On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2011
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| Online Access: | http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf |
| _version_ | 1848776680091418624 |
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| author | Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Accardi, Luigi |
| building | IIUM Repository |
| collection | Online Access |
| description | In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions
of QMC associated with such a model, this means the QMC does not depend on the
boundary conditions. |
| first_indexed | 2025-11-14T14:33:56Z |
| format | Article |
| id | iium-6519 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:33:56Z |
| publishDate | 2011 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-65192014-06-16T04:21:16Z http://irep.iium.edu.my/6519/ On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions of QMC associated with such a model, this means the QMC does not depend on the boundary conditions. World Scientific Publishing 2011-09 Article PeerReviewed application/pdf en http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 14 (3). pp. 443-463. ISSN 0219-0257 http://www.worldscinet.com/idaqp/14/preserved-docs/1403/S021902571100447X.pdf 10.1142/S021902571100447X |
| spellingShingle | QA Mathematics Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title | On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title_full | On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title_fullStr | On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title_full_unstemmed | On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title_short | On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two |
| title_sort | on quantum markov chains on cayley tree i: uniqueness of the associated chain with xy-model on the cayley tree of order two |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf |