function	NOUN
ap-1418	115	10	.	.	PUNCT
ap-1418	116	1	any	any	DET
ap-1418	116	2	complex	complex	ADJ
ap-1418	116	3	wave	wave	NOUN
ap-1418	116	4	function	function	NOUN
ap-1418	116	5	can	can	AUX
ap-1418	116	6	be	be	AUX
ap-1418	116	7	written	write	VERB
ap-1418	116	8	as	as	ADP
ap-1418	116	9	ψ(r	ψ(r	NOUN
ap-1418	116	10	)	)	PUNCT
ap-1418	116	11	=	=	SYM
ap-1418	116	12	eα(r)+iβ(r	eα(r)+iβ(r	PROPN
ap-1418	116	13	)	)	PUNCT
ap-1418	116	14	,	,	PUNCT
ap-1418	116	15	(	(	PUNCT
ap-1418	116	16	4	4	X
ap-1418	116	17	)	)	PUNCT
ap-1418	116	18	where	where	SCONJ
ap-1418	116	19	the	the	DET
ap-1418	116	20	real	real	ADJ
ap-1418	116	21	functions	function	NOUN
ap-1418	116	22	α(r	α(r	NOUN
ap-1418	116	23	)	)	PUNCT
ap-1418	116	24	and	and	CCONJ
ap-1418	116	25	β(r	β(r	NOUN
ap-1418	116	26	)	)	PUNCT
ap-1418	116	27	determine	determine	VERB
ap-1418	116	28	the	the	DET
ap-1418	116	29	amplitude	amplitude	NOUN
ap-1418	116	30	and	and	CCONJ
ap-1418	116	31	phase	phase	NOUN
ap-1418	116	32	of	of	ADP
ap-1418	116	33	the	the	DET
ap-1418	116	34	wave	wave	NOUN
ap-1418	116	35	function	function	NOUN
ap-1418	116	36	,	,	PUNCT
ap-1418	116	37	respectively	respectively	ADV
ap-1418	116	38	.	.	PUNCT
ap-1418	117	1	the	the	DET
ap-1418	117	2	complex	complex	ADJ
ap-1418	117	3	conjugate	conjugate	NOUN
ap-1418	117	4	and	and	CCONJ
ap-1418	117	5	the	the	DET
ap-1418	117	6	square	square	ADJ
ap-1418	117	7	modulus	modulus	NOUN
ap-1418	117	8	of	of	ADP
ap-1418	117	9	ψ(r	ψ(r	NOUN
ap-1418	117	10	)	)	PUNCT
ap-1418	117	11	read	read	VERB
ap-1418	117	12	ψ∗(r	ψ∗(r	NUM
ap-1418	117	13	)	)	PUNCT
ap-1418	117	14	=	=	SYM
ap-1418	117	15	eα(r)−iβ(r	eα(r)−iβ(r	NOUN
ap-1418	117	16	)	)	PUNCT
ap-1418	117	17	,	,	PUNCT
ap-1418	117	18	|ψ(r)|2	|ψ(r)|2	NOUN
ap-1418	117	19	=	=	SYM
ap-1418	117	20	e2α(r	e2α(r	NOUN
ap-1418	117	21	)	)	PUNCT
ap-1418	117	22	.	.	PUNCT
ap-1418	118	1	(	(	PUNCT
ap-1418	118	2	5	5	X
ap-1418	118	3	)	)	PUNCT
ap-1418	118	4	the	the	DET
ap-1418	118	5	gross	gross	ADJ
ap-1418	118	6	-	-	PUNCT
ap-1418	118	7	pitaevskii	pitaevskii	ADJ
ap-1418	118	8	system	system	NOUN
ap-1418	118	9	can	can	AUX
ap-1418	118	10	then	then	ADV
ap-1418	118	11	be	be	AUX
ap-1418	118	12	transformed	transform	VERB
ap-1418	118	13	into	into	ADP
ap-1418	118	14	two	two	NUM
ap-1418	118	15	coupled	couple	VERB
ap-1418	118	16	nonlinear	nonlinear	ADJ
ap-1418	118	17	differential	differential	ADJ
ap-1418	118	18	equations	equation	NOUN
ap-1418	118	19	for	for	ADP
ap-1418	118	20	the	the	DET
ap-1418	118	21	real	real	ADJ
ap-1418	118	22	functions	function	NOUN
ap-1418	118	23	α(r	α(r	NOUN
ap-1418	118	24	)	)	PUNCT
ap-1418	118	25	and	and	CCONJ
ap-1418	118	26	β(r	β(r	NOUN
ap-1418	118	27	)	)	PUNCT
ap-1418	118	28	,	,	PUNCT
ap-1418	118	29	however	however	ADV
ap-1418	118	30	,	,	PUNCT
ap-1418	118	31	without	without	ADP
ap-1418	118	32	any	any	DET
ap-1418	118	33	complex	complex	ADJ
ap-1418	118	34	conjugate	conjugate	ADJ
ap-1418	118	35	or	or	CCONJ
ap-1418	118	36	square	square	ADJ
ap-1418	118	37	modulus	modulus	NOUN
ap-1418	118	38	.	.	PUNCT
ap-1418	119	1	these	these	DET
ap-1418	119	2	equations	equation	NOUN
ap-1418	119	3	can	can	AUX
ap-1418	119	4	now	now	ADV
ap-1418	119	5	be	be	AUX
ap-1418	119	6	continued	continue	VERB
ap-1418	119	7	analytically	analytically	ADV
ap-1418	119	8	by	by	ADP
ap-1418	119	9	allowing	allow	VERB
ap-1418	119	10	for	for	ADP
ap-1418	119	11	complex	complex	ADJ
ap-1418	119	12	valued	value	VERB
ap-1418	119	13	functions	function	NOUN
ap-1418	119	14	α(r	α(r	NOUN
ap-1418	119	15	)	)	PUNCT
ap-1418	119	16	and	and	CCONJ
ap-1418	119	17	β(r	β(r	NOUN
ap-1418	119	18	)	)	PUNCT
ap-1418	119	19	.	.	PUNCT
ap-1418	120	1	this	this	PRON
ap-1418	120	2	implies	imply	VERB
ap-1418	120	3	that	that	SCONJ
ap-1418	120	4	ψ∗(r	ψ∗(r	NOUN
ap-1418	120	5	)	)	PUNCT
ap-1418	120	6	=	=	SYM
ap-1418	120	7	eα(r)−iβ(r	eα(r)−iβ(r	NOUN
ap-1418	120	8	)	)	PUNCT
ap-1418	120	9	,	,	PUNCT
ap-1418	120	10	|ψ(r)|2	|ψ(r)|2	NOUN
ap-1418	120	11	=	=	SYM
ap-1418	120	12	e2α(r	e2α(r	NOUN
ap-1418	120	13	)	)	PUNCT
ap-1418	120	14	.	.	PUNCT
ap-1418	121	1	without	without	ADP
ap-1418	121	2	complex	complex	ADJ
ap-1418	121	3	conjugation	conjugation	NOUN
ap-1418	121	4	of	of	ADP
ap-1418	121	5	α(r	α(r	NOUN
ap-1418	121	6	)	)	PUNCT
ap-1418	121	7	and	and	CCONJ
ap-1418	121	8	β(r	β(r	NOUN
ap-1418	121	9	)	)	PUNCT
ap-1418	121	10	is	be	AUX
ap-1418	121	11	formally	formally	ADV
ap-1418	121	12	used	use	VERB
ap-1418	121	13	for	for	ADP
ap-1418	121	14	the	the	DET
ap-1418	121	15	calculation	calculation	NOUN
ap-1418	121	16	of	of	ADP
ap-1418	121	17	ψ∗	ψ∗	NOUN
ap-1418	121	18	and	and	CCONJ
ap-1418	121	19	|ψ(r)|2	|ψ(r)|2	NOUN
ap-1418	121	20	.	.	PUNCT
ap-1418	122	1	as	as	ADP
ap-1418	122	2	a	a	DET
ap-1418	122	3	consequence	consequence	NOUN
ap-1418	122	4	,	,	PUNCT
ap-1418	122	5	the	the	DET
ap-1418	122	6	square	square	ADJ
ap-1418	122	7	modulus	modulus	NOUN
ap-1418	122	8	of	of	ADP
ap-1418	122	9	ψ	ψ	NOUN
ap-1418	122	10	can	can	AUX
ap-1418	122	11	become	become	VERB
ap-1418	122	12	complex	complex	ADJ
ap-1418	122	13	,	,	PUNCT
ap-1418	122	14	leading	lead	VERB
ap-1418	122	15	to	to	ADP
ap-1418	122	16	a	a	DET
ap-1418	122	17	complex	complex	ADJ
ap-1418	122	18	absorbing	absorbing	ADJ
ap-1418	122	19	potential	potential	NOUN
ap-1418	122	20	in	in	ADP
ap-1418	122	21	the	the	DET
ap-1418	122	22	gross	gross	ADJ
ap-1418	122	23	-	-	PUNCT
ap-1418	122	24	pitaevskii	pitaevskii	ADJ
ap-1418	122	25	equation	equation	NOUN
ap-1418	122	26	.	.	PUNCT
ap-1418	123	1	figure	figure	NOUN
ap-1418	123	2	6	6	NUM
ap-1418	123	3	shows	show	VERB
ap-1418	123	4	a	a	DET
ap-1418	123	5	comparison	comparison	NOUN
ap-1418	123	6	between	between	ADP
ap-1418	123	7	the	the	DET
ap-1418	123	8	results	result	NOUN
ap-1418	123	9	of	of	ADP
ap-1418	123	10	the	the	DET
ap-1418	123	11	variational	variational	NOUN
ap-1418	123	12	and	and	CCONJ
ap-1418	123	13	the	the	DET
ap-1418	123	14	numerically	numerically	ADV
ap-1418	123	15	accurate	accurate	ADJ
ap-1418	123	16	calculation	calculation	NOUN
ap-1418	123	17	.	.	PUNCT
ap-1418	124	1	the	the	DET
ap-1418	124	2	first	first	ADJ
ap-1418	124	3	row	row	NOUN
ap-1418	124	4	shows	show	VERB
ap-1418	124	5	the	the	DET
ap-1418	124	6	circles	circle	NOUN
ap-1418	124	7	of	of	ADP
ap-1418	124	8	radius	radius	NOUN
ap-1418	124	9	r	r	NOUN
ap-1418	124	10	=	=	SYM
ap-1418	124	11	10−3	10−3	NUM
ap-1418	124	12	around	around	ADP
ap-1418	124	13	the	the	DET
ap-1418	124	14	respective	respective	ADJ
ap-1418	124	15	critical	critical	ADJ
ap-1418	124	16	values	value	NOUN
ap-1418	124	17	of	of	ADP
ap-1418	124	18	the	the	DET
ap-1418	124	19	scattering	scatter	VERB
ap-1418	124	20	length	length	NOUN
ap-1418	124	21	where	where	SCONJ
ap-1418	124	22	the	the	DET
ap-1418	124	23	bifurcation	bifurcation	NOUN
ap-1418	124	24	appears	appear	VERB
ap-1418	124	25	.	.	PUNCT
ap-1418	125	1	the	the	DET
ap-1418	125	2	second	second	ADJ
ap-1418	125	3	row	row	NOUN
ap-1418	125	4	compares	compare	VERB
ap-1418	125	5	the	the	DET
ap-1418	125	6	results	result	NOUN
ap-1418	125	7	for	for	ADP
ap-1418	125	8	the	the	DET
ap-1418	125	9	chemical	chemical	NOUN
ap-1418	125	10	potential	potential	NOUN
ap-1418	125	11	,	,	PUNCT
ap-1418	125	12	and	and	CCONJ
ap-1418	125	13	the	the	DET
ap-1418	125	14	third	third	ADJ
ap-1418	125	15	row	row	NOUN
ap-1418	125	16	for	for	ADP
ap-1418	125	17	the	the	DET
ap-1418	125	18	mean	mean	ADJ
ap-1418	125	19	-	-	PUNCT
ap-1418	125	20	field	field	NOUN
ap-1418	125	21	energy	energy	NOUN
ap-1418	125	22	as	as	SCONJ
ap-1418	125	23	the	the	DET
ap-1418	125	24	circles	circle	NOUN
ap-1418	125	25	in	in	ADP
ap-1418	125	26	the	the	DET
ap-1418	125	27	complex	complex	ADJ
ap-1418	125	28	scattering	scattering	NOUN
ap-1418	125	29	length	length	NOUN
ap-1418	125	30	plane	plane	NOUN
ap-1418	125	31	are	be	AUX
ap-1418	125	32	traversed	traverse	VERB
ap-1418	125	33	.	.	PUNCT
ap-1418	126	1	obviously	obviously	ADV
ap-1418	126	2	the	the	DET
ap-1418	126	3	permutation	permutation	NOUN
ap-1418	126	4	behaviour	behaviour	NOUN
ap-1418	126	5	is	be	AUX
ap-1418	126	6	identical	identical	ADJ
ap-1418	126	7	in	in	ADP
ap-1418	126	8	both	both	DET
ap-1418	126	9	approaches	approach	NOUN
ap-1418	126	10	,	,	PUNCT
ap-1418	126	11	proving	prove	VERB
ap-1418	126	12	that	that	SCONJ
