Gegenbauer-solvable quantum chain model

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F10%3A00350891" target="_blank" >RIV/61389005:_____/10:00350891 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Gegenbauer-solvable quantum chain model

Original language 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 liesin 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physical Review. A

ISSN

1050-2947

e-ISSN

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Volume of the periodical

82

Issue of the periodical within the volume

5

Country of publishing house

US - UNITED STATES

Number of pages

10

Pages from-to

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UT code for WoS article

000284257100001

EID of the result in the Scopus database

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