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 |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2008
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| 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 |
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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. en 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.
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| 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. |
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AT anevab tridiagonalsymmetriesofmodelsofnonequilibriumphysics |
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2025-12-07T17:35:29Z |
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2025-12-07T17:35:29Z |
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1850871832007147520 |