ap-1418	126	13	the	the	DET
ap-1418	126	14	bifurcation	bifurcation	NOUN
ap-1418	126	15	point	point	NOUN
ap-1418	126	16	is	be	AUX
ap-1418	126	17	indeed	indeed	ADV
ap-1418	126	18	an	an	DET
ap-1418	126	19	exceptional	exceptional	ADJ
ap-1418	126	20	point	point	NOUN
ap-1418	126	21	also	also	ADV
ap-1418	126	22	in	in	ADP
ap-1418	126	23	the	the	DET
ap-1418	126	24	full	full	ADJ
ap-1418	126	25	numerical	numerical	ADJ
ap-1418	126	26	solution	solution	NOUN
ap-1418	126	27	of	of	ADP
ap-1418	126	28	the	the	DET
ap-1418	126	29	nonlinear	nonlinear	ADJ
ap-1418	126	30	schrödinger	schrödinger	NOUN
ap-1418	126	31	equation	equation	NOUN
ap-1418	126	32	which	which	PRON
ap-1418	126	33	describes	describe	VERB
ap-1418	126	34	the	the	DET
ap-1418	126	35	bose	bose	NOUN
ap-1418	126	36	-	-	PUNCT
ap-1418	126	37	einstein	einstein	NOUN
ap-1418	126	38	condensation	condensation	NOUN
ap-1418	126	39	of	of	ADP
ap-1418	126	40	ultracold	ultracold	PROPN
ap-1418	126	41	atomic	atomic	ADJ
ap-1418	126	42	gases	gas	NOUN
ap-1418	126	43	with	with	ADP
ap-1418	126	44	a	a	DET
ap-1418	126	45	long	long	ADJ
ap-1418	126	46	-	-	PUNCT
ap-1418	126	47	range	range	NOUN
ap-1418	126	48	attractive	attractive	ADJ
ap-1418	126	49	1	1	NUM
ap-1418	126	50	/	/	SYM
ap-1418	126	51	r	r	NOUN
ap-1418	126	52	interaction	interaction	NOUN
ap-1418	126	53	.	.	PUNCT
ap-1418	127	1	3	3	NUM
ap-1418	127	2	dipolar	dipolar	ADJ
ap-1418	127	3	condensates	condensate	NOUN
ap-1418	127	4	to	to	PART
ap-1418	127	5	find	find	VERB
ap-1418	127	6	stationary	stationary	ADJ
ap-1418	127	7	solutions	solution	NOUN
ap-1418	127	8	of	of	ADP
ap-1418	127	9	the	the	DET
ap-1418	127	10	gross	gross	ADJ
ap-1418	127	11	-	-	PUNCT
ap-1418	127	12	pitaevskii	pitaevskii	ADJ
ap-1418	127	13	equation	equation	NOUN
ap-1418	127	14	(	(	PUNCT
ap-1418	127	15	2	2	NUM
ap-1418	127	16	)	)	PUNCT
ap-1418	127	17	of	of	ADP
ap-1418	127	18	dipolar	dipolar	ADJ
ap-1418	127	19	gases	gas	NOUN
ap-1418	127	20	,	,	PUNCT
ap-1418	127	21	we	we	PRON
ap-1418	127	22	could	could	AUX
ap-1418	127	23	of	of	ADV
ap-1418	127	24	course	course	NOUN
ap-1418	127	25	again	again	ADV
ap-1418	127	26	extremize	extremize	VERB
ap-1418	127	27	the	the	DET
ap-1418	127	28	mean	mean	ADJ
ap-1418	127	29	-	-	PUNCT
ap-1418	127	30	field	field	NOUN
ap-1418	127	31	energy	energy	NOUN
ap-1418	127	32	functional	functional	ADJ
ap-1418	127	33	for	for	ADP
ap-1418	127	34	a	a	DET
ap-1418	127	35	given	give	VERB
ap-1418	127	36	variational	variational	ADJ
ap-1418	127	37	ansatz	ansatz	NOUN
ap-1418	127	38	.	.	PUNCT
ap-1418	128	1	a	a	DET
ap-1418	128	2	more	more	ADV
ap-1418	128	3	sophisticated	sophisticated	ADJ
ap-1418	128	4	way	way	NOUN
ap-1418	128	5	is	be	AUX
ap-1418	128	6	to	to	PART
ap-1418	128	7	exploit	exploit	VERB
ap-1418	128	8	the	the	DET
ap-1418	128	9	time	time	NOUN
ap-1418	128	10	-	-	PUNCT
ap-1418	128	11	dependent	dependent	ADJ
ap-1418	128	12	variational	variational	ADJ
ap-1418	128	13	principle	principle	NOUN
ap-1418	128	14	[	[	X
ap-1418	128	15	12	12	NUM
ap-1418	128	16	]	]	X
ap-1418	128	17	||iφ(t	||iφ(t	PROPN
ap-1418	128	18	)	)	PUNCT
ap-1418	128	19	−	−	PROPN
ap-1418	128	20	hψ(t)||2	hψ(t)||2	NOUN
ap-1418	128	21	!	!	PUNCT
ap-1418	129	1	=	=	PRON
ap-1418	129	2	min	min	NOUN
ap-1418	129	3	with	with	ADP
ap-1418	129	4	respect	respect	NOUN
ap-1418	129	5	to	to	ADP
ap-1418	129	6	φ	φ	PROPN
ap-1418	129	7	(	(	PUNCT
ap-1418	129	8	6	6	NUM
ap-1418	129	9	)	)	PUNCT
ap-1418	129	10	and	and	CCONJ
ap-1418	129	11	afterwards	afterwards	ADV
ap-1418	129	12	set	set	VERB
ap-1418	129	13	ψ̇	ψ̇	PROPN
ap-1418	129	14	≡	≡	PROPN
ap-1418	129	15	φ	φ	PROPN
ap-1418	129	16	.	.	PUNCT
ap-1418	130	1	if	if	SCONJ
ap-1418	130	2	a	a	DET
ap-1418	130	3	complex	complex	ADJ
ap-1418	130	4	parametrization	parametrization	NOUN
ap-1418	130	5	of	of	ADP
ap-1418	130	6	the	the	DET
ap-1418	130	7	trial	trial	NOUN
ap-1418	130	8	wave	wave	NOUN
ap-1418	130	9	function	function	VERB
ap-1418	130	10	ψ(t	ψ(t	PROPN
ap-1418	130	11	)	)	PUNCT
ap-1418	130	12	=	=	SYM
ap-1418	130	13	χ(λ(t	χ(λ(t	PROPN
ap-1418	130	14	)	)	PUNCT
ap-1418	130	15	)	)	PUNCT
ap-1418	130	16	is	be	AUX
ap-1418	130	17	assumed	assume	VERB
ap-1418	130	18	,	,	PUNCT
ap-1418	130	19	the	the	DET
ap-1418	130	20	variation	variation	NOUN
ap-1418	130	21	leads	lead	VERB
ap-1418	130	22	to	to	ADP
ap-1418	130	23	equations	equation	NOUN
ap-1418	130	24	of	of	ADP
ap-1418	130	25	motion	motion	NOUN
ap-1418	130	26	for	for	ADP
ap-1418	130	27	these	these	DET
ap-1418	130	28	parameters	parameter	NOUN
ap-1418	130	29	λ(t	λ(t	PRON
ap-1418	130	30	)	)	PUNCT
ap-1418	131	1	[	[	X
ap-1418	131	2	13	13	NUM
ap-1418	131	3	]	]	PUNCT
ap-1418	131	4	.	.	PUNCT
ap-1418	132	1	〈	〈	PROPN
ap-1418	132	2	∂ψ	∂ψ	PROPN
ap-1418	132	3	∂λ	∂λ	PROPN
ap-1418	132	4	∣∣∣iψ̇	∣∣∣iψ̇	ADP
ap-1418	132	5	−	−	NOUN
ap-1418	132	6	hψ	hψ	NOUN
ap-1418	132	7	〉	〉	NOUN
ap-1418	132	8	=	=	SYM
ap-1418	132	9	0	0	NUM
ap-1418	132	10	↔	↔	PROPN
ap-1418	132	11	(	(	PUNCT
ap-1418	132	12	7	7	NUM
ap-1418	132	13	)	)	PUNCT
ap-1418	132	14	kλ̇	kλ̇	PROPN
ap-1418	133	1	=	=	PUNCT
ap-1418	133	2	−ih	−ih	PROPN
ap-1418	133	3	with	with	ADP
ap-1418	133	4	k	k	PROPN
ap-1418	133	5	=	=	PUNCT
ap-1418	133	6	〈	〈	PROPN
ap-1418	133	7	∂ψ	∂ψ	PROPN
ap-1418	134	1	∂λ	∂λ	PROPN
ap-1418	134	2	∣∣∣∂ψ	∣∣∣∂ψ	PROPN
ap-1418	134	3	∂λ	∂λ	ADJ
ap-1418	134	4	〉	〉	NOUN
ap-1418	134	5	,	,	PUNCT
ap-1418	134	6	h	h	NOUN
ap-1418	134	7	=	=	PUNCT
ap-1418	134	8	〈	〈	PROPN
ap-1418	134	9	∂ψ	∂ψ	PROPN
ap-1418	134	10	∂λ	∂λ	PROPN
ap-1418	134	11	∣∣∣h∣∣∣ψ	∣∣∣h∣∣∣ψ	PROPN
ap-1418	134	12	〉	〉	NOUN
ap-1418	134	13	.	.	PUNCT
ap-1418	135	1	3.1	3.1	NUM
ap-1418	135	2	variational	variational	ADJ
ap-1418	135	3	results	result	NOUN
ap-1418	135	4	we	we	PRON
ap-1418	135	5	assume	assume	VERB
ap-1418	135	6	an	an	DET
ap-1418	135	7	axisymmetric	axisymmetric	ADJ
ap-1418	135	8	trapping	trap	VERB
ap-1418	135	9	potential	potential	NOUN
ap-1418	135	10	,	,	PUNCT
ap-1418	135	11	and	and	CCONJ
ap-1418	135	12	take	take	VERB
ap-1418	135	13	the	the	DET
ap-1418	135	14	time	time	NOUN
ap-1418	135	15	-	-	PUNCT
ap-1418	135	16	dependent	dependent	ADJ
ap-1418	135	17	gaussian	gaussian	ADJ
ap-1418	135	18	trial	trial	NOUN
ap-1418	135	19	wave	wave	NOUN
ap-1418	135	20	function	function	NOUN
ap-1418	135	21	ψ(ρ	ψ(ρ	PROPN
ap-1418	135	22	,	,	PUNCT
ap-1418	135	23	z	z	PROPN
ap-1418	135	24	,	,	PUNCT
ap-1418	135	25	t	t	PROPN
ap-1418	135	26	)	)	PUNCT
ap-1418	135	27	=	=	SYM
ap-1418	135	28	ei(aρρ2+azz2+γ	ei(aρρ2+azz2+γ	NOUN
ap-1418	135	29	)	)	PUNCT
ap-1418	135	30	,	,	PUNCT
ap-1418	135	31	(	(	PUNCT
ap-1418	135	32	8)	8)	NUM
ap-1418	135	33	aρ	aρ	NOUN
ap-1418	135	34	=	=	PUNCT
ap-1418	135	35	aρ(t	aρ(t	ADP
ap-1418	135	36	)	)	PUNCT
ap-1418	135	37	,	,	PUNCT
ap-1418	135	38	az	az	PROPN
ap-1418	135	39	=	=	SYM
ap-1418	135	40	az(t	az(t	X
ap-1418	135	41	)	)	PUNCT
ap-1418	135	42	,	,	PUNCT
ap-1418	135	43	γ	γ	X
ap-1418	135	44	=	=	SYM
ap-1418	135	45	γ(t	γ(t	PROPN
ap-1418	135	46	)	)	PUNCT
ap-1418	135	47	,	,	PUNCT
ap-1418	135	48	where	where	SCONJ
ap-1418	135	49	all	all	DET
ap-1418	135	50	three	three	NUM
ap-1418	135	51	parameters	parameter	NOUN
ap-1418	135	52	are	be	AUX
ap-1418	135	53	complex	complex	ADJ
ap-1418	135	54	functions	function	NOUN
ap-1418	135	55	of	of	ADP
ap-1418	135	56	time	time	NOUN
ap-1418	135	57	.	.	PUNCT
ap-1418	136	1	the	the	DET
ap-1418	136	2	equations	equation	NOUN
ap-1418	136	3	of	of	ADP
ap-1418	136	4	motion	motion	NOUN
ap-1418	136	5	that	that	PRON
ap-1418	136	6	follow	follow	VERB
ap-1418	136	7	for	for	ADP
ap-1418	136	8	the	the	DET
ap-1418	136	9	real	real	ADJ
ap-1418	136	10	and	and	CCONJ
ap-1418	136	11	imaginary	imaginary	ADJ
ap-1418	136	12	parts	part	NOUN
ap-1418	136	13	of	of	ADP
ap-1418	136	14	the	the	DET
ap-1418	136	15	variational	variational	ADJ
ap-1418	136	16	parameters	parameter	NOUN
ap-1418	136	17	from	from	ADP
ap-1418	136	18	the	the	DET
ap-1418	136	19	time	time	NOUN
ap-1418	136	20	dependent	dependent	ADJ
ap-1418	136	21	variational	variational	ADJ
ap-1418	136	22	principle	principle	NOUN
ap-1418	136	23	read	read	VERB
ap-1418	136	24	ȧr	ȧr	PROPN
ap-1418	136	25	ρ	ρ	PROPN
ap-1418	136	26	=	=	SYM
ap-1418	136	27	−4((ar	−4((ar	PROPN
ap-1418	136	28	ρ)2	ρ)2	NOUN
ap-1418	136	29	−	−	PROPN
ap-1418	136	30	(	(	PUNCT
ap-1418	136	31	ai	ai	VERB
