id	sid	tid	token	lemma	pos
ap-2085	1	1	acta	acta	PROPN
ap-2085	1	2	polytechnica	polytechnica	PROPN
ap-2085	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2085	1	4	/	/	SYM
ap-2085	1	5	ap.2014.54.0122	ap.2014.54.0122	PROPN
ap-2085	1	6	acta	acta	PROPN
ap-2085	1	7	polytechnica	polytechnica	PROPN
ap-2085	1	8	54(2):122–123	54(2):122–123	PROPN
ap-2085	1	9	,	,	PUNCT
ap-2085	1	10	2014	2014	NUM
ap-2085	1	11	©	©	PROPN
ap-2085	1	12	czech	czech	PROPN
ap-2085	1	13	technical	technical	PROPN
ap-2085	1	14	university	university	PROPN
ap-2085	1	15	in	in	ADP
ap-2085	1	16	prague	prague	PROPN
ap-2085	1	17	,	,	PUNCT
ap-2085	1	18	2014	2014	NUM
ap-2085	1	19	available	available	ADJ
ap-2085	1	20	online	online	ADV
ap-2085	1	21	at	at	ADP
ap-2085	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2085	1	23	the	the	DET
ap-2085	1	24	floquet	floquet	NOUN
ap-2085	1	25	method	method	NOUN
ap-2085	1	26	for	for	ADP
ap-2085	1	27	pt	pt	NOUN
ap-2085	1	28	-	-	ADJ
ap-2085	1	29	symmetric	symmetric	ADJ
ap-2085	1	30	periodic	periodic	ADJ
ap-2085	1	31	potentials	potential	NOUN
ap-2085	1	32	h.	h.	PROPN
ap-2085	1	33	f.	f.	PROPN
ap-2085	1	34	jones	jones	PROPN
ap-2085	1	35	physics	physics	PROPN
ap-2085	1	36	department	department	PROPN
ap-2085	1	37	,	,	PUNCT
ap-2085	1	38	imperial	imperial	ADJ
ap-2085	1	39	college	college	NOUN
ap-2085	1	40	,	,	PUNCT
ap-2085	1	41	london	london	PROPN
ap-2085	1	42	sw7	sw7	PROPN
ap-2085	1	43	2bz	2bz	PROPN
ap-2085	1	44	,	,	PUNCT
ap-2085	1	45	uk	uk	PROPN
ap-2085	1	46	correspondence	correspondence	NOUN
ap-2085	1	47	:	:	PUNCT
ap-2085	1	48	h.f.jones@imperial.ac.uk	h.f.jones@imperial.ac.uk	ADJ
ap-2085	2	1	abstract	abstract	NOUN
ap-2085	2	2	.	.	PUNCT
ap-2085	3	1	by	by	ADP
ap-2085	3	2	the	the	DET
ap-2085	3	3	general	general	ADJ
ap-2085	3	4	theory	theory	NOUN
ap-2085	3	5	of	of	ADP
ap-2085	3	6	pt	pt	X
ap-2085	3	7	-symmetric	-symmetric	ADJ
ap-2085	3	8	quantum	quantum	NOUN
ap-2085	3	9	systems	system	NOUN
ap-2085	3	10	,	,	PUNCT
ap-2085	3	11	their	their	PRON
ap-2085	3	12	energy	energy	NOUN
ap-2085	3	13	levels	level	NOUN
ap-2085	3	14	are	be	AUX
ap-2085	3	15	either	either	CCONJ
ap-2085	3	16	real	real	ADJ
ap-2085	3	17	or	or	CCONJ
ap-2085	3	18	occur	occur	VERB
ap-2085	3	19	in	in	ADP
ap-2085	3	20	complex	complex	ADJ
ap-2085	3	21	-	-	PUNCT
ap-2085	3	22	conjugate	conjugate	NOUN
ap-2085	3	23	pairs	pair	NOUN
ap-2085	3	24	,	,	PUNCT
ap-2085	3	25	which	which	PRON
ap-2085	3	26	implies	imply	VERB
ap-2085	3	27	that	that	SCONJ
ap-2085	3	28	the	the	DET
ap-2085	3	29	secular	secular	ADJ
ap-2085	3	30	equation	equation	NOUN
ap-2085	3	31	must	must	AUX
ap-2085	3	32	be	be	AUX
ap-2085	3	33	real	real	ADJ
ap-2085	3	34	.	.	PUNCT
ap-2085	4	1	however	however	ADV
ap-2085	4	2	,	,	PUNCT
ap-2085	4	3	for	for	ADP
ap-2085	4	4	periodic	periodic	ADJ
ap-2085	4	5	potentials	potential	NOUN
ap-2085	4	6	it	it	PRON
ap-2085	4	7	is	be	AUX
ap-2085	4	8	by	by	ADP
ap-2085	4	9	no	no	DET
ap-2085	4	10	means	means	NOUN
ap-2085	4	11	clear	clear	ADJ
ap-2085	4	12	that	that	SCONJ
ap-2085	4	13	the	the	DET
ap-2085	4	14	secular	secular	ADJ
ap-2085	4	15	equation	equation	NOUN
ap-2085	4	16	arising	arise	VERB
ap-2085	4	17	in	in	ADP
ap-2085	4	18	the	the	DET
ap-2085	4	19	floquet	floquet	NOUN
ap-2085	4	20	method	method	NOUN
ap-2085	4	21	is	be	AUX
ap-2085	4	22	indeed	indeed	ADV
ap-2085	4	23	real	real	ADJ
ap-2085	4	24	,	,	PUNCT
ap-2085	4	25	since	since	SCONJ
ap-2085	4	26	it	it	PRON
ap-2085	4	27	involves	involve	VERB
ap-2085	4	28	two	two	NUM
ap-2085	4	29	linearly	linearly	ADV
ap-2085	4	30	independent	independent	ADJ
ap-2085	4	31	solutions	solution	NOUN
ap-2085	4	32	of	of	ADP
ap-2085	4	33	the	the	DET
ap-2085	4	34	schrödinger	schrödinger	ADJ
ap-2085	4	35	equation	equation	NOUN
ap-2085	4	36	.	.	PUNCT
ap-2085	5	1	in	in	ADP
ap-2085	5	2	this	this	DET
ap-2085	5	3	brief	brief	ADJ
ap-2085	5	4	note	note	NOUN
ap-2085	5	5	we	we	PRON
ap-2085	5	6	elucidate	elucidate	VERB
ap-2085	5	7	how	how	SCONJ
ap-2085	5	8	that	that	DET
ap-2085	5	9	reality	reality	NOUN
ap-2085	5	10	can	can	AUX
ap-2085	5	11	be	be	AUX
ap-2085	5	12	established	establish	VERB
ap-2085	5	13	.	.	PUNCT
ap-2085	6	1	keywords	keyword	NOUN
ap-2085	6	2	:	:	PUNCT
ap-2085	6	3	band	band	NOUN
ap-2085	6	4	structure	structure	NOUN
ap-2085	6	5	,	,	PUNCT
ap-2085	6	6	pt	pt	PROPN
ap-2085	6	7	symmetry	symmetry	NOUN
ap-2085	6	8	,	,	PUNCT
ap-2085	6	9	floquet	floquet	PROPN
ap-2085	6	10	method	method	NOUN
ap-2085	6	11	.	.	PUNCT
ap-2085	7	1	the	the	DET
ap-2085	7	2	study	study	NOUN
ap-2085	7	3	of	of	ADP
ap-2085	7	4	systems	system	NOUN
ap-2085	7	5	governed	govern	VERB
ap-2085	7	6	by	by	ADP
ap-2085	7	7	hamiltonians	hamiltonian	NOUN
ap-2085	7	8	for	for	ADP
ap-2085	7	9	which	which	PRON
ap-2085	7	10	the	the	DET
ap-2085	7	11	standard	standard	ADJ
ap-2085	7	12	requirement	requirement	NOUN
ap-2085	7	13	of	of	ADP
ap-2085	7	14	hermiticity	hermiticity	NOUN
ap-2085	7	15	is	be	AUX
ap-2085	7	16	replaced	replace	VERB
ap-2085	7	17	by	by	ADP
ap-2085	7	18	that	that	PRON
ap-2085	7	19	of	of	ADP
ap-2085	7	20	pt	pt	PROPN
ap-2085	7	21	-symmetry	-symmetry	PROPN
ap-2085	7	22	has	have	AUX
ap-2085	7	23	undergone	undergo	VERB
ap-2085	7	24	significant	significant	ADJ
ap-2085	7	25	development	development	NOUN
ap-2085	7	26	in	in	ADP
ap-2085	7	27	recent	recent	ADJ
ap-2085	7	28	years	year	NOUN
ap-2085	8	1	[	[	X
ap-2085	8	2	1–6	1–6	NUM
ap-2085	8	3	]	]	X
ap-2085	8	4	.	.	PUNCT
ap-2085	9	1	provided	provide	VERB
ap-2085	9	2	that	that	SCONJ
ap-2085	9	3	the	the	DET
ap-2085	9	4	symmetry	symmetry	NOUN
ap-2085	9	5	is	be	AUX
ap-2085	9	6	not	not	PART
ap-2085	9	7	broken	break	VERB
ap-2085	9	8	,	,	PUNCT
ap-2085	9	9	that	that	ADV
ap-2085	9	10	is	is	ADV
ap-2085	9	11	,	,	PUNCT
ap-2085	9	12	that	that	SCONJ
ap-2085	9	13	the	the	DET
ap-2085	9	14	energy	energy	NOUN
ap-2085	9	15	eigenfunctions	eigenfunction	NOUN
ap-2085	9	16	respect	respect	VERB
ap-2085	9	17	the	the	DET
ap-2085	9	18	symmetry	symmetry	NOUN
ap-2085	9	19	of	of	ADP
ap-2085	9	20	the	the	DET
ap-2085	9	21	hamiltonian	hamiltonian	NOUN
ap-2085	9	22	,	,	PUNCT
ap-2085	9	23	the	the	DET
ap-2085	9	24	energy	energy	NOUN
ap-2085	9	25	eigenvalues	eigenvalue	NOUN
ap-2085	9	26	are	be	AUX
ap-2085	9	27	guaranteed	guarantee	VERB
ap-2085	9	28	to	to	PART
ap-2085	9	29	be	be	AUX
ap-2085	9	30	real	real	ADJ
ap-2085	9	31	.	.	PUNCT
