About: Gegenbauer-solvable quantum chain model

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n, a, x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H not equal H-dagger. We managed to (i) start from elementary secular equation G(N, a, E-n) = 0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Theta not equal I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice. An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n, a, x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H not equal H-dagger. We managed to (i) start from elementary secular equation G(N, a, E-n) = 0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Theta not equal I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice. (en)
Title	Gegenbauer-solvable quantum chain model Gegenbauer-solvable quantum chain model (en)
skos:prefLabel	Gegenbauer-solvable quantum chain model Gegenbauer-solvable quantum chain model (en)
skos:notation	RIV/61389005:_____/10:00350891!RIV11-MSM-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Znojil, Miloslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	260268
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/10:00350891
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	NON-HERMITIAN HAMILTONIANS; PSEUDO-HERMITICITY; FIELD-THEORY (en)
http://linked.open.../riv/klicoveSlovo	PSEUDO-HERMITICITY FIELD-THEORY NON-HERMITIAN HAMILTONIANS
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[95A5B3B94F81]
http://linked.open...i/riv/nazevZdroje	Physical Review. A
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	82
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav
http://linked.open...ain/vavai/riv/wos	000284257100001
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	1050-2947
number of pages	10 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Gegenbauer-solvable quantum chain model Gegenbauer-solvable quantum chain model Gegenbauer-solvable quantum chain model

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