ap-1418	136	32	ρ)2	ρ)2	PROPN
ap-1418	136	33	)	)	PUNCT
ap-1418	137	1	+	+	CCONJ
ap-1418	137	2	fρ(ai	fρ(ai	PROPN
ap-1418	137	3	ρ	ρ	PROPN
ap-1418	137	4	,	,	PUNCT
ap-1418	137	5	a	a	PRON
ap-1418	137	6	i	i	PROPN
ap-1418	137	7	z	z	NOUN
ap-1418	137	8	,	,	PUNCT
ap-1418	137	9	γ	γ	PROPN
ap-1418	137	10	i	i	PROPN
ap-1418	137	11	)	)	PUNCT
ap-1418	137	12	ȧi	ȧi	PROPN
ap-1418	137	13	ρ	ρ	NOUN
ap-1418	138	1	=	=	SYM
ap-1418	139	1	−8ar	−8ar	NUM
ap-1418	140	1	ρa	ρa	INTJ
ap-1418	141	1	i	i	PRON
ap-1418	141	2	ρ	ρ	PROPN
ap-1418	141	3	ȧr	ȧr	PROPN
ap-1418	141	4	z	z	PROPN
ap-1418	141	5	=	=	SYM
ap-1418	141	6	−4((ar	−4((ar	PROPN
ap-1418	141	7	z)2	z)2	NOUN
ap-1418	141	8	−	−	PROPN
ap-1418	141	9	(	(	PUNCT
ap-1418	141	10	ai	ai	PROPN
ap-1418	141	11	z)2	z)2	NOUN
ap-1418	141	12	)	)	PUNCT
ap-1418	141	13	+	+	CCONJ
ap-1418	141	14	fz(ai	fz(ai	PROPN
ap-1418	141	15	ρ	ρ	PROPN
ap-1418	141	16	,	,	PUNCT
ap-1418	141	17	a	a	PRON
ap-1418	141	18	i	i	PROPN
ap-1418	141	19	z	z	NOUN
ap-1418	141	20	,	,	PUNCT
ap-1418	141	21	γ	γ	PROPN
ap-1418	141	22	i	i	PROPN
ap-1418	141	23	)	)	PUNCT
ap-1418	141	24	ȧi	ȧi	PROPN
ap-1418	141	25	z	z	NOUN
ap-1418	141	26	=	=	PUNCT
ap-1418	141	27	−8ar	−8ar	NUM
ap-1418	141	28	za	za	PROPN
ap-1418	142	1	i	i	PROPN
ap-1418	142	2	z	z	PROPN
ap-1418	142	3	γ̇r	γ̇r	PROPN
ap-1418	143	1	=	=	SYM
ap-1418	143	2	−4ai	−4ai	NOUN
ap-1418	143	3	ρ	ρ	NOUN
ap-1418	144	1	−	−	PROPN
ap-1418	144	2	2ai	2ai	ADJ
ap-1418	144	3	z	z	NOUN
ap-1418	144	4	+	+	NUM
ap-1418	144	5	fγ(ai	fγ(ai	PROPN
ap-1418	144	6	ρ	ρ	PROPN
ap-1418	144	7	,	,	PUNCT
ap-1418	144	8	a	a	DET
ap-1418	144	9	i	i	PROPN
ap-1418	144	10	z	z	NOUN
ap-1418	144	11	,	,	PUNCT
ap-1418	144	12	γ	γ	PROPN
ap-1418	144	13	i	i	PROPN
ap-1418	144	14	)	)	PUNCT
ap-1418	144	15	γ̇i	γ̇i	PROPN
ap-1418	145	1	=	=	SYM
ap-1418	145	2	4ar	4ar	ADJ
ap-1418	145	3	ρ	ρ	NOUN
ap-1418	145	4	+	+	CCONJ
ap-1418	145	5	2ar	2ar	ADJ
ap-1418	145	6	z	z	NOUN
ap-1418	145	7	and	and	CCONJ
ap-1418	145	8	are	be	AUX
ap-1418	145	9	solved	solve	VERB
ap-1418	145	10	with	with	ADP
ap-1418	145	11	the	the	DET
ap-1418	145	12	initial	initial	ADJ
ap-1418	145	13	values	value	NOUN
ap-1418	145	14	ar	ar	NOUN
ap-1418	145	15	ρ	ρ	PROPN
ap-1418	145	16	=	=	SYM
ap-1418	145	17	0	0	NUM
ap-1418	145	18	,	,	PUNCT
ap-1418	145	19	ai	ai	VERB
ap-1418	145	20	ρ	ρ	PROPN
ap-1418	145	21	>	>	X
ap-1418	145	22	0	0	NUM
ap-1418	145	23	,	,	PUNCT
ap-1418	145	24	ar	ar	NOUN
ap-1418	145	25	z	z	PROPN
ap-1418	145	26	=	=	SYM
ap-1418	145	27	0	0	NUM
ap-1418	145	28	,	,	PUNCT
ap-1418	145	29	ai	ai	VERB
ap-1418	145	30	z	z	NOUN
ap-1418	145	31	>	>	X
ap-1418	145	32	0	0	PUNCT
ap-1418	146	1	and	and	CCONJ
ap-1418	146	2	γi	γi	X
ap-1418	146	3	=	=	SYM
ap-1418	146	4	1	1	NUM
ap-1418	146	5	2	2	NUM
ap-1418	146	6	ln	ln	NOUN
ap-1418	146	7	π3/2	π3/2	NOUN
ap-1418	146	8	2	2	NUM
ap-1418	146	9	√	√	NUM
ap-1418	146	10	2ai	2ai	ADJ
ap-1418	146	11	ρ	ρ	NOUN
ap-1418	146	12	√	√	PROPN
ap-1418	146	13	ai	ai	VERB
ap-1418	146	14	z	z	NOUN
ap-1418	146	15	.	.	PUNCT
ap-1418	147	1	(	(	PUNCT
ap-1418	147	2	9	9	X
ap-1418	147	3	)	)	PUNCT
ap-1418	147	4	this	this	DET
ap-1418	147	5	results	result	VERB
ap-1418	147	6	in	in	ADP
ap-1418	147	7	four	four	NUM
ap-1418	147	8	remaining	remain	VERB
ap-1418	147	9	coupled	couple	VERB
ap-1418	147	10	ordinary	ordinary	ADJ
ap-1418	147	11	differential	differential	ADJ
ap-1418	147	12	equations	equation	NOUN
ap-1418	147	13	for	for	ADP
ap-1418	147	14	ȧr	ȧr	PROPN
ap-1418	147	15	ρ	ρ	PROPN
ap-1418	147	16	,	,	PUNCT
ap-1418	147	17	ȧ	ȧ	PROPN
ap-1418	147	18	i	i	PROPN
ap-1418	147	19	ρ	ρ	PROPN
ap-1418	147	20	,	,	PUNCT
ap-1418	147	21	ȧ	ȧ	PROPN
ap-1418	147	22	r	r	NOUN
ap-1418	147	23	z	z	NOUN
ap-1418	147	24	,	,	PUNCT
ap-1418	147	25	ȧ	ȧ	PROPN
ap-1418	148	1	i	i	PRON
ap-1418	148	2	z.	z.	PROPN
ap-1418	149	1	variational	variational	ADJ
ap-1418	149	2	stationary	stationary	ADJ
ap-1418	149	3	solutions	solution	NOUN
ap-1418	149	4	of	of	ADP
ap-1418	149	5	the	the	DET
ap-1418	149	6	gross	gross	ADJ
ap-1418	149	7	-	-	PUNCT
ap-1418	149	8	pitevskii	pitevskii	NOUN
ap-1418	149	9	equation	equation	NOUN
ap-1418	149	10	(	(	PUNCT
ap-1418	149	11	2	2	X
ap-1418	149	12	)	)	PUNCT
ap-1418	149	13	are	be	AUX
ap-1418	149	14	then	then	ADV
ap-1418	149	15	obtained	obtain	VERB
ap-1418	149	16	by	by	ADP
ap-1418	149	17	searching	search	VERB
ap-1418	149	18	for	for	ADP
ap-1418	149	19	the	the	DET
ap-1418	149	20	fixed	fix	VERB
ap-1418	149	21	points	point	NOUN
ap-1418	149	22	of	of	ADP
ap-1418	149	23	these	these	DET
ap-1418	149	24	differential	differential	ADJ
ap-1418	149	25	equations	equation	NOUN
ap-1418	149	26	.	.	PUNCT
ap-1418	150	1	as	as	ADP
ap-1418	150	2	in	in	ADP
ap-1418	150	3	the	the	DET
ap-1418	150	4	monopolar	monopolar	ADJ
ap-1418	150	5	case	case	NOUN
ap-1418	150	6	two	two	NUM
ap-1418	150	7	stationary	stationary	ADJ
ap-1418	150	8	points	point	NOUN
ap-1418	150	9	are	be	AUX
ap-1418	150	10	found	find	VERB
ap-1418	150	11	,	,	PUNCT
ap-1418	150	12	one	one	NUM
ap-1418	150	13	stable	stable	ADJ
ap-1418	150	14	,	,	PUNCT
ap-1418	150	15	representing	represent	VERB
ap-1418	150	16	the	the	DET
ap-1418	150	17	ground	ground	NOUN
ap-1418	150	18	state	state	NOUN
ap-1418	150	19	,	,	PUNCT
ap-1418	150	20	and	and	CCONJ
ap-1418	150	21	one	one	NUM
ap-1418	150	22	unstable	unstable	ADJ
ap-1418	150	23	,	,	PUNCT
ap-1418	150	24	representing	represent	VERB
ap-1418	150	25	a	a	DET
ap-1418	150	26	collectively	collectively	ADV
ap-1418	150	27	excited	excited	ADJ
ap-1418	150	28	state	state	NOUN
ap-1418	150	29	.	.	PUNCT
ap-1418	151	1	figure	figure	NOUN
ap-1418	151	2	7	7	NUM
ap-1418	151	3	shows	show	VERB
ap-1418	151	4	the	the	DET
ap-1418	151	5	results	result	NOUN
ap-1418	151	6	for	for	ADP
ap-1418	151	7	the	the	DET
ap-1418	151	8	chemical	chemical	NOUN
ap-1418	151	9	potential	potential	NOUN
ap-1418	151	10	and	and	CCONJ
ap-1418	151	11	the	the	DET
ap-1418	151	12	mean	mean	ADJ
ap-1418	151	13	-	-	PUNCT
ap-1418	151	14	field	field	NOUN
ap-1418	151	15	energy	energy	NOUN
ap-1418	151	16	as	as	ADP
ap-1418	151	17	functions	function	NOUN
ap-1418	151	18	of	of	ADP
ap-1418	151	19	the	the	DET
ap-1418	151	20	scattering	scatter	VERB
ap-1418	151	21	length	length	NOUN
ap-1418	151	22	for	for	ADP
ap-1418	151	23	different	different	ADJ
ap-1418	151	24	aspect	aspect	NOUN
ap-1418	151	25	ratios	ratio	NOUN
ap-1418	151	26	.	.	PUNCT
ap-1418	152	1	it	it	PRON
ap-1418	152	2	is	be	AUX
ap-1418	152	3	evident	evident	ADJ
ap-1418	152	4	that	that	SCONJ
ap-1418	152	5	again	again	ADV
ap-1418	152	6	the	the	DET
ap-1418	152	7	two	two	NUM
ap-1418	152	8	stationary	stationary	ADJ
ap-1418	152	9	solutions	solution	NOUN
ap-1418	152	10	are	be	AUX
ap-1418	152	11	born	bear	VERB
ap-1418	152	12	at	at	ADP
ap-1418	152	13	a	a	DET
ap-1418	152	14	critical	critical	ADJ
ap-1418	152	15	scattering	scattering	NOUN
ap-1418	152	16	length	length	NOUN
ap-1418	152	17	in	in	ADP
ap-1418	152	18	a	a	DET
ap-1418	152	19	tangent	tangent	NOUN
ap-1418	152	20	bifurcation	bifurcation	NOUN
ap-1418	152	21	,	,	PUNCT
ap-1418	152	22	and	and	CCONJ
ap-1418	152	23	below	below	ADP
ap-1418	152	24	the	the	DET
ap-1418	152	25	critical	critical	ADJ
ap-1418	152	26	scattering	scattering	NOUN
ap-1418	152	27	length	length	NOUN
ap-1418	152	28	no	no	DET
ap-1418	152	29	stationary	stationary	ADJ
ap-1418	152	30	solutions	solution	NOUN
ap-1418	152	31	exist	exist	VERB
ap-1418	152	32	.	.	PUNCT
ap-1418	153	1	are	be	AUX
ap-1418	153	2	the	the	DET
ap-1418	153	3	bifurcation	bifurcation	NOUN
ap-1418	153	4	points	point	NOUN
ap-1418	153	5	found	find	VERB
ap-1418	153	6	in	in	ADP
ap-1418	153	7	the	the	DET
ap-1418	153	8	variational	variational	ADJ
ap-1418	153	9	calculations	calculation	NOUN
ap-1418	153	10	with	with	ADP
ap-1418	153	11	an	an	DET
ap-1418	153	12	axisymmetric	axisymmetric	ADJ
ap-1418	153	13	gaussian	gaussian	ADJ
ap-1418	153	14	wave	wave	NOUN
ap-1418	153	15	function	function	NOUN
ap-1418	153	16	also	also	ADV
ap-1418	153	17	exceptional	exceptional	ADJ
ap-1418	153	18	points	point	NOUN
ap-1418	153	19	?	?	PUNCT
ap-1418	154	1	to	to	PART
ap-1418	154	2	check	check	VERB
ap-1418	154	3	100	100	NUM
ap-1418	154	4	acta	acta	PROPN
ap-1418	154	5	polytechnica	polytechnica	PROPN
ap-1418	154	6	vol	vol	NOUN
ap-1418	154	7	.	.	PUNCT
ap-1418	155	1	51	51	NUM
ap-1418	155	2	no	no	NOUN