ap-2085	10	1	in	in	ADP
ap-2085	10	2	the	the	DET
ap-2085	10	3	case	case	NOUN
ap-2085	10	4	where	where	SCONJ
ap-2085	10	5	the	the	DET
ap-2085	10	6	symmetry	symmetry	NOUN
ap-2085	10	7	is	be	AUX
ap-2085	10	8	broken	break	VERB
ap-2085	10	9	energy	energy	NOUN
ap-2085	10	10	levels	level	NOUN
ap-2085	10	11	may	may	AUX
ap-2085	10	12	instead	instead	ADV
ap-2085	10	13	appear	appear	VERB
ap-2085	10	14	as	as	ADP
ap-2085	10	15	complex	complex	ADJ
ap-2085	10	16	-	-	PUNCT
ap-2085	10	17	conjugate	conjugate	ADJ
ap-2085	10	18	pairs	pair	NOUN
ap-2085	10	19	.	.	PUNCT
ap-2085	11	1	this	this	DET
ap-2085	11	2	phenomenon	phenomenon	NOUN
ap-2085	11	3	is	be	AUX
ap-2085	11	4	particularly	particularly	ADV
ap-2085	11	5	interesting	interesting	ADJ
ap-2085	11	6	for	for	ADP
ap-2085	11	7	the	the	DET
ap-2085	11	8	case	case	NOUN
ap-2085	11	9	of	of	ADP
ap-2085	11	10	periodic	periodic	ADJ
ap-2085	11	11	pt	pt	NOUN
ap-2085	11	12	-symmetric	-symmetric	ADJ
ap-2085	11	13	potentials	potential	NOUN
ap-2085	11	14	,	,	PUNCT
ap-2085	11	15	where	where	SCONJ
ap-2085	11	16	unusual	unusual	ADJ
ap-2085	11	17	band	band	NOUN
ap-2085	11	18	structures	structure	NOUN
ap-2085	11	19	may	may	AUX
ap-2085	11	20	occur	occur	VERB
ap-2085	11	21	[	[	X
ap-2085	11	22	7	7	NUM
ap-2085	11	23	,	,	PUNCT
ap-2085	11	24	8	8	NUM
ap-2085	11	25	]	]	PUNCT
ap-2085	11	26	.	.	PUNCT
ap-2085	12	1	an	an	DET
ap-2085	12	2	important	important	ADJ
ap-2085	12	3	physical	physical	ADJ
ap-2085	12	4	realization	realization	NOUN
ap-2085	12	5	of	of	ADP
ap-2085	12	6	such	such	ADJ
ap-2085	12	7	systems	system	NOUN
ap-2085	12	8	arises	arise	VERB
ap-2085	12	9	in	in	ADP
ap-2085	12	10	classical	classical	ADJ
ap-2085	12	11	optics	optic	NOUN
ap-2085	12	12	,	,	PUNCT
ap-2085	12	13	because	because	SCONJ
ap-2085	12	14	of	of	ADP
ap-2085	12	15	the	the	DET
ap-2085	12	16	formal	formal	ADJ
ap-2085	12	17	similarity	similarity	NOUN
ap-2085	12	18	of	of	ADP
ap-2085	12	19	the	the	DET
ap-2085	12	20	time	time	NOUN
ap-2085	12	21	-	-	PUNCT
ap-2085	12	22	dependent	dependent	ADJ
ap-2085	12	23	schrödinger	schrödinger	ADJ
ap-2085	12	24	equation	equation	NOUN
ap-2085	12	25	to	to	ADP
ap-2085	12	26	the	the	DET
ap-2085	12	27	paraxial	paraxial	ADJ
ap-2085	12	28	equation	equation	NOUN
ap-2085	12	29	for	for	ADP
ap-2085	12	30	the	the	DET
ap-2085	12	31	propagation	propagation	NOUN
ap-2085	12	32	of	of	ADP
ap-2085	12	33	electromagnetic	electromagnetic	ADJ
ap-2085	12	34	waves	wave	NOUN
ap-2085	12	35	.	.	PUNCT
ap-2085	13	1	this	this	DET
ap-2085	13	2	equation	equation	NOUN
ap-2085	13	3	takes	take	VERB
ap-2085	13	4	the	the	DET
ap-2085	13	5	form	form	NOUN
ap-2085	13	6	[	[	X
ap-2085	13	7	9	9	NUM
ap-2085	13	8	]	]	X
ap-2085	13	9	i	i	PRON
ap-2085	13	10	∂ψ	∂ψ	VERB
ap-2085	13	11	∂z	∂z	PROPN
ap-2085	13	12	=	=	PUNCT
ap-2085	13	13	−	−	PROPN
ap-2085	13	14	(	(	PUNCT
ap-2085	13	15	∂2	∂2	NUM
ap-2085	13	16	∂x2	∂x2	NOUN
ap-2085	13	17	+	+	CCONJ
ap-2085	13	18	v	v	ADJ
ap-2085	13	19	(	(	PUNCT
ap-2085	13	20	x	x	NOUN
ap-2085	13	21	)	)	PUNCT
ap-2085	13	22	)	)	PUNCT
ap-2085	14	1	ψ	ψ	X
ap-2085	14	2	,	,	PUNCT
ap-2085	14	3	(	(	PUNCT
ap-2085	14	4	1	1	X
ap-2085	14	5	)	)	PUNCT
ap-2085	14	6	where	where	SCONJ
ap-2085	14	7	ψ(x	ψ(x	NOUN
ap-2085	14	8	,	,	PUNCT
ap-2085	14	9	z	z	NOUN
ap-2085	14	10	)	)	PUNCT
ap-2085	14	11	represents	represent	VERB
ap-2085	14	12	the	the	DET
ap-2085	14	13	envelope	envelope	NOUN
ap-2085	14	14	function	function	NOUN
ap-2085	14	15	of	of	ADP
ap-2085	14	16	the	the	DET
ap-2085	14	17	amplitude	amplitude	NOUN
ap-2085	14	18	of	of	ADP
ap-2085	14	19	the	the	DET
ap-2085	14	20	electric	electric	ADJ
ap-2085	14	21	field	field	NOUN
ap-2085	14	22	and	and	CCONJ
ap-2085	14	23	z	z	NOUN
ap-2085	14	24	is	be	AUX
ap-2085	14	25	a	a	DET
ap-2085	14	26	scaled	scale	VERB
ap-2085	14	27	propagation	propagation	NOUN
ap-2085	14	28	distance	distance	NOUN
ap-2085	14	29	.	.	PUNCT
ap-2085	15	1	the	the	DET
ap-2085	15	2	optical	optical	ADJ
ap-2085	15	3	potential	potential	NOUN
ap-2085	15	4	v	v	X
ap-2085	15	5	(	(	PUNCT
ap-2085	15	6	x	x	X
ap-2085	15	7	)	)	PUNCT
ap-2085	15	8	is	be	AUX
ap-2085	15	9	proportional	proportional	ADJ
ap-2085	15	10	to	to	ADP
ap-2085	15	11	the	the	DET
ap-2085	15	12	variation	variation	NOUN
ap-2085	15	13	in	in	ADP
ap-2085	15	14	the	the	DET
ap-2085	15	15	refractive	refractive	ADJ
ap-2085	15	16	index	index	NOUN
ap-2085	15	17	of	of	ADP
ap-2085	15	18	the	the	DET
ap-2085	15	19	material	material	NOUN
ap-2085	15	20	through	through	ADP
ap-2085	15	21	which	which	PRON
ap-2085	15	22	the	the	DET
ap-2085	15	23	wave	wave	NOUN
ap-2085	15	24	is	be	AUX
ap-2085	15	25	passing	pass	VERB
ap-2085	15	26	.	.	PUNCT
ap-2085	16	1	in	in	ADP
ap-2085	16	2	optics	optic	NOUN
ap-2085	16	3	this	this	DET
ap-2085	16	4	potential	potential	NOUN
ap-2085	16	5	may	may	AUX
ap-2085	16	6	well	well	ADV
ap-2085	16	7	be	be	AUX
ap-2085	16	8	complex	complex	ADJ
ap-2085	16	9	,	,	PUNCT
ap-2085	16	10	with	with	ADP
ap-2085	16	11	its	its	PRON
ap-2085	16	12	imaginary	imaginary	ADJ
ap-2085	16	13	part	part	NOUN
ap-2085	16	14	representing	represent	VERB
ap-2085	16	15	either	either	CCONJ
ap-2085	16	16	loss	loss	NOUN
ap-2085	16	17	or	or	CCONJ
ap-2085	16	18	gain	gain	NOUN
ap-2085	16	19	.	.	PUNCT
ap-2085	17	1	if	if	SCONJ
ap-2085	17	2	loss	loss	NOUN
ap-2085	17	3	and	and	CCONJ
ap-2085	17	4	gain	gain	NOUN
ap-2085	17	5	are	be	AUX
ap-2085	17	6	balanced	balance	VERB
ap-2085	17	7	in	in	ADP
ap-2085	17	8	a	a	DET
ap-2085	17	9	pt	pt	NOUN
ap-2085	17	10	-symmetric	-symmetric	ADJ
ap-2085	17	11	way	way	NOUN
ap-2085	17	12	,	,	PUNCT
ap-2085	17	13	so	so	SCONJ
ap-2085	17	14	that	that	SCONJ
ap-2085	17	15	v	v	ADP
ap-2085	17	16	∗(x	∗(x	PROPN
ap-2085	17	17	)	)	PUNCT
ap-2085	18	1	=	=	SYM
ap-2085	18	2	v	v	X
ap-2085	18	3	(	(	PUNCT
ap-2085	18	4	−x	−x	NOUN
ap-2085	18	5	)	)	PUNCT
ap-2085	18	6	.	.	PUNCT
ap-2085	19	1	we	we	PRON
ap-2085	19	2	have	have	VERB
ap-2085	19	3	the	the	DET
ap-2085	19	4	situation	situation	NOUN
ap-2085	19	5	described	describe	VERB
ap-2085	19	6	above	above	ADV
ap-2085	19	7	.	.	PUNCT
ap-2085	20	1	optical	optical	ADJ
ap-2085	20	2	systems	system	NOUN
ap-2085	20	3	of	of	ADP
ap-2085	20	4	this	this	DET
ap-2085	20	5	type	type	NOUN
ap-2085	20	6	have	have	VERB
ap-2085	20	7	a	a	DET
ap-2085	20	8	number	number	NOUN
ap-2085	20	9	of	of	ADP
ap-2085	20	10	very	very	ADV
ap-2085	20	11	interesting	interesting	ADJ
