Tridiagonal Symmetries of Models of Nonequilibrium Physics

We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices defining a noncommutative space with a quantum gro...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2008
1. Verfasser: Aneva, B.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2008
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/149025
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Tridiagonal Symmetries of Models of Nonequilibrium Physics / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 36 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149025
record_format dspace
spelling Aneva, B.
2019-02-19T13:08:09Z
2019-02-19T13:08:09Z
2008
Tridiagonal Symmetries of Models of Nonequilibrium Physics / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 36 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 82C10; 60J60; 17B80
https://nasplib.isofts.kiev.ua/handle/123456789/149025
We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices defining a noncommutative space with a quantum group symmetry. Boundary processes lead to a reduction of the bulk symmetry. We argue that the boundary operators of an interacting system with simple exclusion generate a tridiagonal algebra whose irreducible representations are expressed in terms of the Askey-Wilson polynomials. We show that the boundary algebras of the symmetric and the totally asymmetric processes are the proper limits of the partially asymmetric ones. In all three type of processes the tridiagonal algebra arises as a symmetry of the boundary problem and allows for the exact solvability of the model.
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). A CEI grant for participation in the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” is gratefully acknowledged. The author would like to thank the organizers for the invitation to participate the conference Symmetry-2007 and for the warm atmosphere during the stay in Kyiv.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Tridiagonal Symmetries of Models of Nonequilibrium Physics
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Tridiagonal Symmetries of Models of Nonequilibrium Physics
spellingShingle Tridiagonal Symmetries of Models of Nonequilibrium Physics
Aneva, B.
title_short Tridiagonal Symmetries of Models of Nonequilibrium Physics
title_full Tridiagonal Symmetries of Models of Nonequilibrium Physics
title_fullStr Tridiagonal Symmetries of Models of Nonequilibrium Physics
title_full_unstemmed Tridiagonal Symmetries of Models of Nonequilibrium Physics
title_sort tridiagonal symmetries of models of nonequilibrium physics
author Aneva, B.
author_facet Aneva, B.
publishDate 2008
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices defining a noncommutative space with a quantum group symmetry. Boundary processes lead to a reduction of the bulk symmetry. We argue that the boundary operators of an interacting system with simple exclusion generate a tridiagonal algebra whose irreducible representations are expressed in terms of the Askey-Wilson polynomials. We show that the boundary algebras of the symmetric and the totally asymmetric processes are the proper limits of the partially asymmetric ones. In all three type of processes the tridiagonal algebra arises as a symmetry of the boundary problem and allows for the exact solvability of the model.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149025
citation_txt Tridiagonal Symmetries of Models of Nonequilibrium Physics / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 36 назв. — англ.
work_keys_str_mv AT anevab tridiagonalsymmetriesofmodelsofnonequilibriumphysics
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last_indexed 2025-12-07T17:35:29Z
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