ap-1418	155	3	.	.	PUNCT
ap-1418	156	1	4/2011	4/2011	NUM
ap-1418	156	2	fig	fig	NOUN
ap-1418	156	3	.	.	PUNCT
ap-1418	157	1	7	7	NUM
ap-1418	157	2	:	:	PUNCT
ap-1418	157	3	chemical	chemical	ADJ
ap-1418	157	4	potential	potential	NOUN
ap-1418	157	5	(	(	PUNCT
ap-1418	157	6	left	left	ADJ
ap-1418	157	7	)	)	PUNCT
ap-1418	157	8	and	and	CCONJ
ap-1418	157	9	mean	mean	ADJ
ap-1418	157	10	-	-	PUNCT
ap-1418	157	11	field	field	NOUN
ap-1418	157	12	energy	energy	NOUN
ap-1418	157	13	(	(	PUNCT
ap-1418	157	14	right	right	ADJ
ap-1418	157	15	)	)	PUNCT
ap-1418	157	16	as	as	ADP
ap-1418	157	17	functions	function	NOUN
ap-1418	157	18	of	of	ADP
ap-1418	157	19	the	the	DET
ap-1418	157	20	scattering	scatter	VERB
ap-1418	157	21	length	length	NOUN
ap-1418	157	22	for	for	ADP
ap-1418	157	23	an	an	DET
ap-1418	157	24	axisymmetric	axisymmetric	ADJ
ap-1418	157	25	variational	variational	ADJ
ap-1418	157	26	gaussian	gaussian	NOUN
ap-1418	157	27	ansatz	ansatz	ADV
ap-1418	157	28	for	for	ADP
ap-1418	157	29	dipolar	dipolar	ADJ
ap-1418	157	30	condensates	condensate	NOUN
ap-1418	157	31	for	for	ADP
ap-1418	157	32	n2γ̄	n2γ̄	NOUN
ap-1418	157	33	=	=	PUNCT
ap-1418	157	34	3.4×	3.4×	NUM
ap-1418	157	35	104	104	NUM
ap-1418	157	36	,	,	PUNCT
ap-1418	157	37	and	and	CCONJ
ap-1418	157	38	different	different	ADJ
ap-1418	157	39	aspect	aspect	NOUN
ap-1418	157	40	ratios	ratio	NOUN
ap-1418	157	41	fig	fig	NOUN
ap-1418	157	42	.	.	PUNCT
ap-1418	158	1	8	8	NUM
ap-1418	158	2	:	:	PUNCT
ap-1418	158	3	chemical	chemical	NOUN
ap-1418	158	4	potentials	potential	NOUN
ap-1418	158	5	(	(	PUNCT
ap-1418	158	6	middle	middle	ADJ
ap-1418	158	7	)	)	PUNCT
ap-1418	158	8	and	and	CCONJ
ap-1418	158	9	mean	mean	ADJ
ap-1418	158	10	-	-	PUNCT
ap-1418	158	11	field	field	NOUN
ap-1418	158	12	energies	energy	NOUN
ap-1418	158	13	(	(	PUNCT
ap-1418	158	14	right	right	ADJ
ap-1418	158	15	)	)	PUNCT
ap-1418	158	16	for	for	ADP
ap-1418	158	17	the	the	DET
ap-1418	158	18	two	two	NUM
ap-1418	158	19	stationary	stationary	ADJ
ap-1418	158	20	solutions	solution	NOUN
ap-1418	158	21	that	that	PRON
ap-1418	158	22	emerge	emerge	VERB
ap-1418	158	23	in	in	ADP
ap-1418	158	24	a	a	DET
ap-1418	158	25	tangent	tangent	ADJ
ap-1418	158	26	bifurcation	bifurcation	NOUN
ap-1418	158	27	when	when	SCONJ
ap-1418	158	28	a	a	DET
ap-1418	158	29	circle	circle	NOUN
ap-1418	158	30	with	with	ADP
ap-1418	158	31	radius	radius	NOUN
ap-1418	158	32	r	r	NOUN
ap-1418	158	33	=	=	SYM
ap-1418	158	34	10−3	10−3	NUM
ap-1418	158	35	around	around	ADP
ap-1418	158	36	the	the	DET
ap-1418	158	37	critical	critical	ADJ
ap-1418	158	38	scattering	scattering	NOUN
ap-1418	158	39	length	length	NOUN
ap-1418	158	40	acrit	acrit	NOUN
ap-1418	158	41	is	be	AUX
ap-1418	158	42	traversed	traverse	VERB
ap-1418	158	43	in	in	ADP
ap-1418	158	44	the	the	DET
ap-1418	158	45	complex	complex	ADJ
ap-1418	158	46	extended	extend	VERB
ap-1418	158	47	parameter	parameter	NOUN
ap-1418	158	48	plane	plane	NOUN
ap-1418	158	49	(	(	PUNCT
ap-1418	158	50	left	leave	VERB
ap-1418	158	51	)	)	PUNCT
ap-1418	158	52	(	(	PUNCT
ap-1418	158	53	for	for	ADP
ap-1418	158	54	n2γ̄	n2γ̄	NUM
ap-1418	158	55	=	=	PUNCT
ap-1418	158	56	3.4×	3.4×	NUM
ap-1418	158	57	104	104	NUM
ap-1418	158	58	,	,	PUNCT
ap-1418	158	59	and	and	CCONJ
ap-1418	158	60	two	two	NUM
ap-1418	158	61	different	different	ADJ
ap-1418	158	62	aspect	aspect	NOUN
ap-1418	158	63	ratios	ratio	NOUN
ap-1418	158	64	)	)	PUNCT
ap-1418	158	65	.	.	PUNCT
ap-1418	159	1	the	the	DET
ap-1418	159	2	permutation	permutation	NOUN
ap-1418	159	3	of	of	ADP
ap-1418	159	4	the	the	DET
ap-1418	159	5	quantities	quantity	NOUN
ap-1418	159	6	after	after	ADP
ap-1418	159	7	one	one	NUM
ap-1418	159	8	cycle	cycle	NOUN
ap-1418	159	9	proves	prove	VERB
ap-1418	159	10	that	that	SCONJ
ap-1418	159	11	the	the	DET
ap-1418	159	12	bifurcation	bifurcation	NOUN
ap-1418	159	13	points	point	NOUN
ap-1418	159	14	are	be	AUX
ap-1418	159	15	exceptional	exceptional	ADJ
ap-1418	159	16	points	point	NOUN
ap-1418	159	17	this	this	PRON
ap-1418	159	18	,	,	PUNCT
ap-1418	159	19	an	an	DET
ap-1418	159	20	extension	extension	NOUN
ap-1418	159	21	of	of	ADP
ap-1418	159	22	the	the	DET
ap-1418	159	23	scattering	scatter	VERB
ap-1418	159	24	length	length	NOUN
ap-1418	159	25	to	to	ADP
ap-1418	159	26	complex	complex	ADJ
ap-1418	159	27	values	value	NOUN
ap-1418	159	28	is	be	AUX
ap-1418	159	29	again	again	ADV
ap-1418	159	30	necessary	necessary	ADJ
ap-1418	159	31	.	.	PUNCT
ap-1418	160	1	in	in	ADP
ap-1418	160	2	contrast	contrast	NOUN
ap-1418	160	3	to	to	ADP
ap-1418	160	4	the	the	DET
ap-1418	160	5	self	self	NOUN
ap-1418	160	6	-	-	PUNCT
ap-1418	160	7	trapped	trap	VERB
ap-1418	160	8	monopolar	monopolar	ADJ
ap-1418	160	9	case	case	NOUN
ap-1418	160	10	analytical	analytical	ADJ
ap-1418	160	11	investigations	investigation	NOUN
ap-1418	160	12	are	be	AUX
ap-1418	160	13	no	no	ADV
ap-1418	160	14	longer	long	ADV
ap-1418	160	15	possible	possible	ADJ
ap-1418	160	16	,	,	PUNCT
ap-1418	160	17	and	and	CCONJ
ap-1418	160	18	the	the	DET
ap-1418	160	19	analysis	analysis	NOUN
ap-1418	160	20	has	have	VERB
ap-1418	160	21	to	to	PART
ap-1418	160	22	be	be	AUX
ap-1418	160	23	carried	carry	VERB
ap-1418	160	24	out	out	ADP
ap-1418	160	25	numerically	numerically	ADV
ap-1418	160	26	.	.	PUNCT
ap-1418	161	1	figure	figure	NOUN
ap-1418	161	2	8	8	NUM
ap-1418	161	3	shows	show	VERB
ap-1418	161	4	the	the	DET
ap-1418	161	5	results	result	NOUN
ap-1418	161	6	for	for	ADP
ap-1418	161	7	the	the	DET
ap-1418	161	8	behaviour	behaviour	NOUN
ap-1418	161	9	of	of	ADP
ap-1418	161	10	the	the	DET
ap-1418	161	11	chemical	chemical	NOUN
ap-1418	161	12	potential	potential	NOUN
ap-1418	161	13	and	and	CCONJ
ap-1418	161	14	the	the	DET
ap-1418	161	15	mean	mean	ADJ
ap-1418	161	16	-	-	PUNCT
ap-1418	161	17	field	field	NOUN
ap-1418	161	18	energy	energy	NOUN
ap-1418	161	19	when	when	SCONJ
ap-1418	161	20	the	the	DET
ap-1418	161	21	scattering	scatter	VERB
ap-1418	161	22	lengths	length	NOUN
ap-1418	161	23	corresponding	correspond	VERB
ap-1418	161	24	to	to	ADP
ap-1418	161	25	the	the	DET
ap-1418	161	26	bifurcation	bifurcation	NOUN
ap-1418	161	27	points	point	NOUN
ap-1418	161	28	in	in	ADP
ap-1418	161	29	figure	figure	NOUN
ap-1418	161	30	7	7	NUM
ap-1418	161	31	for	for	ADP
ap-1418	161	32	the	the	DET
ap-1418	161	33	aspect	aspect	NOUN
ap-1418	161	34	ratios	ratio	NOUN
ap-1418	161	35	λ	λ	X
ap-1418	161	36	=	=	SYM
ap-1418	161	37	1	1	NUM
ap-1418	161	38	and	and	CCONJ
ap-1418	161	39	λ	λ	X
ap-1418	161	40	=	=	NOUN
ap-1418	161	41	6	6	NUM
ap-1418	161	42	are	be	AUX
ap-1418	161	43	circled	circle	VERB
ap-1418	161	44	in	in	ADP
ap-1418	161	45	the	the	DET
ap-1418	161	46	complex	complex	ADJ
ap-1418	161	47	plane	plane	NOUN
ap-1418	161	48	with	with	ADP
ap-1418	161	49	a	a	DET
ap-1418	161	50	radius	radius	NOUN
ap-1418	161	51	r	r	NOUN
ap-1418	161	52	=	=	SYM
ap-1418	161	53	10−3	10−3	NUM
ap-1418	161	54	.	.	PUNCT
ap-1418	162	1	it	it	PRON
ap-1418	162	2	is	be	AUX
ap-1418	162	3	evident	evident	ADJ
ap-1418	162	4	that	that	SCONJ
ap-1418	162	5	both	both	CCONJ
ap-1418	162	6	the	the	DET
ap-1418	162	7	values	value	NOUN
ap-1418	162	8	of	of	ADP
ap-1418	162	9	the	the	DET
ap-1418	162	10	chemical	chemical	NOUN
ap-1418	162	11	potentials	potential	NOUN
ap-1418	162	12	and	and	CCONJ
ap-1418	162	13	the	the	DET
ap-1418	162	14	mean	mean	ADJ
ap-1418	162	15	-	-	PUNCT
ap-1418	162	16	field	field	NOUN
ap-1418	162	17	energies	energy	NOUN
ap-1418	162	18	of	of	ADP
ap-1418	162	19	the	the	DET
ap-1418	162	20	two	two	NUM
ap-1418	162	21	solutions	solution	NOUN
ap-1418	162	22	permute	permute	NOUN
ap-1418	162	23	as	as	ADP
ap-1418	162	24	one	one	NUM
ap-1418	162	25	full	full	ADJ
ap-1418	162	26	cycle	cycle	NOUN
ap-1418	162	27	is	be	AUX
ap-1418	162	28	traversed	traverse	VERB
ap-1418	162	29	,	,	PUNCT
ap-1418	162	30	an	an	DET
ap-1418	162	31	unambiguous	unambiguous	ADJ
ap-1418	162	32	sign	sign	NOUN
ap-1418	162	33	that	that	SCONJ
ap-1418	162	34	the	the	DET
ap-1418	162	35	bifurcation	bifurcation	NOUN
ap-1418	162	36	points	point	NOUN
ap-1418	162	37	found	find	VERB
ap-1418	162	38	in	in	ADP
ap-1418	162	39	the	the	DET
ap-1418	162	40	solution	solution	NOUN
ap-1418	162	41	of	of	ADP
ap-1418	162	42	the	the	DET
ap-1418	162	43	nonlinear	nonlinear	ADJ