ap-2085	20	12	properties	property	NOUN
ap-2085	20	13	[	[	X
ap-2085	20	14	9–14	9–14	X
ap-2085	20	15	]	]	X
ap-2085	20	16	,	,	PUNCT
ap-2085	20	17	particularly	particularly	ADV
ap-2085	20	18	when	when	SCONJ
ap-2085	20	19	they	they	PRON
ap-2085	20	20	are	be	AUX
ap-2085	20	21	periodic	periodic	ADJ
ap-2085	20	22	.	.	PUNCT
ap-2085	21	1	in	in	ADP
ap-2085	21	2	such	such	DET
ap-2085	21	3	a	a	DET
ap-2085	21	4	case	case	NOUN
ap-2085	21	5	the	the	DET
ap-2085	21	6	potential	potential	ADJ
ap-2085	21	7	v	v	X
ap-2085	21	8	(	(	PUNCT
ap-2085	21	9	x	x	NOUN
ap-2085	21	10	)	)	PUNCT
ap-2085	21	11	,	,	PUNCT
ap-2085	21	12	whose	whose	DET
ap-2085	21	13	period	period	NOUN
ap-2085	21	14	we	we	PRON
ap-2085	21	15	can	can	AUX
ap-2085	21	16	take	take	VERB
ap-2085	21	17	as	as	ADP
ap-2085	21	18	π	π	PROPN
ap-2085	21	19	,	,	PUNCT
ap-2085	21	20	without	without	ADP
ap-2085	21	21	loss	loss	NOUN
ap-2085	21	22	of	of	ADP
ap-2085	21	23	generality	generality	NOUN
ap-2085	21	24	,	,	PUNCT
ap-2085	21	25	satisfies	satisfy	VERB
ap-2085	21	26	the	the	DET
ap-2085	21	27	two	two	NUM
ap-2085	21	28	conditions	condition	NOUN
ap-2085	21	29	v	v	ADP
ap-2085	21	30	∗(−x	∗(−x	NOUN
ap-2085	21	31	)	)	PUNCT
ap-2085	21	32	=	=	SYM
ap-2085	21	33	v	v	X
ap-2085	21	34	(	(	PUNCT
ap-2085	21	35	x	x	NOUN
ap-2085	21	36	)	)	PUNCT
ap-2085	21	37	=	=	SYM
ap-2085	21	38	v	v	NOUN
ap-2085	21	39	(	(	PUNCT
ap-2085	21	40	x+	x+	PROPN
ap-2085	21	41	π	π	NOUN
ap-2085	21	42	)	)	PUNCT
ap-2085	21	43	.	.	PUNCT
ap-2085	22	1	for	for	ADP
ap-2085	22	2	periodic	periodic	ADJ
ap-2085	22	3	potentials	potential	NOUN
ap-2085	22	4	we	we	PRON
ap-2085	22	5	are	be	AUX
ap-2085	22	6	interested	interested	ADJ
ap-2085	22	7	in	in	ADP
ap-2085	22	8	finding	find	VERB
ap-2085	22	9	the	the	DET
ap-2085	22	10	bloch	bloch	PROPN
ap-2085	22	11	solutions	solution	NOUN
ap-2085	22	12	,	,	PUNCT
ap-2085	22	13	which	which	PRON
ap-2085	22	14	are	be	AUX
ap-2085	22	15	solutions	solution	NOUN
ap-2085	22	16	of	of	ADP
ap-2085	22	17	the	the	DET
ap-2085	22	18	time	time	NOUN
ap-2085	22	19	-	-	PUNCT
ap-2085	22	20	independent	independent	ADJ
ap-2085	22	21	schrödinger	schrödinger	ADJ
ap-2085	22	22	equation	equation	NOUN
ap-2085	23	1	−	−	PROPN
ap-2085	24	1	(	(	PUNCT
ap-2085	24	2	∂2	∂2	NUM
ap-2085	24	3	∂x2	∂x2	NOUN
ap-2085	24	4	+	+	CCONJ
ap-2085	24	5	v	v	ADJ
ap-2085	24	6	(	(	PUNCT
ap-2085	24	7	x	x	NOUN
ap-2085	24	8	)	)	PUNCT
ap-2085	24	9	)	)	PUNCT
ap-2085	24	10	ψk(x	ψk(x	NOUN
ap-2085	24	11	)	)	PUNCT
ap-2085	24	12	=	=	SYM
ap-2085	24	13	eψk(x	eψk(x	PROPN
ap-2085	24	14	)	)	PUNCT
ap-2085	24	15	(	(	PUNCT
ap-2085	24	16	2	2	NUM
ap-2085	24	17	)	)	PUNCT
ap-2085	24	18	with	with	ADP
ap-2085	24	19	the	the	DET
ap-2085	24	20	periodicity	periodicity	NOUN
ap-2085	24	21	property	property	NOUN
ap-2085	24	22	ψk(x+	ψk(x+	NOUN
ap-2085	24	23	π	π	X
ap-2085	24	24	)	)	PUNCT
ap-2085	24	25	=	=	SYM
ap-2085	24	26	eikπψk(x	eikπψk(x	PROPN
ap-2085	24	27	)	)	PUNCT
ap-2085	24	28	.	.	PUNCT
ap-2085	25	1	the	the	DET
ap-2085	25	2	standard	standard	ADJ
ap-2085	25	3	way	way	NOUN
ap-2085	25	4	of	of	ADP
ap-2085	25	5	obtaining	obtain	VERB
ap-2085	25	6	such	such	ADJ
ap-2085	25	7	solutions	solution	NOUN
ap-2085	25	8	is	be	AUX
ap-2085	25	9	the	the	DET
ap-2085	25	10	floquet	floquet	NOUN
ap-2085	25	11	method	method	NOUN
ap-2085	25	12	,	,	PUNCT
ap-2085	25	13	whereby	whereby	SCONJ
ap-2085	25	14	ψk(x	ψk(x	NOUN
ap-2085	25	15	)	)	PUNCT
ap-2085	25	16	is	be	AUX
ap-2085	25	17	expressed	express	VERB
ap-2085	25	18	in	in	ADP
ap-2085	25	19	terms	term	NOUN
ap-2085	25	20	of	of	ADP
ap-2085	25	21	two	two	NUM
ap-2085	25	22	linearly	linearly	ADV
ap-2085	25	23	-	-	PUNCT
ap-2085	25	24	independent	independent	ADJ
ap-2085	25	25	solutions	solution	NOUN
ap-2085	25	26	,	,	PUNCT
ap-2085	25	27	u1(x	u1(x	NOUN
ap-2085	25	28	)	)	PUNCT
ap-2085	25	29	and	and	CCONJ
ap-2085	25	30	u2(x	u2(x	NUM
ap-2085	25	31	)	)	PUNCT
ap-2085	25	32	,	,	PUNCT
ap-2085	25	33	of	of	ADP
ap-2085	25	34	eq	eq	NOUN
ap-2085	25	35	.	.	PUNCT
ap-2085	26	1	(	(	PUNCT
ap-2085	26	2	2	2	NUM
ap-2085	26	3	)	)	PUNCT
ap-2085	26	4	,	,	PUNCT
ap-2085	26	5	with	with	ADP
ap-2085	26	6	initial	initial	ADJ
ap-2085	26	7	conditions	condition	NOUN
ap-2085	26	8	u1(0	u1(0	NOUN
ap-2085	26	9	)	)	PUNCT
ap-2085	26	10	=	=	SYM
ap-2085	26	11	1	1	NUM
ap-2085	26	12	,	,	PUNCT
ap-2085	26	13	u′1(0	u′1(0	PROPN
ap-2085	26	14	)	)	PUNCT
ap-2085	27	1	=	=	SYM
ap-2085	27	2	0	0	NUM
ap-2085	27	3	,	,	PUNCT
ap-2085	27	4	u2(0	u2(0	NOUN
ap-2085	27	5	)	)	PUNCT
ap-2085	27	6	=	=	SYM
ap-2085	27	7	0	0	NUM
ap-2085	27	8	,	,	PUNCT
ap-2085	27	9	u′2(0	u′2(0	PROPN
ap-2085	27	10	)	)	PUNCT
ap-2085	27	11	=	=	SYM
ap-2085	28	1	1	1	X
ap-2085	28	2	.	.	PUNCT
ap-2085	28	3	(	(	PUNCT
ap-2085	28	4	3	3	NUM
ap-2085	28	5	)	)	PUNCT
ap-2085	28	6	then	then	ADV
ap-2085	28	7	ψk(x	ψk(x	NOUN
ap-2085	28	8	)	)	PUNCT
ap-2085	28	9	is	be	AUX
ap-2085	28	10	written	write	VERB
ap-2085	28	11	as	as	ADP
ap-2085	28	12	the	the	DET
ap-2085	28	13	superposition	superposition	NOUN
ap-2085	28	14	ψk(x	ψk(x	NOUN
ap-2085	28	15	)	)	PUNCT
ap-2085	28	16	=	=	SYM
ap-2085	28	17	cku1(x	cku1(x	NOUN
ap-2085	28	18	)	)	PUNCT
ap-2085	28	19	+	+	CCONJ
ap-2085	28	20	dku2(x	dku2(x	NUM
ap-2085	28	21	)	)	PUNCT
ap-2085	28	22	.	.	PUNCT
ap-2085	29	1	(	(	PUNCT
ap-2085	29	2	4	4	X
ap-2085	29	3	)	)	PUNCT
ap-2085	29	4	imposing	impose	VERB
ap-2085	29	5	the	the	DET
ap-2085	29	6	conditions	condition	NOUN
ap-2085	29	7	ψk(π	ψk(π	PUNCT
ap-2085	29	8	)	)	PUNCT
ap-2085	29	9	=	=	SYM
ap-2085	29	10	eikπψ(0	eikπψ(0	X
ap-2085	29	11	)	)	PUNCT
ap-2085	29	12	and	and	CCONJ
ap-2085	29	13	ψ′k(π	ψ′k(π	NOUN
ap-2085	29	14	)	)	PUNCT
ap-2085	29	15	=	=	SYM
ap-2085	29	16	eikπψ′(0	eikπψ′(0	NOUN
ap-2085	29	17	)	)	PUNCT
ap-2085	29	18	and	and	CCONJ
ap-2085	29	19	exploiting	exploit	VERB
ap-2085	29	20	the	the	DET
ap-2085	29	21	invariance	invariance	NOUN
ap-2085	29	22	of	of	ADP
ap-2085	29	23	the	the	DET
ap-2085	29	24	wronskian	wronskian	PROPN
ap-2085	29	25	w	w	PROPN
ap-2085	29	26	(	(	PUNCT
ap-2085	29	27	u1	u1	PROPN
ap-2085	29	28	,	,	PUNCT
ap-2085	29	29	u2	u2	PROPN
ap-2085	29	30	)	)	PUNCT
ap-2085	29	31	one	one	NOUN
ap-2085	29	32	arrives	arrive	VERB
ap-2085	29	33	at	at	ADP
ap-2085	29	34	the	the	DET
ap-2085	29	35	secular	secular	ADJ
ap-2085	29	36	equation	equation	NOUN
ap-2085	30	1	cos	cos	INTJ
ap-2085	30	2	kπ	kπ	PROPN
ap-2085	30	3	=	=	PUNCT