ap-1418	162	44	schrödinger	schrödinger	NOUN
ap-1418	162	45	equation	equation	NOUN
ap-1418	162	46	which	which	PRON
ap-1418	162	47	describes	describe	VERB
ap-1418	162	48	the	the	DET
ap-1418	162	49	bose	bose	NOUN
ap-1418	162	50	-	-	PUNCT
ap-1418	162	51	einstein	einstein	NOUN
ap-1418	162	52	condensation	condensation	NOUN
ap-1418	162	53	of	of	ADP
ap-1418	162	54	ultracold	ultracold	PROPN
ap-1418	162	55	atomic	atomic	ADJ
ap-1418	162	56	gases	gas	NOUN
ap-1418	162	57	with	with	ADP
ap-1418	162	58	a	a	DET
ap-1418	162	59	long	long	ADJ
ap-1418	162	60	-	-	PUNCT
ap-1418	162	61	range	range	NOUN
ap-1418	162	62	dipole	dipole	NOUN
ap-1418	162	63	-	-	PUNCT
ap-1418	162	64	dipole	dipole	NOUN
ap-1418	162	65	interaction	interaction	NOUN
ap-1418	162	66	are	be	AUX
ap-1418	162	67	also	also	ADV
ap-1418	162	68	exceptional	exceptional	ADJ
ap-1418	162	69	points	point	NOUN
ap-1418	162	70	.	.	PUNCT
ap-1418	163	1	3.2	3.2	NUM
ap-1418	163	2	numerical	numerical	ADJ
ap-1418	163	3	results	result	NOUN
ap-1418	163	4	more	more	ADV
ap-1418	163	5	sophisticated	sophisticated	ADJ
ap-1418	163	6	variational	variational	ADJ
ap-1418	163	7	calculations	calculation	NOUN
ap-1418	163	8	for	for	ADP
ap-1418	163	9	dipolar	dipolar	ADJ
ap-1418	163	10	condensates	condensate	NOUN
ap-1418	163	11	can	can	AUX
ap-1418	163	12	be	be	AUX
ap-1418	163	13	performed	perform	VERB
ap-1418	163	14	using	use	VERB
ap-1418	163	15	the	the	DET
ap-1418	163	16	method	method	NOUN
ap-1418	163	17	of	of	ADP
ap-1418	163	18	coupled	couple	VERB
ap-1418	163	19	gaussian	gaussian	ADJ
ap-1418	163	20	wave	wave	NOUN
ap-1418	163	21	packets	packet	NOUN
ap-1418	163	22	.	.	PUNCT
ap-1418	164	1	for	for	ADP
ap-1418	164	2	the	the	DET
ap-1418	164	3	grosspitaevskii	grosspitaevskii	ADJ
ap-1418	164	4	equation	equation	NOUN
ap-1418	164	5	with	with	ADP
ap-1418	164	6	dipolar	dipolar	ADJ
ap-1418	164	7	interaction	interaction	NOUN
ap-1418	164	8	the	the	DET
ap-1418	164	9	method	method	NOUN
ap-1418	164	10	has	have	AUX
ap-1418	164	11	been	be	AUX
ap-1418	164	12	shown	show	VERB
ap-1418	164	13	[	[	PUNCT
ap-1418	164	14	14	14	NUM
ap-1418	164	15	,	,	PUNCT
ap-1418	164	16	15	15	NUM
ap-1418	164	17	]	]	PUNCT
ap-1418	164	18	to	to	PART
ap-1418	164	19	be	be	AUX
ap-1418	164	20	a	a	DET
ap-1418	164	21	full	full	ADV
ap-1418	164	22	-	-	PUNCT
ap-1418	164	23	fledged	fledged	ADJ
ap-1418	164	24	alternative	alternative	NOUN
ap-1418	164	25	to	to	ADP
ap-1418	164	26	numerical	numerical	ADJ
ap-1418	164	27	computations	computation	NOUN
ap-1418	164	28	on	on	ADP
ap-1418	164	29	a	a	DET
ap-1418	164	30	grid	grid	NOUN
ap-1418	164	31	with	with	ADP
ap-1418	164	32	the	the	DET
ap-1418	164	33	method	method	NOUN
ap-1418	164	34	of	of	ADP
ap-1418	164	35	imaginary	imaginary	ADJ
ap-1418	164	36	time	time	NOUN
ap-1418	164	37	evolution	evolution	NOUN
ap-1418	164	38	.	.	PUNCT
ap-1418	165	1	in	in	ADP
ap-1418	165	2	contrast	contrast	NOUN
ap-1418	165	3	to	to	ADP
ap-1418	165	4	the	the	DET
ap-1418	165	5	latter	latter	ADJ
ap-1418	165	6	,	,	PUNCT
ap-1418	165	7	the	the	DET
ap-1418	165	8	method	method	NOUN
ap-1418	165	9	allows	allow	VERB
ap-1418	165	10	us	we	PRON
ap-1418	165	11	to	to	PART
ap-1418	165	12	find	find	VERB
ap-1418	165	13	both	both	CCONJ
ap-1418	165	14	stable	stable	ADJ
ap-1418	165	15	and	and	CCONJ
ap-1418	165	16	unstable	unstable	ADJ
ap-1418	165	17	solutions	solution	NOUN
ap-1418	165	18	.	.	PUNCT
ap-1418	166	1	the	the	DET
ap-1418	166	2	idea	idea	NOUN
ap-1418	166	3	is	be	AUX
ap-1418	166	4	to	to	PART
ap-1418	166	5	take	take	VERB
ap-1418	166	6	as	as	ADP
ap-1418	166	7	trial	trial	NOUN
ap-1418	166	8	functions	function	NOUN
ap-1418	166	9	superpositions	superposition	NOUN
ap-1418	166	10	of	of	ADP
ap-1418	166	11	n	n	DET
ap-1418	166	12	different	different	ADJ
ap-1418	166	13	gaussians	gaussian	NOUN
ap-1418	166	14	centered	center	VERB
ap-1418	166	15	at	at	ADP
ap-1418	166	16	the	the	DET
ap-1418	166	17	origin	origin	NOUN
ap-1418	166	18	ψ(r	ψ(r	NOUN
ap-1418	166	19	)	)	PUNCT
ap-1418	167	1	=	=	SYM
ap-1418	168	1	n∑	n∑	NOUN
ap-1418	168	2	k=1	k=1	PUNCT
ap-1418	169	1	ei(ak	ei(ak	PROPN
ap-1418	169	2	x(t	x(t	PROPN
ap-1418	169	3	)	)	PUNCT
ap-1418	170	1	x2+ak	x2+ak	PROPN
ap-1418	171	1	y(t	y(t	PROPN
ap-1418	171	2	)	)	PUNCT
ap-1418	172	1	y2+ak	y2+ak	PROPN
ap-1418	172	2	z(t	z(t	NOUN
ap-1418	172	3	)	)	PUNCT
ap-1418	172	4	z2+γk(t	z2+γk(t	NOUN
ap-1418	172	5	)	)	PUNCT
ap-1418	172	6	)	)	PUNCT
ap-1418	173	1	≡	≡	PROPN
ap-1418	173	2	n∑	n∑	PROPN
ap-1418	173	3	k=1	k=1	PROPN
ap-1418	174	1	gk(yk(t	gk(yk(t	NOUN
ap-1418	174	2	)	)	PUNCT
ap-1418	174	3	,	,	PUNCT
ap-1418	174	4	r	r	NOUN
ap-1418	174	5	)	)	PUNCT
ap-1418	174	6	,	,	PUNCT
ap-1418	174	7	101	101	NUM
ap-1418	174	8	acta	acta	PROPN
ap-1418	174	9	polytechnica	polytechnica	PROPN
ap-1418	174	10	vol	vol	NOUN
ap-1418	174	11	.	.	PUNCT
ap-1418	175	1	51	51	NUM
ap-1418	175	2	no	no	NOUN
ap-1418	175	3	.	.	PUNCT
ap-1418	176	1	4/2011	4/2011	NUM
ap-1418	176	2	fig	fig	NOUN
ap-1418	176	3	.	.	PUNCT
ap-1418	177	1	9	9	NUM
ap-1418	177	2	:	:	PUNCT
ap-1418	177	3	mean	mean	ADJ
ap-1418	177	4	-	-	PUNCT
ap-1418	177	5	field	field	NOUN
ap-1418	177	6	energy	energy	NOUN
ap-1418	177	7	of	of	ADP
ap-1418	177	8	a	a	DET
ap-1418	177	9	dipolar	dipolar	ADJ
ap-1418	177	10	condensate	condensate	NOUN
ap-1418	177	11	for	for	ADP
ap-1418	177	12	(	(	PUNCT
ap-1418	177	13	particle	particle	NOUN
ap-1418	177	14	number	number	NOUN
ap-1418	177	15	scaled	scale	VERB
ap-1418	177	16	)	)	PUNCT
ap-1418	177	17	trap	trap	NOUN
ap-1418	177	18	frequencies	frequency	NOUN
ap-1418	177	19	n2γz	n2γz	PRON
ap-1418	177	20	=	=	SYM
ap-1418	178	1	25	25	NUM
ap-1418	178	2	200	200	NUM
ap-1418	178	3	and	and	CCONJ
ap-1418	178	4	n2γρ	n2γρ	NOUN
ap-1418	178	5	=	=	SYM
ap-1418	178	6	3600	3600	NUM
ap-1418	178	7	as	as	ADP
ap-1418	178	8	a	a	DET
ap-1418	178	9	function	function	NOUN
ap-1418	178	10	of	of	ADP
ap-1418	178	11	the	the	DET
ap-1418	178	12	scattering	scatter	VERB
ap-1418	178	13	length	length	NOUN
ap-1418	178	14	in	in	ADP
ap-1418	178	15	units	unit	NOUN
ap-1418	178	16	of	of	ADP
ap-1418	178	17	ad	ad	NOUN
ap-1418	178	18	.	.	PUNCT
ap-1418	179	1	in	in	ADP
ap-1418	179	2	the	the	DET
ap-1418	179	3	variational	variational	ADJ
ap-1418	179	4	calculation	calculation	NOUN
ap-1418	179	5	with	with	ADP
ap-1418	179	6	one	one	NUM
ap-1418	179	7	gaussian	gaussian	NOUN
ap-1418	179	8	a	a	DET
ap-1418	179	9	stable	stable	ADJ
ap-1418	179	10	ground	ground	NOUN
ap-1418	179	11	state	state	NOUN
ap-1418	179	12	(	(	PUNCT
ap-1418	179	13	gn=1	gn=1	PROPN
ap-1418	179	14	)	)	PUNCT
ap-1418	179	15	and	and	CCONJ
ap-1418	179	16	an	an	DET
ap-1418	179	17	unstable	unstable	ADJ
ap-1418	179	18	excited	excited	ADJ
ap-1418	179	19	state	state	NOUN
ap-1418	179	20	(	(	PUNCT
ap-1418	179	21	en=1	en=1	PROPN
ap-1418	179	22	)	)	PUNCT
ap-1418	179	23	emerge	emerge	VERB
ap-1418	179	24	in	in	ADP
ap-1418	179	25	a	a	DET
ap-1418	179	26	tangent	tangent	ADJ
ap-1418	179	27	bifurcation	bifurcation	NOUN
ap-1418	179	28	.	.	PUNCT
ap-1418	180	1	in	in	ADP
ap-1418	180	2	the	the	DET
ap-1418	180	3	calculation	calculation	NOUN
ap-1418	180	4	with	with	ADP
ap-1418	180	5	coupled	couple	VERB
ap-1418	180	6	gaussians	gaussian	NOUN
ap-1418	180	7	two	two	NUM
ap-1418	180	8	unstable	unstable	ADJ
ap-1418	180	9	states	state	NOUN
ap-1418	180	10	emerge	emerge	VERB
ap-1418	180	11	(	(	PUNCT
ap-1418	180	12	labeled	label	VERB
ap-1418	180	13	ucoupled	ucoupled	ADJ
ap-1418	180	14	)	)	PUNCT
ap-1418	180	15	,	,	PUNCT
ap-1418	180	16	of	of	ADP
ap-1418	180	17	which	which	PRON
ap-1418	180	18	the	the	DET
ap-1418	180	19	lower	low	ADJ
ap-1418	180	20	one	one	NOUN
ap-1418	180	21	turns	turn	VERB
ap-1418	180	22	into	into	ADP
ap-1418	180	23	a	a	DET
ap-1418	180	24	stable	stable	ADJ
ap-1418	180	25	ground	ground	NOUN
ap-1418	180	26	state	state	NOUN
ap-1418	180	27	(	(	PUNCT
ap-1418	180	28	gcoupled	gcouple	VERB
ap-1418	180	29	)	)	PUNCT
ap-1418	180	30	in	in	ADP
ap-1418	180	31	the	the	DET
ap-1418	180	32	region	region	NOUN
ap-1418	180	33	of	of	ADP
ap-1418	180	34	the	the	DET
ap-1418	180	35	small	small	ADJ
ap-1418	180	36	rectangle	rectangle	NOUN
ap-1418	180	37	in	in	ADP
ap-1418	180	38	a	a	DET
ap-1418	180	39	pitchfork	pitchfork	NOUN
ap-1418	180	40	bifurcation	bifurcation	NOUN
ap-1418	180	41	.	.	PUNCT
ap-1418	181	1	(	(	PUNCT
ap-1418	181	2	adapted	adapt	VERB
ap-1418	181	3	from	from	ADP
ap-1418	181	4	[	[	X
ap-1418	181	5	14	14	NUM
ap-1418	181	6	]	]	SYM
ap-1418	181	7	)	)	PUNCT
ap-1418	181	8	where	where	SCONJ
ap-1418	181	9	the	the	DET
ap-1418	181	10	ak(t	ak(t	NOUN
ap-1418	181	11	)	)	PUNCT
ap-1418	181	12	are	be	AUX
ap-1418	181	13	complex	complex	ADJ
ap-1418	181	14	width	width	ADJ
ap-1418	181	15	parameter	parameter	NOUN
ap-1418	181	16	functions	function	NOUN
ap-1418	181	17	(	(	PUNCT
ap-1418	181	18	3n	3n	NUM
ap-1418	181	19	)	)	PUNCT
ap-1418	181	20	and	and	CCONJ
ap-1418	181	21	the	the	DET
ap-1418	181	22	γk(t	γk(t	NOUN
ap-1418	181	23	)	)	PUNCT
ap-1418	181	24	fix	fix	VERB
ap-1418	181	25	the	the	DET
ap-1418	181	26	weights	weight	NOUN
ap-1418	181	27	and	and	CCONJ
ap-1418	181	28	phases	phase	NOUN
ap-1418	181	29	of	of	ADP
ap-1418	181	30	the	the	DET
ap-1418	181	31	individual	individual	ADJ
ap-1418	181	32	gaussians	gaussians	PROPN
ap-1418	181	33	(	(	PUNCT
ap-1418	181	34	n	n	CCONJ
ap-1418	181	35	)	)	PUNCT
ap-1418	181	36	.	.	PUNCT
ap-1418	182	1	equations	equation	NOUN
ap-1418	182	2	of	of	ADP
ap-1418	182	3	motion	motion	NOUN
ap-1418	182	4	of	of	ADP
ap-1418	182	5	the	the	DET
ap-1418	182	6	variational	variational	ADJ
ap-1418	182	7	parameters	parameter	NOUN
ap-1418	182	8	again	again	ADV
ap-1418	182	9	follow	follow	VERB
ap-1418	182	10	from	from	ADP
ap-1418	182	11	the	the	DET
ap-1418	182	12	time	time	NOUN
ap-1418	182	13	-	-	PUNCT
ap-1418	182	14	dependent	dependent	ADJ
ap-1418	182	15	variational	variational	ADJ
ap-1418	182	16	principle	principle	NOUN
ap-1418	182	17	.	.	PUNCT
ap-1418	183	1	figure	figure	NOUN
ap-1418	183	2	9	9	NUM
ap-1418	183	3	shows	show	VERB
ap-1418	183	4	the	the	DET
ap-1418	183	5	results	result	NOUN
ap-1418	183	6	for	for	ADP
ap-1418	183	7	a	a	DET
ap-1418	183	8	dipolar	dipolar	ADJ
ap-1418	183	9	condensate	condensate	NOUN
ap-1418	183	10	as	as	ADP
ap-1418	183	11	a	a	DET
ap-1418	183	12	function	function	NOUN
ap-1418	183	13	of	of	ADP
ap-1418	183	14	the	the	DET
ap-1418	183	15	scattering	scatter	VERB
ap-1418	183	16	length	length	NOUN
ap-1418	183	17	for	for	ADP
ap-1418	183	18	trap	trap	NOUN
ap-1418	183	19	frequencies	frequency	NOUN
ap-1418	183	20	n2γz	n2γz	PUNCT
ap-1418	183	21	=	=	SYM
ap-1418	183	22	25	25	NUM
ap-1418	183	23	200	200	NUM
ap-1418	183	24	and	and	CCONJ
ap-1418	183	25	n2γρ	n2γρ	PUNCT
ap-1418	183	26	=	=	SYM
ap-1418	183	27	3	3	NUM
ap-1418	183	28	600	600	NUM
ap-1418	183	29	.	.	PUNCT
ap-1418	184	1	in	in	ADP
ap-1418	184	2	the	the	DET
ap-1418	184	3	calculation	calculation	NOUN
ap-1418	184	4	with	with	ADP
ap-1418	184	5	five	five	NUM
ap-1418	184	6	gaussians	gaussian	NOUN
ap-1418	184	7	the	the	DET
ap-1418	184	8	results	result	NOUN
ap-1418	184	9	from	from	ADP
ap-1418	184	10	a	a	DET
ap-1418	184	11	grid	grid	NOUN
ap-1418	184	12	calculation	calculation	NOUN
ap-1418	184	13	are	be	AUX
ap-1418	184	14	well	well	ADV
ap-1418	184	15	reproduced	reproduce	VERB
ap-1418	184	16	,	,	PUNCT
ap-1418	184	17	and	and	CCONJ
ap-1418	184	18	the	the	DET
ap-1418	184	19	bifurcation	bifurcation	NOUN
ap-1418	184	20	of	of	ADP
ap-1418	184	21	the	the	DET
ap-1418	184	22	mean	mean	ADJ
ap-1418	184	23	-	-	PUNCT
ap-1418	184	24	field	field	NOUN
ap-1418	184	25	energy	energy	NOUN
ap-1418	184	26	is	be	AUX
ap-1418	184	27	confirmed	confirm	VERB
ap-1418	184	28	.	.	PUNCT
ap-1418	185	1	again	again	ADV
ap-1418	185	2	the	the	DET
ap-1418	185	3	variational	variational	ADJ
ap-1418	185	4	calculation	calculation	NOUN
ap-1418	185	5	with	with	ADP
ap-1418	185	6	a	a	DET
ap-1418	185	7	single	single	ADJ
ap-1418	185	8	gaussian	gaussian	NOUN
ap-1418	185	9	underestimates	underestimate	VERB
ap-1418	185	10	the	the	DET
ap-1418	185	11	critical	critical	ADJ
ap-1418	185	12	scattering	scattering	NOUN
ap-1418	185	13	length	length	NOUN
ap-1418	185	14	where	where	SCONJ
ap-1418	185	15	the	the	DET
ap-1418	185	16	bifurcation	bifurcation	NOUN
ap-1418	185	17	appears	appear	VERB
ap-1418	185	18	.	.	PUNCT
ap-1418	186	1	however	however	ADV
ap-1418	186	2	,	,	PUNCT
ap-1418	186	3	a	a	DET
ap-1418	186	4	more	more	ADV
ap-1418	186	5	complicated	complicated	ADJ
ap-1418	186	6	bifurcation	bifurcation	NOUN
ap-1418	186	7	scenario	scenario	NOUN
ap-1418	186	8	evolves	evolve	VERB
ap-1418	186	9	:	:	PUNCT
ap-1418	186	10	as	as	SCONJ
ap-1418	186	11	the	the	DET
ap-1418	186	12	scattering	scattering	NOUN
ap-1418	186	13	length	length	NOUN
ap-1418	186	14	is	be	AUX
ap-1418	186	15	decreased	decrease	VERB
ap-1418	186	16	the	the	DET
ap-1418	186	17	stable	stable	ADJ
ap-1418	186	18	ground	ground	NOUN
ap-1418	186	19	state	state	NOUN
ap-1418	186	20	solution	solution	NOUN
ap-1418	186	21	already	already	ADV
ap-1418	186	22	turns	turn	VERB
ap-1418	186	23	unstable	unstable	ADJ
ap-1418	186	24	before	before	ADP
ap-1418	186	25	reaching	reach	VERB
ap-1418	186	26	the	the	DET
ap-1418	186	27	tangent	tangent	NOUN
ap-1418	186	28	bifurcation	bifurcation	NOUN
ap-1418	186	29	point	point	NOUN
ap-1418	186	30	,	,	PUNCT
ap-1418	186	31	indicating	indicate	VERB
ap-1418	186	32	a	a	DET
ap-1418	186	33	pitchfork	pitchfork	NOUN
ap-1418	186	34	bifurcation	bifurcation	NOUN
ap-1418	186	35	in	in	ADP
ap-1418	186	36	the	the	DET
ap-1418	186	37	region	region	NOUN
ap-1418	186	38	of	of	ADP
ap-1418	186	39	the	the	DET
ap-1418	186	40	small	small	ADJ
ap-1418	186	41	rectangle	rectangle	NOUN
ap-1418	186	42	shown	show	VERB
ap-1418	186	43	in	in	ADP
ap-1418	186	44	the	the	DET
ap-1418	186	45	figure	figure	NOUN
ap-1418	186	46	.	.	PUNCT
ap-1418	187	1	neither	neither	CCONJ
ap-1418	187	2	the	the	DET
ap-1418	187	3	tangent	tangent	NOUN
ap-1418	187	4	nor	nor	CCONJ
ap-1418	187	5	the	the	DET
ap-1418	187	6	pitchfork	pitchfork	NOUN
ap-1418	187	7	bifurcation	bifurcation	NOUN
ap-1418	187	8	point	point	NOUN
ap-1418	187	9	have	have	AUX
ap-1418	187	10	been	be	AUX
ap-1418	187	11	conclusively	conclusively	ADV
ap-1418	187	12	analyzed	analyze	VERB
ap-1418	187	13	so	so	ADV
ap-1418	187	14	far	far	ADV
ap-1418	187	15	as	as	ADP
ap-1418	187	16	to	to	ADP
ap-1418	187	17	their	their	PRON
ap-1418	187	18	properties	property	NOUN
ap-1418	187	19	as	as	ADP
ap-1418	187	20	exceptional	exceptional	ADJ
ap-1418	187	21	points	point	NOUN
ap-1418	187	22	,	,	PUNCT
ap-1418	187	23	but	but	CCONJ
ap-1418	187	24	the	the	DET
ap-1418	187	25	analysis	analysis	NOUN
ap-1418	187	26	should	should	AUX
ap-1418	187	27	reveal	reveal	VERB
ap-1418	187	28	new	new	ADJ
ap-1418	187	29	features	feature	NOUN
ap-1418	187	30	,	,	PUNCT
ap-1418	187	31	in	in	ADP
ap-1418	187	32	particular	particular	ADJ
ap-1418	187	33	when	when	SCONJ
ap-1418	187	34	the	the	DET
ap-1418	187	35	tangent	tangent	NOUN
ap-1418	187	36	bifurcation	bifurcation	NOUN
ap-1418	187	37	point	point	NOUN
ap-1418	187	38	is	be	AUX
ap-1418	187	39	encircled	encircle	VERB
ap-1418	187	40	with	with	ADP
ap-1418	187	41	a	a	DET
ap-1418	187	42	radius	radius	NOUN
ap-1418	187	43	that	that	PRON
ap-1418	187	44	also	also	ADV
ap-1418	187	45	encompasses	encompass	VERB
ap-1418	187	46	the	the	DET
ap-1418	187	47	pitchfork	pitchfork	NOUN
ap-1418	187	48	bifurcation	bifurcation	NOUN
ap-1418	187	49	.	.	PUNCT
ap-1418	188	1	4	4	NUM
ap-1418	188	2	summary	summary	NOUN
ap-1418	188	3	we	we	PRON
ap-1418	188	4	have	have	AUX
ap-1418	188	5	demonstrated	demonstrate	VERB
ap-1418	188	6	that	that	SCONJ
ap-1418	188	7	“	"	PUNCT
ap-1418	188	8	nonlinear	nonlinear	ADJ
ap-1418	188	9	versions	version	NOUN
ap-1418	188	10	”	"	PUNCT
ap-1418	188	11	of	of	ADP
ap-1418	188	12	exceptional	exceptional	ADJ
ap-1418	188	13	points	point	NOUN
ap-1418	188	14	appear	appear	VERB
ap-1418	188	15	in	in	ADP
ap-1418	188	16	bifurcating	bifurcate	VERB
ap-1418	188	17	solutions	solution	NOUN
ap-1418	188	18	of	of	ADP
ap-1418	188	19	the	the	DET
ap-1418	188	20	(	(	PUNCT
ap-1418	188	21	extended	extended	ADJ
ap-1418	188	22	)	)	PUNCT
ap-1418	188	23	gross	gross	ADJ
ap-1418	188	24	-	-	PUNCT
ap-1418	188	25	pitaevskii	pitaevskii	ADJ
ap-1418	188	26	equations	equation	NOUN
ap-1418	188	27	describing	describe	VERB
ap-1418	188	28	the	the	DET
ap-1418	188	29	bose	bose	NOUN
ap-1418	188	30	-	-	PUNCT
ap-1418	188	31	einstein	einstein	NOUN
ap-1418	188	32	condensation	condensation	NOUN
ap-1418	188	33	of	of	ADP