ap-2085	30	4	∆	∆	PROPN
ap-2085	30	5	≡	≡	PROPN
ap-2085	30	6	1	1	NUM
ap-2085	30	7	2	2	NUM
ap-2085	30	8	(	(	PUNCT
ap-2085	30	9	u1(π	u1(π	PROPN
ap-2085	30	10	)	)	PUNCT
ap-2085	30	11	+	+	NUM
ap-2085	30	12	u′2(π	u′2(π	NOUN
ap-2085	30	13	)	)	PUNCT
ap-2085	30	14	)	)	PUNCT
ap-2085	30	15	.	.	PUNCT
ap-2085	31	1	(	(	PUNCT
ap-2085	31	2	5	5	X
ap-2085	31	3	)	)	PUNCT
ap-2085	31	4	in	in	ADP
ap-2085	31	5	the	the	DET
ap-2085	31	6	hermitian	hermitian	ADJ
ap-2085	31	7	situation	situation	NOUN
ap-2085	31	8	both	both	DET
ap-2085	31	9	u1(π	u1(π	PROPN
ap-2085	31	10	)	)	PUNCT
ap-2085	31	11	and	and	CCONJ
ap-2085	31	12	u2(π	u2(π	NUM
ap-2085	31	13	)	)	PUNCT
ap-2085	31	14	are	be	AUX
ap-2085	31	15	real	real	ADJ
ap-2085	31	16	,	,	PUNCT
ap-2085	31	17	and	and	CCONJ
ap-2085	31	18	the	the	DET
ap-2085	31	19	equation	equation	NOUN
ap-2085	31	20	for	for	ADP
ap-2085	31	21	e	e	NOUN
ap-2085	31	22	has	have	VERB
ap-2085	31	23	real	real	ADJ
ap-2085	31	24	solutions	solution	NOUN
ap-2085	31	25	(	(	PUNCT
ap-2085	31	26	bands	band	NOUN
ap-2085	31	27	)	)	PUNCT
ap-2085	31	28	when	when	SCONJ
ap-2085	31	29	|∆|	|∆|	NUM
ap-2085	31	30	≤	≤	NUM
ap-2085	31	31	1	1	NUM
ap-2085	31	32	.	.	PUNCT
ap-2085	32	1	however	however	ADV
ap-2085	32	2	,	,	PUNCT
ap-2085	32	3	in	in	ADP
ap-2085	32	4	the	the	DET
ap-2085	32	5	non	non	ADJ
ap-2085	32	6	-	-	ADJ
ap-2085	32	7	hermitian	hermitian	ADJ
ap-2085	32	8	,	,	PUNCT
ap-2085	32	9	pt	pt	X
ap-2085	32	10	symmetric	symmetric	NOUN
ap-2085	32	11	,	,	PUNCT
ap-2085	32	12	situation	situation	NOUN
ap-2085	32	13	it	it	PRON
ap-2085	32	14	is	be	AUX
ap-2085	32	15	not	not	PART
ap-2085	32	16	at	at	ADV
ap-2085	32	17	all	all	ADV
ap-2085	32	18	obvious	obvious	ADJ
ap-2085	32	19	that	that	SCONJ
ap-2085	32	20	∆	∆	PROPN
ap-2085	32	21	is	be	AUX
ap-2085	32	22	real	real	ADJ
ap-2085	32	23	,	,	PUNCT
ap-2085	32	24	since	since	SCONJ
ap-2085	32	25	that	that	PRON
ap-2085	32	26	implies	imply	VERB
ap-2085	32	27	a	a	DET
ap-2085	32	28	relation	relation	NOUN
ap-2085	32	29	between	between	ADP
ap-2085	32	30	u1(π	u1(π	PROPN
ap-2085	32	31	)	)	PUNCT
ap-2085	32	32	and	and	CCONJ
ap-2085	32	33	u′2(π	u′2(π	NOUN
ap-2085	32	34	)	)	PUNCT
ap-2085	32	35	,	,	PUNCT
ap-2085	32	36	even	even	ADV
ap-2085	32	37	though	though	SCONJ
ap-2085	32	38	u1(x	u1(x	NUM
ap-2085	32	39	)	)	PUNCT
ap-2085	32	40	and	and	CCONJ
ap-2085	32	41	u2(x	u2(x	X
ap-2085	32	42	)	)	PUNCT
ap-2085	32	43	are	be	AUX
ap-2085	32	44	linearly	linearly	ADV
ap-2085	32	45	independent	independent	ADJ
ap-2085	32	46	solutions	solution	NOUN
ap-2085	32	47	of	of	ADP
ap-2085	32	48	eq	eq	PROPN
ap-2085	32	49	.	.	PUNCT
ap-2085	33	1	(	(	PUNCT
ap-2085	33	2	2	2	NUM
ap-2085	33	3	)	)	PUNCT
ap-2085	33	4	.	.	PUNCT
ap-2085	34	1	it	it	PRON
ap-2085	34	2	is	be	AUX
ap-2085	34	3	that	that	DET
ap-2085	34	4	problem	problem	NOUN
ap-2085	34	5	that	that	SCONJ
ap-2085	34	6	we	we	PRON
ap-2085	34	7	wish	wish	VERB
ap-2085	34	8	to	to	PART
ap-2085	34	9	address	address	VERB
ap-2085	34	10	in	in	ADP
ap-2085	34	11	the	the	DET
ap-2085	34	12	present	present	ADJ
ap-2085	34	13	note	note	NOUN
ap-2085	34	14	.	.	PUNCT
ap-2085	35	1	in	in	ADP
ap-2085	35	2	fact	fact	NOUN
ap-2085	35	3	we	we	PRON
ap-2085	35	4	will	will	AUX
ap-2085	35	5	show	show	VERB
ap-2085	35	6	that	that	SCONJ
ap-2085	35	7	u′2(π	u′2(π	NOUN
ap-2085	35	8	)	)	PUNCT
ap-2085	35	9	=	=	SYM
ap-2085	35	10	u∗1(π	u∗1(π	PROPN
ap-2085	35	11	)	)	PUNCT
ap-2085	35	12	.	.	PUNCT
ap-2085	36	1	the	the	DET
ap-2085	36	2	clue	clue	NOUN
ap-2085	36	3	to	to	ADP
ap-2085	36	4	relating	relate	VERB
ap-2085	36	5	u1(π	u1(π	NOUN
ap-2085	36	6	)	)	PUNCT
ap-2085	36	7	and	and	CCONJ
ap-2085	36	8	u2(π	u2(π	NUM
ap-2085	36	9	)	)	PUNCT
ap-2085	36	10	comes	come	VERB
ap-2085	36	11	from	from	ADP
ap-2085	36	12	considering	consider	VERB
ap-2085	36	13	a	a	DET
ap-2085	36	14	half	half	ADJ
ap-2085	36	15	-	-	PUNCT
ap-2085	36	16	period	period	NOUN
ap-2085	36	17	shift	shift	NOUN
ap-2085	36	18	,	,	PUNCT
ap-2085	36	19	namely	namely	ADV
ap-2085	36	20	x	x	PUNCT
ap-2085	37	1	=	=	PUNCT
ap-2085	37	2	z	z	PROPN
ap-2085	37	3	+	+	NOUN
ap-2085	37	4	π/2	π/2	NUM
ap-2085	37	5	.	.	PUNCT
ap-2085	38	1	we	we	PRON
ap-2085	38	2	write	write	VERB
ap-2085	38	3	ϕ(z	ϕ(z	NOUN
ap-2085	38	4	)	)	PUNCT
ap-2085	39	1	=	=	SYM
ap-2085	39	2	ψ(z	ψ(z	PROPN
ap-2085	39	3	+	+	CCONJ
ap-2085	39	4	π/2	π/2	NUM
ap-2085	39	5	)	)	PUNCT
ap-2085	39	6	and	and	CCONJ
ap-2085	39	7	u(z	u(z	NOUN
ap-2085	39	8	)	)	PUNCT
ap-2085	39	9	=	=	SYM
ap-2085	39	10	v	v	X
ap-2085	39	11	(	(	PUNCT
ap-2085	39	12	z	z	NOUN
ap-2085	39	13	+	+	NOUN
ap-2085	39	14	π/2	π/2	NUM
ap-2085	39	15	)	)	PUNCT
ap-2085	39	16	.	.	PUNCT
ap-2085	40	1	then	then	ADV
ap-2085	40	2	ϕ(z	ϕ(z	PROPN
ap-2085	40	3	)	)	PUNCT
ap-2085	40	4	satisfies	satisfy	VERB
ap-2085	40	5	the	the	DET
ap-2085	40	6	schrödinger	schrödinger	ADJ
ap-2085	40	7	equation	equation	NOUN
ap-2085	40	8	−	−	PROPN
ap-2085	41	1	(	(	PUNCT
ap-2085	41	2	∂2	∂2	PROPN
ap-2085	41	3	∂z2	∂z2	PROPN
ap-2085	41	4	+	+	CCONJ
ap-2085	41	5	u(z	u(z	NOUN
ap-2085	41	6	)	)	PUNCT
ap-2085	41	7	)	)	PUNCT
ap-2085	42	1	ϕk(z	ϕk(z	PUNCT
ap-2085	42	2	)	)	PUNCT
ap-2085	43	1	=	=	SYM
ap-2085	43	2	eϕk(z	eϕk(z	PROPN
ap-2085	43	3	)	)	PUNCT
ap-2085	43	4	.	.	PUNCT
ap-2085	44	1	(	(	PUNCT
ap-2085	44	2	6	6	X
ap-2085	44	3	)	)	PUNCT
ap-2085	44	4	the	the	DET
ap-2085	44	5	crucial	crucial	ADJ
ap-2085	44	6	point	point	NOUN
ap-2085	44	7	is	be	AUX
ap-2085	44	8	that	that	SCONJ
ap-2085	44	9	because	because	SCONJ
ap-2085	44	10	of	of	ADP
ap-2085	44	11	the	the	DET
ap-2085	44	12	periodicity	periodicity	NOUN
ap-2085	44	13	and	and	CCONJ
ap-2085	44	14	pt	pt	NOUN
ap-2085	44	15	-symmetry	-symmetry	NOUN
ap-2085	44	16	of	of	ADP
ap-2085	44	17	v	v	NOUN
ap-2085	44	18	(	(	PUNCT
ap-2085	44	19	x	x	X
ap-2085	44	20	)	)	PUNCT
ap-2085	44	21	the	the	DET
ap-2085	44	22	new	new	ADJ
ap-2085	44	23	potential	potential	ADJ
ap-2085	44	24	u(z	u(z	NOUN
ap-2085	44	25	)	)	PUNCT
ap-2085	44	26	is	be	AUX
ap-2085	44	27	also	also	ADV
ap-2085	44	28	pt	pt	NOUN
ap-2085	44	29	-symmetric	-symmetric	NOUN
ap-2085	44	30	.	.	PUNCT
ap-2085	45	1	thus	thus	ADV
ap-2085	45	2	u(−z	u(−z	ADV
ap-2085	45	3	)	)	PUNCT
ap-2085	45	4	=	=	SYM
ap-2085	45	5	v	v	X
ap-2085	45	6	(	(	PUNCT
ap-2085	45	7	−z	−z	NOUN
ap-2085	45	8	+	+	NOUN
ap-2085	45	9	π/2	π/2	NUM
ap-2085	45	10	)	)	PUNCT
ap-2085	46	1	=	=	SYM
ap-2085	46	2	v	v	X
ap-2085	46	3	(	(	PUNCT
ap-2085	46	4	−z	−z	NOUN