ap-1418	188	34	ultracold	ultracold	PROPN
ap-1418	188	35	atomic	atomic	ADJ
ap-1418	188	36	gases	gas	NOUN
ap-1418	188	37	with	with	ADP
ap-1418	188	38	attractive	attractive	ADJ
ap-1418	188	39	1	1	NUM
ap-1418	188	40	/	/	SYM
ap-1418	188	41	r	r	NOUN
ap-1418	188	42	interaction	interaction	NOUN
ap-1418	188	43	and	and	CCONJ
ap-1418	188	44	with	with	ADP
ap-1418	188	45	dipoledipole	dipoledipole	NOUN
ap-1418	188	46	interaction	interaction	NOUN
ap-1418	188	47	.	.	PUNCT
ap-1418	189	1	the	the	DET
ap-1418	189	2	identification	identification	NOUN
ap-1418	189	3	as	as	ADP
ap-1418	189	4	exceptional	exceptional	ADJ
ap-1418	189	5	points	point	NOUN
ap-1418	189	6	required	require	VERB
ap-1418	189	7	a	a	DET
ap-1418	189	8	complex	complex	ADJ
ap-1418	189	9	extension	extension	NOUN
ap-1418	189	10	of	of	ADP
ap-1418	189	11	the	the	DET
ap-1418	189	12	scattering	scatter	VERB
ap-1418	189	13	length	length	NOUN
ap-1418	189	14	.	.	PUNCT
ap-1418	190	1	in	in	ADP
ap-1418	190	2	summary	summary	NOUN
ap-1418	190	3	,	,	PUNCT
ap-1418	190	4	bose	bose	NOUN
ap-1418	190	5	-	-	PUNCT
ap-1418	190	6	einstein	einstein	NOUN
ap-1418	190	7	condensates	condensate	NOUN
ap-1418	190	8	near	near	ADP
ap-1418	190	9	the	the	DET
ap-1418	190	10	collapse	collapse	NOUN
ap-1418	190	11	point	point	NOUN
ap-1418	190	12	can	can	AUX
ap-1418	190	13	be	be	AUX
ap-1418	190	14	regarded	regard	VERB
ap-1418	190	15	as	as	ADP
ap-1418	190	16	realizations	realization	NOUN
ap-1418	190	17	of	of	ADP
ap-1418	190	18	physical	physical	ADJ
ap-1418	190	19	systems	system	NOUN
ap-1418	190	20	close	close	ADJ
ap-1418	190	21	to	to	ADP
ap-1418	190	22	exceptional	exceptional	ADJ
ap-1418	190	23	points	point	NOUN
ap-1418	190	24	.	.	PUNCT
ap-1418	191	1	references	reference	NOUN
ap-1418	191	2	[	[	X
ap-1418	191	3	1	1	NUM
ap-1418	191	4	]	]	X
ap-1418	191	5	kapitza	kapitza	NOUN
ap-1418	191	6	,	,	PUNCT
ap-1418	191	7	p.	p.	PROPN
ap-1418	191	8	,	,	PUNCT
ap-1418	191	9	allen	allen	PROPN
ap-1418	191	10	,	,	PUNCT
ap-1418	191	11	j.	j.	PROPN
ap-1418	191	12	f.	f.	PROPN
ap-1418	191	13	,	,	PUNCT
ap-1418	191	14	misener	misener	PROPN
ap-1418	191	15	,	,	PUNCT
ap-1418	191	16	a.	a.	PROPN
ap-1418	191	17	d.	d.	PROPN
ap-1418	191	18	:	:	PUNCT
ap-1418	191	19	nature	nature	NOUN
ap-1418	191	20	141	141	NUM
ap-1418	191	21	,	,	PUNCT
ap-1418	191	22	(	(	PUNCT
ap-1418	191	23	1938	1938	NUM
ap-1418	191	24	)	)	PUNCT
ap-1418	191	25	,	,	PUNCT
ap-1418	191	26	74	74	NUM
ap-1418	191	27	,	,	PUNCT
ap-1418	191	28	75	75	NUM
ap-1418	191	29	.	.	PUNCT
ap-1418	192	1	[	[	X
ap-1418	192	2	2	2	NUM
ap-1418	192	3	]	]	PUNCT
ap-1418	192	4	anderson	anderson	PROPN
ap-1418	192	5	,	,	PUNCT
ap-1418	192	6	m.	m.	PROPN
ap-1418	192	7	h.	h.	PROPN
ap-1418	192	8	,	,	PUNCT
ap-1418	192	9	ensher	ensher	PROPN
ap-1418	192	10	,	,	PUNCT
ap-1418	192	11	j.	j.	PROPN
ap-1418	192	12	r.	r.	PROPN
ap-1418	192	13	,	,	PUNCT
ap-1418	192	14	matthews	matthews	PROPN
ap-1418	192	15	,	,	PUNCT
ap-1418	192	16	m.	m.	NOUN
ap-1418	192	17	r.	r.	PROPN
ap-1418	192	18	,	,	PUNCT
ap-1418	192	19	wieman	wieman	NOUN
ap-1418	192	20	,	,	PUNCT
ap-1418	192	21	c.	c.	PROPN
ap-1418	192	22	e.	e.	PROPN
ap-1418	192	23	,	,	PUNCT
ap-1418	192	24	cornell	cornell	PROPN
ap-1418	192	25	,	,	PUNCT
ap-1418	192	26	e.	e.	PROPN
ap-1418	192	27	a.	a.	PROPN
ap-1418	192	28	:	:	PUNCT
ap-1418	192	29	science	science	NOUN
ap-1418	192	30	269	269	NUM
ap-1418	192	31	(	(	PUNCT
ap-1418	192	32	1995	1995	NUM
ap-1418	192	33	)	)	PUNCT
ap-1418	192	34	,	,	PUNCT
ap-1418	192	35	198	198	NUM
ap-1418	192	36	.	.	PUNCT
ap-1418	193	1	[	[	X
ap-1418	193	2	3	3	X
ap-1418	193	3	]	]	X
ap-1418	193	4	davis	davis	PROPN
ap-1418	193	5	,	,	PUNCT
ap-1418	193	6	k.	k.	PROPN
ap-1418	193	7	b.	b.	PROPN
ap-1418	193	8	,	,	PUNCT
ap-1418	193	9	mewes	mewes	PROPN
ap-1418	193	10	,	,	PUNCT
ap-1418	193	11	m.	m.	NOUN
ap-1418	193	12	o.	o.	PROPN
ap-1418	193	13	,	,	PUNCT
ap-1418	193	14	andrews	andrews	PROPN
ap-1418	193	15	,	,	PUNCT
ap-1418	193	16	m.	m.	PROPN
ap-1418	193	17	r.	r.	PROPN
ap-1418	193	18	,	,	PUNCT
ap-1418	193	19	van	van	PROPN
ap-1418	193	20	druten	druten	PROPN
ap-1418	193	21	,	,	PUNCT
ap-1418	193	22	n.	n.	PROPN
ap-1418	193	23	j.	j.	PROPN
ap-1418	193	24	,	,	PUNCT
ap-1418	193	25	durfee	durfee	PROPN
ap-1418	193	26	,	,	PUNCT
ap-1418	193	27	d.	d.	PROPN
ap-1418	193	28	s.	s.	PROPN
ap-1418	193	29	,	,	PUNCT
ap-1418	193	30	kurn	kurn	PROPN
ap-1418	193	31	,	,	PUNCT
ap-1418	193	32	d.	d.	PROPN
ap-1418	193	33	m.	m.	PROPN
ap-1418	193	34	,	,	PUNCT
ap-1418	193	35	ketterle	ketterle	PROPN
ap-1418	193	36	,	,	PUNCT
ap-1418	193	37	w.	w.	NOUN
ap-1418	193	38	:	:	PUNCT
ap-1418	193	39	phys	phy	NOUN
ap-1418	193	40	.	.	PUNCT
ap-1418	193	41	rev	rev	PROPN
ap-1418	193	42	.	.	PROPN
ap-1418	193	43	lett	lett	PROPN
ap-1418	193	44	.	.	PUNCT
ap-1418	194	1	75	75	NUM
ap-1418	194	2	(	(	PUNCT
ap-1418	194	3	1995	1995	NUM
ap-1418	194	4	)	)	PUNCT
ap-1418	194	5	,	,	PUNCT
ap-1418	194	6	3	3	NUM
ap-1418	194	7	969	969	NUM
ap-1418	194	8	.	.	PUNCT
ap-1418	195	1	[	[	X
ap-1418	195	2	4	4	NUM
ap-1418	195	3	]	]	X
ap-1418	195	4	ueda	ueda	PROPN
ap-1418	195	5	,	,	PUNCT
ap-1418	195	6	m.	m.	NOUN
ap-1418	195	7	:	:	PUNCT
ap-1418	195	8	fundamentals	fundamental	NOUN
ap-1418	195	9	and	and	CCONJ
ap-1418	195	10	new	new	ADJ
ap-1418	195	11	frontiers	frontier	NOUN
ap-1418	195	12	of	of	ADP
ap-1418	195	13	bose	bose	NOUN
ap-1418	195	14	-	-	PUNCT
ap-1418	195	15	einstein	einstein	NOUN
ap-1418	195	16	condensation	condensation	NOUN
ap-1418	195	17	,	,	PUNCT
ap-1418	195	18	world	world	NOUN
ap-1418	195	19	scientific	scientific	ADJ
ap-1418	195	20	publishing	publishing	NOUN
ap-1418	195	21	,	,	PUNCT
ap-1418	195	22	2010	2010	NUM
ap-1418	195	23	.	.	PUNCT
ap-1418	196	1	[	[	X
ap-1418	196	2	5	5	NUM
ap-1418	196	3	]	]	PUNCT
ap-1418	196	4	griesmaier	griesmaier	NOUN
ap-1418	196	5	,	,	PUNCT
ap-1418	196	6	a.	a.	NOUN
ap-1418	196	7	,	,	PUNCT
ap-1418	196	8	werner	werner	PROPN
ap-1418	196	9	,	,	PUNCT
ap-1418	196	10	j.	j.	PROPN
ap-1418	196	11	,	,	PUNCT
ap-1418	196	12	hensler	hensler	NOUN
ap-1418	196	13	,	,	PUNCT
ap-1418	196	14	s.	s.	PROPN
ap-1418	196	15	,	,	PUNCT
ap-1418	196	16	stuhler	stuhler	PROPN
ap-1418	196	17	,	,	PUNCT
ap-1418	196	18	j.	j.	PROPN
ap-1418	196	19	,	,	PUNCT
ap-1418	196	20	pfau	pfau	NOUN
ap-1418	196	21	,	,	PUNCT
ap-1418	196	22	t.	t.	PROPN
ap-1418	196	23	:	:	PUNCT
ap-1418	196	24	phys	phy	NOUN
ap-1418	196	25	.	.	PUNCT
ap-1418	197	1	rev	rev	PROPN
ap-1418	197	2	.	.	PROPN
ap-1418	197	3	lett	lett	PROPN
ap-1418	197	4	.	.	PUNCT
ap-1418	198	1	94	94	NUM
ap-1418	198	2	(	(	PUNCT
ap-1418	198	3	2005	2005	NUM
ap-1418	198	4	)	)	PUNCT
ap-1418	198	5	,	,	PUNCT
ap-1418	198	6	160	160	NUM
ap-1418	198	7	401	401	NUM
ap-1418	198	8	.	.	PUNCT
ap-1418	199	1	[	[	X
ap-1418	199	2	6	6	NUM
ap-1418	199	3	]	]	X
ap-1418	199	4	koch	koch	PROPN
ap-1418	199	5	,	,	PUNCT
ap-1418	199	6	t.	t.	PROPN
ap-1418	199	7	,	,	PUNCT
ap-1418	199	8	lahaye	lahaye	NOUN
ap-1418	199	9	,	,	PUNCT
ap-1418	199	10	t.	t.	PROPN
ap-1418	199	11	,	,	PUNCT
ap-1418	199	12	metz	metz	PROPN
ap-1418	199	13	,	,	PUNCT
ap-1418	199	14	j.	j.	PROPN
ap-1418	199	15	,	,	PUNCT
ap-1418	199	16	fröhlich	fröhlich	PROPN
ap-1418	199	17	,	,	PUNCT
ap-1418	199	18	b.	b.	PROPN
ap-1418	199	19	,	,	PUNCT
ap-1418	199	20	griesmaier	griesmaier	NOUN
ap-1418	199	21	,	,	PUNCT
ap-1418	199	22	a.	a.	NOUN
ap-1418	199	23	,	,	PUNCT
ap-1418	199	24	pfau	pfau	NOUN
ap-1418	199	25	,	,	PUNCT
ap-1418	199	26	t.	t.	PROPN
ap-1418	199	27	:	:	PUNCT
ap-1418	199	28	nature	nature	PROPN
ap-1418	199	29	physics	physics	PROPN
ap-1418	199	30	4	4	NUM
ap-1418	199	31	(	(	PUNCT
ap-1418	199	32	2008	2008	NUM
ap-1418	199	33	)	)	PUNCT
ap-1418	199	34	,	,	PUNCT
ap-1418	199	35	218	218	NUM
ap-1418	199	36	.	.	PUNCT
ap-1418	200	1	[	[	X
ap-1418	200	2	7	7	NUM
ap-1418	200	3	]	]	X
ap-1418	200	4	lahaye	lahaye	NOUN
ap-1418	200	5	,	,	PUNCT
ap-1418	200	6	t.	t.	PROPN
ap-1418	200	7	,	,	PUNCT
ap-1418	200	8	menotti	menotti	PROPN
ap-1418	200	9	,	,	PUNCT
ap-1418	200	10	c.	c.	PROPN
ap-1418	200	11	,	,	PUNCT
ap-1418	200	12	santos	santos	PROPN
ap-1418	200	13	,	,	PUNCT
ap-1418	200	14	l.	l.	PROPN
ap-1418	200	15	,	,	PUNCT
ap-1418	200	16	lewenstein	lewenstein	PROPN
ap-1418	200	17	,	,	PUNCT
ap-1418	200	18	m.	m.	NOUN
ap-1418	200	19	,	,	PUNCT
ap-1418	200	20	pfau	pfau	NOUN