ap-2085	46	5	−	−	PROPN
ap-2085	46	6	π/2	π/2	NUM
ap-2085	46	7	)	)	PUNCT
ap-2085	47	1	=	=	PUNCT
ap-2085	47	2	v	v	ADP
ap-2085	47	3	∗(z	∗(z	NOUN
ap-2085	47	4	+	+	CCONJ
ap-2085	47	5	π/2	π/2	NUM
ap-2085	47	6	)	)	PUNCT
ap-2085	48	1	=	=	SYM
ap-2085	48	2	u∗(z	u∗(z	NOUN
ap-2085	48	3	)	)	PUNCT
ap-2085	48	4	.	.	PUNCT
ap-2085	49	1	122	122	NUM
ap-2085	49	2	http://dx.doi.org/10.14311/ap.2014.54.0122	http://dx.doi.org/10.14311/ap.2014.54.0122	NOUN
ap-2085	49	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2085	49	4	vol	vol	NOUN
ap-2085	49	5	.	.	PUNCT
ap-2085	50	1	54	54	NUM
ap-2085	50	2	no	no	NOUN
ap-2085	50	3	.	.	PUNCT
ap-2085	51	1	2/2014	2/2014	PROPN
ap-2085	52	1	the	the	DET
ap-2085	52	2	floquet	floquet	NOUN
ap-2085	52	3	method	method	NOUN
ap-2085	52	4	for	for	ADP
ap-2085	52	5	pt	pt	NOUN
ap-2085	52	6	-	-	ADJ
ap-2085	52	7	symmetric	symmetric	ADJ
ap-2085	52	8	periodic	periodic	ADJ
ap-2085	52	9	potentials	potential	NOUN
ap-2085	52	10	now	now	ADV
ap-2085	52	11	we	we	PRON
ap-2085	52	12	can	can	AUX
ap-2085	52	13	express	express	VERB
ap-2085	52	14	the	the	DET
ap-2085	52	15	floquet	floquet	NOUN
ap-2085	52	16	functions	function	NOUN
ap-2085	52	17	u1(x	u1(x	ADV
ap-2085	52	18	)	)	PUNCT
ap-2085	52	19	,	,	PUNCT
ap-2085	52	20	u2(x	u2(x	X
ap-2085	52	21	)	)	PUNCT
ap-2085	52	22	in	in	ADP
ap-2085	52	23	terms	term	NOUN
ap-2085	52	24	of	of	ADP
ap-2085	52	25	floquet	floquet	NOUN
ap-2085	52	26	functions	function	NOUN
ap-2085	52	27	v1(z	v1(z	PROPN
ap-2085	52	28	)	)	PUNCT
ap-2085	52	29	,	,	PUNCT
ap-2085	52	30	v2(z	v2(z	NOUN
ap-2085	52	31	)	)	PUNCT
ap-2085	52	32	of	of	ADP
ap-2085	52	33	the	the	DET
ap-2085	52	34	transformed	transform	VERB
ap-2085	52	35	equation	equation	NOUN
ap-2085	52	36	(	(	PUNCT
ap-2085	52	37	6	6	NUM
ap-2085	52	38	)	)	PUNCT
ap-2085	52	39	,	,	PUNCT
ap-2085	52	40	satisfying	satisfy	VERB
ap-2085	52	41	v1(0	v1(0	NOUN
ap-2085	52	42	)	)	PUNCT
ap-2085	53	1	=	=	SYM
ap-2085	53	2	1	1	NUM
ap-2085	53	3	,	,	PUNCT
ap-2085	53	4	v′1(0	v′1(0	PROPN
ap-2085	53	5	)	)	PUNCT
ap-2085	53	6	=	=	SYM
ap-2085	53	7	0	0	NUM
ap-2085	53	8	,	,	PUNCT
ap-2085	53	9	v2(0	v2(0	NOUN
ap-2085	53	10	)	)	PUNCT
ap-2085	53	11	=	=	SYM
ap-2085	53	12	0	0	NUM
ap-2085	53	13	,	,	PUNCT
ap-2085	53	14	v′2(0	v′2(0	NUM
ap-2085	53	15	)	)	PUNCT
ap-2085	53	16	=	=	SYM
ap-2085	54	1	1	1	X
ap-2085	54	2	.	.	PUNCT
ap-2085	54	3	(	(	PUNCT
ap-2085	54	4	7	7	X
ap-2085	54	5	)	)	PUNCT
ap-2085	54	6	it	it	PRON
ap-2085	54	7	is	be	AUX
ap-2085	54	8	easily	easily	ADV
ap-2085	54	9	seen	see	VERB
ap-2085	54	10	that	that	SCONJ
ap-2085	54	11	the	the	DET
ap-2085	54	12	relation	relation	NOUN
ap-2085	54	13	is	be	AUX
ap-2085	54	14	u1(x	u1(x	ADV
ap-2085	54	15	)	)	PUNCT
ap-2085	54	16	=	=	SYM
ap-2085	54	17	v′2(−π/2)v1(z)−	v′2(−π/2)v1(z)−	PROPN
ap-2085	54	18	v′1(−π/2)v2(z	v′1(−π/2)v2(z	PROPN
ap-2085	54	19	)	)	PUNCT
ap-2085	54	20	,	,	PUNCT
ap-2085	54	21	u2(x	u2(x	X
ap-2085	54	22	)	)	PUNCT
ap-2085	54	23	=	=	SYM
ap-2085	54	24	−v2(−π/2)v1(z	−v2(−π/2)v1(z	PROPN
ap-2085	54	25	)	)	PUNCT
ap-2085	54	26	+	+	NUM
ap-2085	54	27	v1(−π/2)v2(z	v1(−π/2)v2(z	NOUN
ap-2085	54	28	)	)	PUNCT
ap-2085	54	29	,	,	PUNCT
ap-2085	54	30	(	(	PUNCT
ap-2085	54	31	8)	8)	NUM
ap-2085	54	32	in	in	ADP
ap-2085	54	33	order	order	NOUN
ap-2085	54	34	to	to	PART
ap-2085	54	35	satisfy	satisfy	VERB
ap-2085	54	36	the	the	DET
ap-2085	54	37	initial	initial	ADJ
ap-2085	54	38	conditions	condition	NOUN
ap-2085	54	39	on	on	ADP
ap-2085	54	40	u1(x	u1(x	NOUN
ap-2085	54	41	)	)	PUNCT
ap-2085	54	42	,	,	PUNCT
ap-2085	54	43	u2(x	u2(x	NOUN
ap-2085	54	44	)	)	PUNCT
ap-2085	54	45	.	.	PUNCT
ap-2085	55	1	so	so	ADV
ap-2085	55	2	u1(π	u1(π	ADJ
ap-2085	55	3	)	)	PUNCT
ap-2085	55	4	=	=	NOUN
ap-2085	55	5	v′2(−π/2)v1(π/2)−	v′2(−π/2)v1(π/2)−	NOUN
ap-2085	55	6	v′1(−π/2)v2(π/2	v′1(−π/2)v2(π/2	NOUN
ap-2085	55	7	)	)	PUNCT
ap-2085	55	8	,	,	PUNCT
ap-2085	55	9	u′1(π	u′1(π	ADJ
ap-2085	55	10	)	)	PUNCT
ap-2085	55	11	=	=	SYM
ap-2085	56	1	v′2(−π/2)v′1(π/2)−	v′2(−π/2)v′1(π/2)−	PUNCT
ap-2085	56	2	v′1(−π/2)v′2(π/2	v′1(−π/2)v′2(π/2	NOUN
ap-2085	56	3	)	)	PUNCT
ap-2085	56	4	,	,	PUNCT
ap-2085	56	5	u2(π	u2(π	NUM
ap-2085	56	6	)	)	PUNCT
ap-2085	56	7	=	=	SYM
ap-2085	56	8	−v2(−π/2)v1(π/2	−v2(−π/2)v1(π/2	PROPN
ap-2085	56	9	)	)	PUNCT
ap-2085	56	10	+	+	NUM
ap-2085	57	1	v1(−π/2)v2(π/2	v1(−π/2)v2(π/2	NOUN
ap-2085	57	2	)	)	PUNCT
ap-2085	57	3	,	,	PUNCT
ap-2085	57	4	u′2(π	u′2(π	PROPN
ap-2085	57	5	)	)	PUNCT
ap-2085	57	6	=	=	SYM
ap-2085	57	7	−v2(−π/2)v′1(π/2	−v2(−π/2)v′1(π/2	NUM
ap-2085	57	8	)	)	PUNCT
ap-2085	57	9	+	+	NUM
ap-2085	57	10	v1(−π/2)v′2(π/2	v1(−π/2)v′2(π/2	NUM
ap-2085	57	11	)	)	PUNCT
ap-2085	57	12	.	.	PUNCT
ap-2085	58	1	(	(	PUNCT
ap-2085	58	2	9	9	NUM
ap-2085	58	3	)	)	PUNCT
ap-2085	58	4	but	but	CCONJ
ap-2085	58	5	,	,	PUNCT
ap-2085	58	6	because	because	SCONJ
ap-2085	58	7	of	of	ADP
ap-2085	58	8	the	the	DET
ap-2085	58	9	pt	pt	NOUN
ap-2085	58	10	-symmetry	-symmetry	NOUN
ap-2085	58	11	of	of	ADP
ap-2085	58	12	eq	eq	PROPN
ap-2085	58	13	.	.	PUNCT
ap-2085	59	1	(	(	PUNCT
ap-2085	59	2	6	6	NUM
ap-2085	59	3	)	)	PUNCT
ap-2085	59	4	and	and	CCONJ
ap-2085	59	5	the	the	DET
ap-2085	59	6	initial	initial	ADJ
ap-2085	59	7	conditions	condition	NOUN
ap-2085	59	8	satisfied	satisfy	VERB
ap-2085	59	9	by	by	ADP
ap-2085	59	10	v1(z	v1(z	PROPN
ap-2085	59	11	)	)	PUNCT
ap-2085	59	12	,	,	PUNCT
ap-2085	59	13	v2(z	v2(z	NOUN
ap-2085	59	14	)	)	PUNCT
ap-2085	59	15	,	,	PUNCT
ap-2085	59	16	v1(−π/2	v1(−π/2	PROPN
ap-2085	59	17	)	)	PUNCT
ap-2085	59	18	=	=	SYM
ap-2085	59	19	(	(	PUNCT
ap-2085	59	20	v1(π/2))∗	v1(π/2))∗	NUM
ap-2085	59	21	,	,	PUNCT
ap-2085	59	22	v′1(−π/2	v′1(−π/2	PROPN
ap-2085	59	23	)	)	PUNCT
ap-2085	59	24	=	=	SYM
ap-2085	59	25	−(v′1(π/2))∗	−(v′1(π/2))∗	NOUN
ap-2085	59	26	,	,	PUNCT
ap-2085	59	27	v2(−π/2	v2(−π/2	PROPN
ap-2085	59	28	)	)	PUNCT
ap-2085	59	29	=	=	SYM
ap-2085	59	30	−(v2(π/2))∗	−(v2(π/2))∗	NOUN
ap-2085	59	31	,	,	PUNCT
ap-2085	59	32	v′2(−π/2	v′2(−π/2	PROPN
ap-2085	59	33	)	)	PUNCT
ap-2085	59	34	=	=	PRON
ap-2085	60	1	(	(	PUNCT
ap-2085	60	2	v′2(π/2))∗.	v′2(π/2))∗.	INTJ
ap-2085	60	3	(	(	PUNCT
ap-2085	60	4	10	10	NUM
ap-2085	60	5	)	)	PUNCT
ap-2085	60	6	hence	hence	ADV
ap-2085	60	7	,	,	PUNCT
ap-2085	60	8	indeed	indeed	ADV
ap-2085	60	9	,	,	PUNCT
ap-2085	60	10	u1(π	u1(π	PROPN
ap-2085	60	11	)	)	PUNCT
ap-2085	60	12	=	=	SYM
ap-2085	60	13	(	(	PUNCT
ap-2085	60	14	u′2(π))∗	u′2(π))∗	ADV
ap-2085	60	15	,	,	PUNCT
ap-2085	60	16	so	so	SCONJ
ap-2085	60	17	that	that	SCONJ
ap-2085	60	18	∆	∆	PROPN
ap-2085	60	19	in	in	ADP
ap-2085	60	20	eq	eq	ADP
ap-2085	60	21	.	.	PUNCT
ap-2085	61	1	(	(	PUNCT
ap-2085	61	2	5	5	NUM
ap-2085	61	3	)	)	PUNCT
ap-2085	61	4	is	be	AUX
ap-2085	61	5	real	real	ADJ
ap-2085	61	6	and	and	CCONJ
ap-2085	61	7	the	the	DET
ap-2085	61	8	energy	energy	NOUN
ap-2085	61	9	eigenvalues	eigenvalue	NOUN
ap-2085	61	10	of	of	ADP
ap-2085	61	11	the	the	DET
ap-2085	61	12	bloch	bloch	PROPN
ap-2085	61	13	wavefunctions	wavefunction	NOUN
ap-2085	61	14	are	be	AUX
ap-2085	61	15	either	either	CCONJ
ap-2085	61	16	real	real	ADJ
ap-2085	61	17	or	or	CCONJ
ap-2085	61	18	occur	occur	VERB
ap-2085	61	19	in	in	ADP
ap-2085	61	20	complex	complex	ADJ
ap-2085	61	21	conjugate	conjugate	ADJ
ap-2085	61	22	pairs	pair	NOUN
ap-2085	61	23	.	.	PUNCT
ap-2085	62	1	from	from	ADP
ap-2085	62	2	eq	eq	ADP
ap-2085	62	3	.	.	PUNCT
ap-2085	63	1	(	(	PUNCT
ap-2085	63	2	10	10	NUM
ap-2085	63	3	)	)	PUNCT
ap-2085	63	4	we	we	PRON
ap-2085	63	5	also	also	ADV
ap-2085	63	6	see	see	VERB
ap-2085	63	7	that	that	SCONJ
ap-2085	63	8	u′1(π	u′1(π	ADJ
ap-2085	63	9	)	)	PUNCT
ap-2085	63	10	and	and	CCONJ
ap-2085	63	11	u2(π	u2(π	X
ap-2085	63	12	)	)	PUNCT
ap-2085	63	13	are	be	AUX
ap-2085	63	14	real	real	ADJ
ap-2085	63	15	.	.	PUNCT
ap-2085	64	1	the	the	DET
ap-2085	64	2	statement	statement	NOUN
ap-2085	64	3	u1(π	u1(π	NOUN
ap-2085	64	4	)	)	PUNCT
ap-2085	64	5	=	=	SYM
ap-2085	64	6	(	(	PUNCT
ap-2085	64	7	u′2(π))∗	u′2(π))∗	X
ap-2085	64	8	is	be	AUX
ap-2085	64	9	in	in	ADP
ap-2085	64	10	fact	fact	NOUN
ap-2085	64	11	the	the	DET
ap-2085	64	12	pt	pt	NOUN
ap-2085	64	13	-generalization	-generalization	NOUN
ap-2085	64	14	of	of	ADP
ap-2085	64	15	the	the	DET
ap-2085	64	16	relation	relation	NOUN
ap-2085	64	17	u1(π	u1(π	NOUN
ap-2085	64	18	)	)	PUNCT
ap-2085	64	19	=	=	SYM
ap-2085	64	20	u′2(π	u′2(π	PROPN
ap-2085	64	21	)	)	PUNCT
ap-2085	64	22	implied	imply	VERB
ap-2085	64	23	without	without	ADP
ap-2085	64	24	proof	proof	NOUN
ap-2085	64	25	by	by	ADP
ap-2085	64	26	eq	eq	PROPN
ap-2085	64	27	.	.	PUNCT
ap-2085	64	28	(	(	PUNCT
ap-2085	64	29	20.3.10	20.3.10	PROPN
ap-2085	64	30	)	)	PUNCT
ap-2085	64	31	of	of	ADP
ap-2085	64	32	ref	ref	NOUN
ap-2085	64	33	.	.	PUNCT
ap-2085	65	1	[	[	X
ap-2085	65	2	16	16	NUM
ap-2085	65	3	]	]	PUNCT
ap-2085	65	4	for	for	ADP
ap-2085	65	5	the	the	DET
ap-2085	65	6	hermitian	hermitian	ADJ
ap-2085	65	7	case	case	NOUN
ap-2085	65	8	of	of	ADP
ap-2085	65	9	the	the	DET
ap-2085	65	10	mathieu	mathieu	PROPN
ap-2085	65	11	equation	equation	NOUN
ap-2085	65	12	,	,	PUNCT
ap-2085	65	13	where	where	SCONJ
ap-2085	65	14	v	v	X
ap-2085	65	15	(	(	PUNCT
ap-2085	65	16	x	x	NOUN
ap-2085	65	17	)	)	PUNCT
ap-2085	65	18	=	=	SYM
ap-2085	65	19	cos(2x	cos(2x	VERB
ap-2085	65	20	)	)	PUNCT
ap-2085	65	21	.	.	PUNCT
ap-2085	66	1	if	if	SCONJ
ap-2085	66	2	we	we	PRON
ap-2085	66	3	wish	wish	VERB
ap-2085	66	4	,	,	PUNCT
ap-2085	66	5	we	we	PRON
ap-2085	66	6	may	may	AUX
ap-2085	66	7	express	express	VERB
ap-2085	66	8	everything	everything	PRON
ap-2085	66	9	in	in	ADP
ap-2085	66	10	terms	term	NOUN
ap-2085	66	11	of	of	ADP
ap-2085	66	12	u1	u1	NOUN
ap-2085	66	13	,	,	PUNCT
ap-2085	66	14	u2	u2	PROPN
ap-2085	66	15	because	because	SCONJ
ap-2085	66	16	from	from	ADP
ap-2085	66	17	eq	eq	NOUN
ap-2085	66	18	.	.	PUNCT
ap-2085	67	1	(	(	PUNCT
ap-2085	67	2	8)	8)	NUM
ap-2085	67	3	u1(π/2	u1(π/2	NUM
ap-2085	67	4	)	)	PUNCT
ap-2085	68	1	=	=	SYM
ap-2085	68	2	v′2(−π/2	v′2(−π/2	PROPN
ap-2085	68	3	)	)	PUNCT
ap-2085	68	4	,	,	PUNCT
ap-2085	68	5	u′1(π/2	u′1(π/2	ADJ
ap-2085	68	6	)	)	PUNCT
ap-2085	68	7	=	=	SYM
ap-2085	68	8	−v′1(−π/2	−v′1(−π/2	PROPN
ap-2085	68	9	)	)	PUNCT
ap-2085	68	10	,	,	PUNCT
ap-2085	68	11	u2(π/2	u2(π/2	NOUN
ap-2085	68	12	)	)	PUNCT
ap-2085	68	13	=	=	SYM
ap-2085	68	14	−v2(−π/2	−v2(−π/2	PROPN
ap-2085	68	15	)	)	PUNCT
ap-2085	68	16	,	,	PUNCT
ap-2085	68	17	u′2(π/2	u′2(π/2	PROPN
ap-2085	68	18	)	)	PUNCT
ap-2085	68	19	=	=	PUNCT
ap-2085	69	1	v1(−π/2	v1(−π/2	NOUN
ap-2085	69	2	)	)	PUNCT
ap-2085	69	3	.	.	PUNCT
ap-2085	70	1	(	(	PUNCT
ap-2085	70	2	11	11	NUM
ap-2085	70	3	)	)	PUNCT
ap-2085	70	4	hence	hence	ADV
ap-2085	70	5	u1(π	u1(π	ADJ
ap-2085	70	6	)	)	PUNCT
ap-2085	70	7	=	=	PRON
ap-2085	71	1	(	(	PUNCT
ap-2085	71	2	u′2(π))∗	u′2(π))∗	NOUN
ap-2085	71	3	=	=	SYM
ap-2085	71	4	u1(π/2)(u′2(π/2))∗	u1(π/2)(u′2(π/2))∗	PROPN
ap-2085	71	5	+	+	CCONJ
ap-2085	71	6	u′1(π/2)(u2(π/2))∗	u′1(π/2)(u2(π/2))∗	PROPN
ap-2085	71	7	,	,	PUNCT
ap-2085	71	8	(	(	PUNCT
ap-2085	71	9	12	12	NUM
ap-2085	71	10	)	)	PUNCT
ap-2085	71	11	which	which	PRON
ap-2085	71	12	is	be	AUX
ap-2085	71	13	the	the	DET
ap-2085	71	14	pt	pt	NOUN
ap-2085	71	15	-generalization	-generalization	NOUN
ap-2085	71	16	of	of	ADP
ap-2085	71	17	a	a	DET
ap-2085	71	18	relation	relation	NOUN
ap-2085	71	19	implied	imply	VERB
ap-2085	71	20	by	by	ADP
ap-2085	71	21	eq	eq	PROPN
ap-2085	71	22	.	.	PUNCT
ap-2085	72	1	(	(	PUNCT
ap-2085	72	2	20.3.11	20.3.11	NUM
ap-2085	72	3	)	)	PUNCT
ap-2085	72	4	of	of	ADP
ap-2085	72	5	ref	ref	NOUN
ap-2085	72	6	.	.	PUNCT
ap-2085	73	1	[	[	X
ap-2085	73	2	16	16	NUM
ap-2085	73	3	]	]	PUNCT
ap-2085	73	4	after	after	ADP
ap-2085	73	5	the	the	DET
ap-2085	73	6	use	use	NOUN
ap-2085	73	7	of	of	ADP
ap-2085	73	8	the	the	DET
ap-2085	73	9	invariance	invariance	NOUN
ap-2085	73	10	of	of	ADP
ap-2085	73	11	the	the	DET
ap-2085	73	12	wronskian	wronskian	NOUN
ap-2085	73	13	.	.	PUNCT
ap-2085	74	1	similarly	similarly	ADV
ap-2085	74	2	u′1(π	u′1(π	ADJ
ap-2085	74	3	)	)	PUNCT
ap-2085	75	1	=	=	SYM
ap-2085	75	2	2re	2re	ADJ
ap-2085	75	3	(	(	PUNCT
ap-2085	75	4	u∗1(π/2)u′1(π/2	u∗1(π/2)u′1(π/2	PROPN
ap-2085	75	5	)	)	PUNCT
ap-2085	75	6	)	)	PUNCT
ap-2085	75	7	,	,	PUNCT
ap-2085	75	8	u2(π	u2(π	X
ap-2085	75	9	)	)	PUNCT
ap-2085	75	10	=	=	SYM
ap-2085	75	11	2re	2re	NOUN
ap-2085	75	12	(	(	PUNCT
ap-2085	75	13	u∗2(π/2)u′2(π/2	u∗2(π/2)u′2(π/2	PROPN
ap-2085	75	14	)	)	PUNCT
ap-2085	75	15	)	)	PUNCT
ap-2085	75	16	.	.	PUNCT
ap-2085	76	1	(	(	PUNCT
ap-2085	76	2	13	13	NUM
ap-2085	76	3	)	)	PUNCT
ap-2085	76	4	to	to	PART
ap-2085	76	5	conclude	conclude	VERB
ap-2085	76	6	,	,	PUNCT
ap-2085	76	7	we	we	PRON
ap-2085	76	8	have	have	AUX
ap-2085	76	9	shown	show	VERB
ap-2085	76	10	that	that	SCONJ
ap-2085	76	11	the	the	DET
ap-2085	76	12	secular	secular	ADJ
ap-2085	76	13	equation	equation	NOUN