ap-1418	200	21	,	,	PUNCT
ap-1418	200	22	t.	t.	PROPN
ap-1418	200	23	:	:	PUNCT
ap-1418	200	24	rep	rep	PROPN
ap-1418	200	25	.	.	PROPN
ap-1418	200	26	prog	prog	PROPN
ap-1418	200	27	.	.	PUNCT
ap-1418	201	1	phys	phy	NOUN
ap-1418	201	2	.	.	PUNCT
ap-1418	202	1	72	72	NUM
ap-1418	202	2	(	(	PUNCT
ap-1418	202	3	2009	2009	NUM
ap-1418	202	4	)	)	PUNCT
ap-1418	202	5	,	,	PUNCT
ap-1418	202	6	126	126	NUM
ap-1418	202	7	401	401	NUM
ap-1418	202	8	.	.	PUNCT
ap-1418	203	1	102	102	NUM
ap-1418	203	2	acta	acta	PROPN
ap-1418	203	3	polytechnica	polytechnica	PROPN
ap-1418	203	4	vol	vol	NOUN
ap-1418	203	5	.	.	PUNCT
ap-1418	204	1	51	51	NUM
ap-1418	204	2	no	no	INTJ
ap-1418	204	3	.	.	PUNCT
ap-1418	204	4	4/2011	4/2011	NUM
ap-1418	205	1	[	[	NOUN
ap-1418	205	2	8	8	NUM
ap-1418	205	3	]	]	SYM
ap-1418	205	4	o	o	NOUN
ap-1418	205	5	’	'	PUNCT
ap-1418	205	6	dell	dell	NOUN
ap-1418	205	7	,	,	PUNCT
ap-1418	205	8	d.	d.	PROPN
ap-1418	205	9	,	,	PUNCT
ap-1418	205	10	giovanazzi	giovanazzi	PROPN
ap-1418	205	11	,	,	PUNCT
ap-1418	205	12	s.	s.	PROPN
ap-1418	205	13	,	,	PUNCT
ap-1418	205	14	kurizki	kurizki	PROPN
ap-1418	205	15	,	,	PUNCT
ap-1418	205	16	g.	g.	PROPN
ap-1418	205	17	,	,	PUNCT
ap-1418	205	18	akulin	akulin	PROPN
ap-1418	205	19	,	,	PUNCT
ap-1418	205	20	v.	v.	ADP
ap-1418	205	21	m.	m.	NOUN
ap-1418	205	22	:	:	PUNCT
ap-1418	205	23	phys	phy	NOUN
ap-1418	205	24	.	.	PUNCT
ap-1418	206	1	rev	rev	PROPN
ap-1418	206	2	.	.	PROPN
ap-1418	206	3	lett	lett	PROPN
ap-1418	206	4	.	.	PUNCT
ap-1418	207	1	84	84	NUM
ap-1418	207	2	(	(	PUNCT
ap-1418	207	3	2000	2000	NUM
ap-1418	207	4	)	)	PUNCT
ap-1418	207	5	,	,	PUNCT
ap-1418	207	6	5	5	NUM
ap-1418	207	7	687	687	NUM
ap-1418	207	8	.	.	PUNCT
ap-1418	208	1	[	[	X
ap-1418	208	2	9	9	NUM
ap-1418	208	3	]	]	X
ap-1418	208	4	papadopoulos	papadopoulos	PROPN
ap-1418	208	5	,	,	PUNCT
ap-1418	208	6	i.	i.	PROPN
ap-1418	208	7	,	,	PUNCT
ap-1418	208	8	wagner	wagner	PROPN
ap-1418	208	9	,	,	PUNCT
ap-1418	208	10	p.	p.	NOUN
ap-1418	208	11	,	,	PUNCT
ap-1418	208	12	wunner	wunner	NOUN
ap-1418	208	13	,	,	PUNCT
ap-1418	208	14	g.	g.	NOUN
ap-1418	208	15	,	,	PUNCT
ap-1418	208	16	main	main	ADJ
ap-1418	208	17	,	,	PUNCT
ap-1418	208	18	j.	j.	PROPN
ap-1418	208	19	:	:	PUNCT
ap-1418	208	20	phys	phy	NOUN
ap-1418	208	21	.	.	PUNCT
ap-1418	208	22	rev	rev	PROPN
ap-1418	208	23	.	.	PUNCT
ap-1418	209	1	a	a	DET
ap-1418	209	2	76	76	NUM
ap-1418	209	3	(	(	PUNCT
ap-1418	209	4	2007	2007	NUM
ap-1418	209	5	)	)	PUNCT
ap-1418	209	6	,	,	PUNCT
ap-1418	209	7	053	053	NUM
ap-1418	209	8	604	604	NUM
ap-1418	209	9	.	.	PUNCT
ap-1418	210	1	[	[	X
ap-1418	210	2	10	10	NUM
ap-1418	210	3	]	]	X
ap-1418	210	4	köberle	köberle	NOUN
ap-1418	210	5	,	,	PUNCT
ap-1418	210	6	p.	p.	NOUN
ap-1418	210	7	,	,	PUNCT
ap-1418	210	8	cartarius	cartarius	NOUN
ap-1418	210	9	,	,	PUNCT
ap-1418	210	10	h.	h.	PROPN
ap-1418	210	11	,	,	PUNCT
ap-1418	210	12	fabčič	fabčič	PROPN
ap-1418	210	13	,	,	PUNCT
ap-1418	210	14	t.	t.	NOUN
ap-1418	210	15	,	,	PUNCT
ap-1418	210	16	main	main	ADJ
ap-1418	210	17	,	,	PUNCT
ap-1418	210	18	j.	j.	PROPN
ap-1418	210	19	,	,	PUNCT
ap-1418	210	20	wunner	wunner	NOUN
ap-1418	210	21	,	,	PUNCT
ap-1418	210	22	g.	g.	PROPN
ap-1418	210	23	:	:	PUNCT
ap-1418	210	24	new	new	ADJ
ap-1418	210	25	j.	j.	PROPN
ap-1418	210	26	phys	phys	PROPN
ap-1418	210	27	.	.	PUNCT
ap-1418	211	1	11	11	NUM
ap-1418	211	2	(	(	PUNCT
ap-1418	211	3	2009	2009	NUM
ap-1418	211	4	)	)	PUNCT
ap-1418	211	5	,	,	PUNCT
ap-1418	211	6	023	023	NUM
ap-1418	211	7	017	017	NUM
ap-1418	211	8	.	.	PUNCT
ap-1418	212	1	[	[	X
ap-1418	212	2	11	11	NUM
ap-1418	212	3	]	]	X
ap-1418	212	4	cartarius	cartarius	NOUN
ap-1418	212	5	,	,	PUNCT
ap-1418	212	6	h.	h.	NOUN
ap-1418	212	7	,	,	PUNCT
ap-1418	212	8	main	main	ADJ
ap-1418	212	9	,	,	PUNCT
ap-1418	212	10	j.	j.	PROPN
ap-1418	212	11	,	,	PUNCT
ap-1418	212	12	wunner	wunner	NOUN
ap-1418	212	13	,	,	PUNCT
ap-1418	212	14	g.	g.	NOUN
ap-1418	212	15	:	:	PUNCT
ap-1418	212	16	phys	phy	NOUN
ap-1418	212	17	.	.	PUNCT
ap-1418	212	18	rev	rev	PROPN
ap-1418	212	19	.	.	PUNCT
ap-1418	213	1	a	a	DET
ap-1418	213	2	77	77	NUM
ap-1418	213	3	(	(	PUNCT
ap-1418	213	4	2008	2008	NUM
ap-1418	213	5	)	)	PUNCT
ap-1418	213	6	,	,	PUNCT
ap-1418	213	7	013	013	NUM
ap-1418	213	8	618	618	NUM
ap-1418	213	9	.	.	PUNCT
ap-1418	214	1	[	[	X
ap-1418	214	2	12	12	NUM
ap-1418	214	3	]	]	SYM
ap-1418	214	4	mclachlan	mclachlan	NOUN
ap-1418	214	5	,	,	PUNCT
ap-1418	214	6	a.	a.	PROPN
ap-1418	214	7	d.	d.	PROPN
ap-1418	214	8	:	:	PUNCT
ap-1418	214	9	mol	mol	PROPN
ap-1418	214	10	.	.	PUNCT
ap-1418	214	11	phys	phy	NOUN
ap-1418	214	12	.	.	PUNCT
ap-1418	214	13	8	8	NUM
ap-1418	214	14	(	(	PUNCT
ap-1418	214	15	1964	1964	NUM
ap-1418	214	16	)	)	PUNCT
ap-1418	214	17	,	,	PUNCT
ap-1418	214	18	39	39	NUM
ap-1418	214	19	.	.	PUNCT
ap-1418	215	1	[	[	X
ap-1418	215	2	13	13	NUM
ap-1418	215	3	]	]	SYM
ap-1418	215	4	cartarius	cartarius	NOUN
ap-1418	215	5	,	,	PUNCT
ap-1418	215	6	h.	h.	PROPN
ap-1418	215	7	,	,	PUNCT
ap-1418	215	8	fabčič	fabčič	PROPN
ap-1418	215	9	,	,	PUNCT
ap-1418	215	10	t.	t.	NOUN
ap-1418	215	11	,	,	PUNCT
ap-1418	215	12	main	main	ADJ
ap-1418	215	13	,	,	PUNCT
ap-1418	215	14	j.	j.	PROPN
ap-1418	215	15	,	,	PUNCT
ap-1418	215	16	wunner	wunner	NOUN
ap-1418	215	17	,	,	PUNCT
ap-1418	215	18	g.	g.	NOUN
ap-1418	215	19	:	:	PUNCT
ap-1418	215	20	phys	phy	NOUN
ap-1418	215	21	.	.	PUNCT
ap-1418	215	22	rev	rev	PROPN
ap-1418	215	23	.	.	PUNCT
ap-1418	216	1	a	a	DET
ap-1418	216	2	78	78	NUM
ap-1418	216	3	(	(	PUNCT
ap-1418	216	4	2008	2008	NUM
ap-1418	216	5	)	)	PUNCT
ap-1418	216	6	,	,	PUNCT
ap-1418	216	7	013	013	NUM
ap-1418	216	8	615	615	NUM
ap-1418	216	9	.	.	PUNCT
ap-1418	217	1	[	[	X
ap-1418	217	2	14	14	NUM
ap-1418	217	3	]	]	X
ap-1418	217	4	rau	rau	PROPN
ap-1418	217	5	,	,	PUNCT
ap-1418	217	6	s.	s.	PROPN
ap-1418	217	7	,	,	PUNCT
ap-1418	217	8	main	main	ADJ
ap-1418	217	9	,	,	PUNCT
ap-1418	217	10	j.	j.	PROPN
ap-1418	217	11	,	,	PUNCT
ap-1418	217	12	köberle	köberle	NOUN
ap-1418	217	13	,	,	PUNCT
ap-1418	217	14	p.	p.	NOUN
ap-1418	217	15	,	,	PUNCT
ap-1418	217	16	wunner	wunner	NOUN
ap-1418	217	17	,	,	PUNCT
ap-1418	217	18	g.	g.	NOUN
ap-1418	217	19	:	:	PUNCT
ap-1418	217	20	phys	phy	NOUN
ap-1418	217	21	.	.	PUNCT
ap-1418	218	1	rev	rev	VERB
ap-1418	218	2	a	a	DET
ap-1418	218	3	81	81	NUM
ap-1418	218	4	(	(	PUNCT
ap-1418	218	5	2010	2010	NUM
ap-1418	218	6	)	)	PUNCT
ap-1418	218	7	,	,	PUNCT
ap-1418	218	8	031	031	NUM
ap-1418	218	9	605(r	605(r	NOUN
ap-1418	218	10	)	)	PUNCT
ap-1418	218	11	.	.	PUNCT
ap-1418	219	1	[	[	X
ap-1418	219	2	15	15	NUM
ap-1418	219	3	]	]	X
ap-1418	219	4	rau	rau	PROPN
ap-1418	219	5	,	,	PUNCT
ap-1418	219	6	s.	s.	PROPN
ap-1418	219	7	,	,	PUNCT
ap-1418	219	8	main	main	ADJ
ap-1418	219	9	,	,	PUNCT
ap-1418	219	10	j.	j.	PROPN
ap-1418	219	11	,	,	PUNCT
ap-1418	219	12	köberle	köberle	NOUN
ap-1418	219	13	,	,	PUNCT
ap-1418	219	14	p.	p.	NOUN
ap-1418	219	15	,	,	PUNCT
ap-1418	219	16	wunner	wunner	NOUN
ap-1418	219	17	,	,	PUNCT
ap-1418	219	18	g.	g.	NOUN
ap-1418	219	19	:	:	PUNCT
ap-1418	219	20	phys	phy	NOUN
ap-1418	219	21	.	.	PUNCT
ap-1418	220	1	rev	rev	VERB
ap-1418	220	2	a	a	DET
ap-1418	220	3	82	82	NUM
ap-1418	220	4	(	(	PUNCT
ap-1418	220	5	2010	2010	NUM
ap-1418	220	6	)	)	PUNCT
ap-1418	220	7	,	,	PUNCT
ap-1418	220	8	046	046	NUM
ap-1418	220	9	201	201	NUM
ap-1418	220	10	.	.	PUNCT
ap-1418	221	1	guenter	guenter	NOUN
ap-1418	221	2	wunner	wunner	PROPN
ap-1418	221	3	e	e	NOUN
ap-1418	221	4	-	-	NOUN
ap-1418	221	5	mail	mail	NOUN
ap-1418	221	6	:	:	PUNCT
ap-1418	222	1	wunner@itp1.uni-stuttgart.de	wunner@itp1.uni-stuttgart.de	PROPN
ap-1418	222	2	h.	h.	PROPN
ap-1418	222	3	cartarius	cartarius	PROPN
ap-1418	222	4	p.	p.	PROPN
ap-1418	222	5	köberle	köberle	PROPN
ap-1418	222	6	j.	j.	PROPN
ap-1418	222	7	main	main	PROPN
ap-1418	222	8	s.	s.	PROPN
ap-1418	222	9	rau	rau	PROPN
ap-1418	222	10	institute	institute	PROPN
ap-1418	222	11	for	for	ADP
ap-1418	222	12	theoretical	theoretical	ADJ
ap-1418	222	13	physics	physics	NOUN
ap-1418	222	14	1	1	NUM
ap-1418	222	15	university	university	PROPN
ap-1418	222	16	of	of	ADP
ap-1418	222	17	stuttgart	stuttgart	PROPN
ap-1418	222	18	70550	70550	NUM
ap-1418	222	19	stuttgart	stuttgart	PROPN
ap-1418	222	20	,	,	PUNCT
ap-1418	222	21	germany	germany	PROPN
ap-1418	222	22	103	103	NUM