ap-2085	76	14	for	for	ADP
ap-2085	76	15	the	the	DET
ap-2085	76	16	band	band	NOUN
ap-2085	76	17	structure	structure	NOUN
ap-2085	76	18	of	of	ADP
ap-2085	76	19	pt	pt	NOUN
ap-2085	76	20	-symmetric	-symmetric	ADJ
ap-2085	76	21	periodic	periodic	ADJ
ap-2085	76	22	potentials	potential	NOUN
ap-2085	76	23	is	be	AUX
ap-2085	76	24	indeed	indeed	ADV
ap-2085	76	25	real	real	ADJ
ap-2085	76	26	,	,	PUNCT
ap-2085	76	27	even	even	ADV
ap-2085	76	28	though	though	SCONJ
ap-2085	76	29	in	in	ADP
ap-2085	76	30	the	the	DET
ap-2085	76	31	floquet	floquet	NOUN
ap-2085	76	32	method	method	NOUN
ap-2085	76	33	the	the	DET
ap-2085	76	34	discriminant	discriminant	NOUN
ap-2085	76	35	involves	involve	VERB
ap-2085	76	36	the	the	DET
ap-2085	76	37	two	two	NUM
ap-2085	76	38	ostensibly	ostensibly	ADV
ap-2085	76	39	independent	independent	ADJ
ap-2085	76	40	functions	function	NOUN
ap-2085	76	41	u1(x	u1(x	ADV
ap-2085	76	42	)	)	PUNCT
ap-2085	76	43	and	and	CCONJ
ap-2085	76	44	u2(x	u2(x	NUM
ap-2085	76	45	)	)	PUNCT
ap-2085	76	46	.	.	PUNCT
ap-2085	77	1	the	the	DET
ap-2085	77	2	crucial	crucial	ADJ
ap-2085	77	3	point	point	NOUN
ap-2085	77	4	is	be	AUX
ap-2085	77	5	that	that	SCONJ
ap-2085	77	6	for	for	ADP
ap-2085	77	7	such	such	ADJ
ap-2085	77	8	potentials	potential	NOUN
ap-2085	77	9	there	there	PRON
ap-2085	77	10	is	be	VERB
ap-2085	77	11	also	also	ADV
ap-2085	77	12	a	a	DET
ap-2085	77	13	pt	pt	NOUN
ap-2085	77	14	symmetry	symmetry	NOUN
ap-2085	77	15	about	about	ADP
ap-2085	77	16	the	the	DET
ap-2085	77	17	midpoint	midpoint	NOUN
ap-2085	77	18	of	of	ADP
ap-2085	77	19	the	the	DET
ap-2085	77	20	brillouin	brillouin	NOUN
ap-2085	77	21	zone	zone	NOUN
ap-2085	77	22	.	.	PUNCT
ap-2085	78	1	the	the	DET
ap-2085	78	2	proof	proof	NOUN
ap-2085	78	3	involves	involve	VERB
ap-2085	78	4	expressing	express	VERB
ap-2085	78	5	u1(x	u1(x	NOUN
ap-2085	78	6	)	)	PUNCT
ap-2085	78	7	and	and	CCONJ
ap-2085	78	8	u2(x	u2(x	NUM
ap-2085	78	9	)	)	PUNCT
ap-2085	78	10	in	in	ADP
ap-2085	78	11	terms	term	NOUN
ap-2085	78	12	of	of	ADP
ap-2085	78	13	shifted	shift	VERB
ap-2085	78	14	functions	function	NOUN
ap-2085	78	15	v1(x	v1(x	NOUN
ap-2085	78	16	)	)	PUNCT
ap-2085	78	17	and	and	CCONJ
ap-2085	78	18	v2(x	v2(x	NOUN
ap-2085	78	19	)	)	PUNCT
ap-2085	78	20	,	,	PUNCT
ap-2085	78	21	and	and	CCONJ
ap-2085	78	22	shows	show	VERB
ap-2085	78	23	that	that	SCONJ
ap-2085	78	24	u1(π	u1(π	NOUN
ap-2085	78	25	)	)	PUNCT
ap-2085	78	26	and	and	CCONJ
ap-2085	78	27	u′2(π	u′2(π	NOUN
ap-2085	78	28	)	)	PUNCT
ap-2085	78	29	are	be	AUX
ap-2085	78	30	actually	actually	ADV
ap-2085	78	31	complex	complex	ADJ
ap-2085	78	32	conjugates	conjugate	NOUN
ap-2085	78	33	of	of	ADP
ap-2085	78	34	each	each	DET
ap-2085	78	35	other	other	ADJ
ap-2085	78	36	.	.	PUNCT
ap-2085	79	1	the	the	DET
ap-2085	79	2	proof	proof	NOUN
ap-2085	79	3	incidentally	incidentally	ADV
ap-2085	79	4	casts	cast	VERB
ap-2085	79	5	light	light	NOUN
ap-2085	79	6	on	on	ADP
ap-2085	79	7	certain	certain	ADJ
ap-2085	79	8	relations	relation	NOUN
ap-2085	79	9	that	that	PRON
ap-2085	79	10	hold	hold	VERB
ap-2085	79	11	for	for	ADP
ap-2085	79	12	real	real	ADJ
ap-2085	79	13	symmetric	symmetric	ADJ
ap-2085	79	14	potentials	potential	NOUN
ap-2085	79	15	,	,	PUNCT
ap-2085	79	16	such	such	ADJ
ap-2085	79	17	as	as	ADP
ap-2085	79	18	cos	cos	PROPN
ap-2085	79	19	(	(	PUNCT
ap-2085	79	20	2x	2x	NUM
ap-2085	79	21	)	)	PUNCT
ap-2085	79	22	.	.	PUNCT
ap-2085	80	1	references	reference	NOUN
ap-2085	80	2	[	[	X
ap-2085	80	3	1	1	NUM
ap-2085	80	4	]	]	PUNCT
ap-2085	80	5	c.	c.	PROPN
ap-2085	80	6	m.	m.	PROPN
ap-2085	80	7	bender	bender	PROPN
ap-2085	80	8	and	and	CCONJ
ap-2085	80	9	s.	s.	PROPN
ap-2085	80	10	boettcher	boettcher	PROPN
ap-2085	80	11	,	,	PUNCT
ap-2085	80	12	phys	phys	PROPN
ap-2085	80	13	.	.	PUNCT
ap-2085	81	1	rev	rev	PROPN
ap-2085	81	2	.	.	PROPN
ap-2085	81	3	lett	lett	PROPN
ap-2085	81	4	.	.	PROPN
ap-2085	81	5	80	80	NUM
ap-2085	81	6	,	,	PUNCT
ap-2085	81	7	5243	5243	NUM
ap-2085	81	8	(	(	PUNCT
ap-2085	81	9	1998	1998	NUM
ap-2085	81	10	)	)	PUNCT
ap-2085	81	11	.	.	PUNCT
ap-2085	82	1	doi	doi	NOUN
ap-2085	82	2	:	:	PUNCT
ap-2085	82	3	10.1103	10.1103	NUM
ap-2085	82	4	/	/	SYM
ap-2085	82	5	physrevlett.80.5243	physrevlett.80.5243	NOUN
ap-2085	83	1	[	[	X
ap-2085	83	2	2	2	NUM
ap-2085	83	3	]	]	PUNCT
ap-2085	83	4	c.	c.	PROPN
ap-2085	83	5	m.	m.	PROPN
ap-2085	83	6	bender	bender	PROPN
ap-2085	83	7	,	,	PUNCT
ap-2085	83	8	contemp	contemp	NOUN
ap-2085	83	9	.	.	PUNCT
ap-2085	84	1	phys	phy	NOUN
ap-2085	84	2	.	.	PUNCT
ap-2085	85	1	46	46	NUM
ap-2085	85	2	,	,	PUNCT
ap-2085	85	3	277	277	NUM
ap-2085	85	4	(	(	PUNCT
ap-2085	85	5	2005	2005	NUM
ap-2085	85	6	)	)	PUNCT
ap-2085	85	7	;	;	PUNCT
ap-2085	85	8	rep	rep	PROPN
ap-2085	85	9	.	.	PROPN
ap-2085	85	10	prog	prog	PROPN
ap-2085	85	11	.	.	PUNCT
ap-2085	86	1	phys	phy	NOUN
ap-2085	86	2	.	.	PUNCT
ap-2085	87	1	70	70	NUM
ap-2085	87	2	,	,	PUNCT
ap-2085	87	3	947	947	NUM
ap-2085	87	4	(	(	PUNCT
ap-2085	87	5	2007	2007	NUM
ap-2085	87	6	)	)	PUNCT
ap-2085	87	7	.	.	PUNCT
ap-2085	88	1	doi	doi	NOUN
ap-2085	88	2	:	:	PUNCT
ap-2085	89	1	10.1080/00107500072632	10.1080/00107500072632	NUM
ap-2085	89	2	[	[	X
ap-2085	89	3	3	3	NUM
ap-2085	89	4	]	]	PUNCT
ap-2085	89	5	a.	a.	NOUN
ap-2085	89	6	mostafazadeh	mostafazadeh	PROPN
ap-2085	89	7	,	,	PUNCT
ap-2085	89	8	int	int	PROPN
ap-2085	89	9	.	.	PUNCT
ap-2085	90	1	j.	j.	PROPN
ap-2085	90	2	geom	geom	PROPN
ap-2085	90	3	.	.	PUNCT
ap-2085	91	1	meth	meth	PROPN
ap-2085	91	2	.	.	PUNCT
ap-2085	92	1	mod	mod	PROPN
ap-2085	92	2	.	.	PUNCT
ap-2085	93	1	phys	phy	NOUN
ap-2085	93	2	.	.	PUNCT
ap-2085	94	1	7	7	NUM
ap-2085	94	2	,	,	PUNCT
ap-2085	94	3	1191	1191	NUM
ap-2085	94	4	(	(	PUNCT
ap-2085	94	5	2010	2010	NUM
ap-2085	94	6	)	)	PUNCT
ap-2085	94	7	.	.	PUNCT
ap-2085	95	1	doi	doi	NOUN
ap-2085	95	2	:	:	PUNCT
ap-2085	95	3	10.1142	10.1142	NUM
ap-2085	95	4	/	/	SYM
ap-2085	95	5	s0219887810004816	s0219887810004816	PROPN
ap-2085	96	1	[	[	X
ap-2085	96	2	4	4	NUM
ap-2085	96	3	]	]	X
ap-2085	96	4	c.	c.	PROPN
ap-2085	96	5	m.	m.	PROPN
ap-2085	96	6	bender	bender	PROPN
ap-2085	96	7	,	,	PUNCT
ap-2085	96	8	d.	d.	PROPN
ap-2085	96	9	c.	c.	PROPN
ap-2085	96	10	brody	brody	PROPN
ap-2085	96	11	and	and	CCONJ
ap-2085	96	12	h.	h.	PROPN
ap-2085	96	13	f.	f.	PROPN
ap-2085	96	14	jones	jones	PROPN
ap-2085	96	15	,	,	PUNCT
ap-2085	96	16	phys	phys	PROPN
ap-2085	96	17	.	.	PUNCT
ap-2085	97	1	rev	rev	PROPN
ap-2085	97	2	.	.	PROPN
ap-2085	97	3	lett	lett	PROPN
ap-2085	97	4	.	.	PROPN
ap-2085	97	5	89	89	NUM
ap-2085	97	6	,	,	PUNCT
ap-2085	97	7	270401	270401	NUM
ap-2085	97	8	(	(	PUNCT
ap-2085	97	9	2002	2002	NUM
ap-2085	97	10	)	)	PUNCT
ap-2085	97	11	doi	doi	NOUN
ap-2085	97	12	:	:	PUNCT
ap-2085	97	13	10.1103	10.1103	NUM
ap-2085	97	14	/	/	SYM
ap-2085	97	15	physrevlett.89.270401	physrevlett.89.270401	NOUN
ap-2085	97	16	;	;	PUNCT
ap-2085	97	17	92	92	NUM
ap-2085	97	18	,	,	PUNCT
ap-2085	97	19	119902(e	119902(e	NUM
ap-2085	97	20	)	)	PUNCT
ap-2085	97	21	(	(	PUNCT
ap-2085	97	22	2004	2004	NUM
ap-2085	97	23	)	)	PUNCT
ap-2085	97	24	.	.	PUNCT
ap-2085	98	1	doi	doi	NOUN
ap-2085	98	2	:	:	PUNCT
ap-2085	98	3	10.1103	10.1103	NUM
ap-2085	98	4	/	/	SYM
ap-2085	98	5	physrevlett.92.119902	physrevlett.92.119902	PROPN
ap-2085	99	1	[	[	X
ap-2085	99	2	5	5	NUM
ap-2085	99	3	]	]	PUNCT
ap-2085	99	4	c.	c.	PROPN
ap-2085	99	5	m.	m.	PROPN
ap-2085	99	6	bender	bender	PROPN
ap-2085	99	7	,	,	PUNCT
ap-2085	99	8	d.	d.	PROPN
ap-2085	99	9	c.	c.	PROPN
ap-2085	99	10	brody	brody	PROPN
ap-2085	99	11	and	and	CCONJ
ap-2085	99	12	h.	h.	PROPN
ap-2085	99	13	f.	f.	PROPN
ap-2085	99	14	jones	jones	PROPN
ap-2085	99	15	,	,	PUNCT
ap-2085	99	16	phys	phys	PROPN
ap-2085	99	17	.	.	PUNCT
ap-2085	99	18	rev	rev	PROPN
ap-2085	99	19	.	.	PUNCT
ap-2085	100	1	d	d	PROPN
ap-2085	100	2	70	70	NUM
ap-2085	100	3	,	,	PUNCT
ap-2085	100	4	025001	025001	NUM
ap-2085	100	5	(	(	PUNCT
ap-2085	100	6	2004	2004	NUM
ap-2085	100	7	)	)	PUNCT
ap-2085	100	8	doi	doi	NOUN
ap-2085	100	9	:	:	PUNCT
ap-2085	100	10	10.1103	10.1103	NUM
ap-2085	100	11	/	/	SYM
ap-2085	100	12	physrevd.70.025001	physrevd.70.025001	NOUN
ap-2085	100	13	;	;	PUNCT
ap-2085	100	14	71	71	NUM
ap-2085	100	15	,	,	PUNCT
ap-2085	100	16	049901(e	049901(e	PUNCT
ap-2085	100	17	)	)	PUNCT
ap-2085	100	18	(	(	PUNCT
ap-2085	100	19	2005	2005	NUM
ap-2085	100	20	)	)	PUNCT
ap-2085	100	21	.	.	PUNCT
ap-2085	101	1	doi	doi	NOUN
ap-2085	101	2	:	:	PUNCT
ap-2085	101	3	10.1103	10.1103	NUM
ap-2085	101	4	/	/	SYM
ap-2085	101	5	physrevd.71.049901	physrevd.71.049901	NOUN
ap-2085	102	1	[	[	X
ap-2085	102	2	6	6	NUM
ap-2085	102	3	]	]	PUNCT
ap-2085	102	4	a.	a.	NOUN
ap-2085	102	5	mostafazadeh	mostafazadeh	PROPN
ap-2085	102	6	,	,	PUNCT
ap-2085	102	7	j.	j.	PROPN
ap-2085	102	8	math	math	PROPN
ap-2085	102	9	.	.	PUNCT
ap-2085	103	1	phys	phy	NOUN
ap-2085	103	2	.	.	PUNCT
ap-2085	104	1	43	43	NUM
ap-2085	104	2	,	,	PUNCT
ap-2085	104	3	205	205	NUM
ap-2085	104	4	(	(	PUNCT
ap-2085	104	5	2002	2002	NUM
ap-2085	104	6	)	)	PUNCT
ap-2085	104	7	;	;	PUNCT
ap-2085	104	8	j.	j.	PROPN
ap-2085	104	9	phys	phys	PROPN
ap-2085	104	10	.	.	PUNCT
ap-2085	105	1	a	a	DET
ap-2085	105	2	36	36	NUM
ap-2085	105	3	,	,	PUNCT
ap-2085	105	4	7081	7081	NUM
ap-2085	105	5	(	(	PUNCT
ap-2085	105	6	2003	2003	NUM
ap-2085	105	7	)	)	PUNCT
ap-2085	105	8	.	.	PUNCT
ap-2085	106	1	[	[	X
ap-2085	106	2	7	7	X
ap-2085	106	3	]	]	X
ap-2085	106	4	c.	c.	PROPN
ap-2085	106	5	m.	m.	PROPN
ap-2085	106	6	bender	bender	PROPN
ap-2085	106	7	,	,	PUNCT
ap-2085	106	8	g.	g.	PROPN
ap-2085	106	9	v.	v.	PROPN
ap-2085	106	10	dunne	dunne	PROPN
ap-2085	106	11	,	,	PUNCT
ap-2085	106	12	p.	p.	PROPN
ap-2085	106	13	n.	n.	PROPN
ap-2085	106	14	meisinger	meisinger	NOUN
ap-2085	106	15	,	,	PUNCT
ap-2085	106	16	phys	phy	NOUN
ap-2085	106	17	.	.	PUNCT
ap-2085	107	1	lett	lett	PROPN
ap-2085	107	2	.	.	PUNCT
ap-2085	108	1	a	a	DET
ap-2085	108	2	252	252	NUM
ap-2085	108	3	,	,	PUNCT
ap-2085	108	4	272	272	NUM
ap-2085	108	5	(	(	PUNCT
ap-2085	108	6	1999	1999	NUM
ap-2085	108	7	)	)	PUNCT
ap-2085	108	8	.	.	PUNCT
ap-2085	109	1	[	[	X
ap-2085	109	2	8	8	X
ap-2085	109	3	]	]	X
ap-2085	109	4	h.	h.	PROPN
ap-2085	109	5	f.	f.	PROPN
ap-2085	109	6	jones	jones	PROPN
ap-2085	109	7	,	,	PUNCT
ap-2085	109	8	phys	phys	PROPN
ap-2085	109	9	.	.	PUNCT
ap-2085	110	1	lett	lett	PROPN
ap-2085	110	2	.	.	PUNCT
ap-2085	111	1	a	a	DET
ap-2085	111	2	262	262	NUM
ap-2085	111	3	,	,	PUNCT
ap-2085	111	4	242	242	NUM
ap-2085	111	5	(	(	PUNCT
ap-2085	111	6	1999	1999	NUM
ap-2085	111	7	)	)	PUNCT
ap-2085	111	8	.	.	PUNCT
ap-2085	112	1	[	[	X
ap-2085	112	2	9	9	NUM
ap-2085	112	3	]	]	PUNCT
ap-2085	112	4	r.	r.	PROPN
ap-2085	112	5	el	el	PROPN
ap-2085	112	6	-	-	PUNCT
ap-2085	112	7	ganainy	ganainy	PROPN
ap-2085	112	8	,	,	PUNCT
ap-2085	112	9	k.	k.	PROPN
ap-2085	112	10	g.	g.	PROPN
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ap-2085	112	12	,	,	PUNCT
ap-2085	112	13	d.	d.	PROPN
ap-2085	112	14	n.	n.	PROPN
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ap-2085	112	16	and	and	CCONJ
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ap-2085	112	18	h.	h.	PROPN
ap-2085	112	19	musslimani	musslimani	PROPN
ap-2085	112	20	,	,	PUNCT
ap-2085	112	21	optics	optic	NOUN
ap-2085	112	22	letters	letter	NOUN
ap-2085	112	23	32	32	NUM
ap-2085	112	24	,	,	PUNCT
ap-2085	112	25	2632	2632	NUM
ap-2085	112	26	(	(	PUNCT
ap-2085	112	27	2007	2007	NUM
ap-2085	112	28	)	)	PUNCT
ap-2085	112	29	.	.	PUNCT
ap-2085	113	1	[	[	X
ap-2085	113	2	10	10	NUM
ap-2085	113	3	]	]	PUNCT
ap-2085	113	4	z.	z.	PROPN
ap-2085	113	5	musslimani	musslimani	PROPN
ap-2085	113	6	,	,	PUNCT
ap-2085	113	7	k.	k.	PROPN
ap-2085	113	8	g.	g.	PROPN
ap-2085	113	9	makris	makris	PROPN
ap-2085	113	10	,	,	PUNCT
ap-2085	113	11	r.	r.	PROPN
ap-2085	113	12	el	el	PROPN
ap-2085	113	13	-	-	PUNCT
ap-2085	113	14	ganainy	ganainy	PROPN
ap-2085	113	15	and	and	CCONJ
ap-2085	113	16	d.	d.	PROPN
ap-2085	113	17	n.	n.	PROPN
ap-2085	113	18	christodoulides	christodoulides	PROPN
ap-2085	113	19	,	,	PUNCT
ap-2085	113	20	phys	phy	NOUN
ap-2085	113	21	.	.	PUNCT
ap-2085	114	1	rev	rev	PROPN
ap-2085	114	2	.	.	PROPN
ap-2085	114	3	lett	lett	PROPN
ap-2085	114	4	.	.	PROPN
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ap-2085	115	2	,	,	PUNCT
ap-2085	115	3	030402	030402	NUM
ap-2085	115	4	(	(	PUNCT
ap-2085	115	5	2008	2008	NUM
ap-2085	115	6	)	)	PUNCT
ap-2085	115	7	.	.	PUNCT
ap-2085	116	1	doi	doi	NOUN
ap-2085	116	2	:	:	PUNCT
ap-2085	116	3	10.1103	10.1103	NUM
ap-2085	116	4	/	/	SYM
ap-2085	116	5	physrevlett.100.030402	physrevlett.100.030402	NOUN
ap-2085	117	1	[	[	X
ap-2085	117	2	11	11	NUM
ap-2085	117	3	]	]	PUNCT
ap-2085	117	4	k.	k.	PROPN
ap-2085	117	5	makris	makris	PROPN
ap-2085	117	6	,	,	PUNCT
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