On phase transitions in Quantum Markov Chains on Cayley tree
In the present paper we continue our investigations started in [Accardi L. , Ohno, H. , Mukhamedov, F. , Quantum Markov fields on graphs, Inf. Dim. Analysis, Quantum Probab. Related Topics (accepted) arxi v: 0911 . 1667]. In [Accardi L., Mukhamedov, F., Saburov M. On Quantum Markov chains on Cayley...
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| Format: | Book Chapter |
| Language: | English |
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World Scientific
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/12133/ http://irep.iium.edu.my/12133/1/acmfms-quantumBio-Info-IV_2.pdf |
| _version_ | 1848777405139779584 |
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| author | Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author2 | Accardi, Luigi |
| author_facet | Accardi, Luigi Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Accardi, Luigi |
| building | IIUM Repository |
| collection | Online Access |
| description | In the present paper we continue our investigations started in [Accardi L. , Ohno, H. , Mukhamedov, F. , Quantum Markov fields on graphs, Inf. Dim. Analysis, Quantum Probab. Related Topics (accepted) arxi v: 0911 . 1667]. In [Accardi L., Mukhamedov, F., Saburov M. On Quantum Markov chains on Cayley tree and associated chains with XY-model arxiv: 1004.3623] we provided a construction of forward and backward Quantum Markov Chains (QMC) defined on the Cayley
tree, and established uniqueness of QMC associated with XY-model on a Cayley tree order 2. In the present paper we study the same model on a Cayley tree order 3. Surprisingly in this case, we establish a phase transition (i.e. existence of two distinct quantum Markov chains) for the considered model on the Cayley tree order 3. |
| first_indexed | 2025-11-14T14:45:27Z |
| format | Book Chapter |
| id | iium-12133 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:45:27Z |
| publishDate | 2011 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-121332012-12-28T06:52:41Z http://irep.iium.edu.my/12133/ On phase transitions in Quantum Markov Chains on Cayley tree Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper we continue our investigations started in [Accardi L. , Ohno, H. , Mukhamedov, F. , Quantum Markov fields on graphs, Inf. Dim. Analysis, Quantum Probab. Related Topics (accepted) arxi v: 0911 . 1667]. In [Accardi L., Mukhamedov, F., Saburov M. On Quantum Markov chains on Cayley tree and associated chains with XY-model arxiv: 1004.3623] we provided a construction of forward and backward Quantum Markov Chains (QMC) defined on the Cayley tree, and established uniqueness of QMC associated with XY-model on a Cayley tree order 2. In the present paper we study the same model on a Cayley tree order 3. Surprisingly in this case, we establish a phase transition (i.e. existence of two distinct quantum Markov chains) for the considered model on the Cayley tree order 3. World Scientific Accardi, Luigi Freudenberg, Wolfgang Ohya, Masanori 2011 Book Chapter PeerReviewed application/pdf en http://irep.iium.edu.my/12133/1/acmfms-quantumBio-Info-IV_2.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) On phase transitions in Quantum Markov Chains on Cayley tree. In: Quantum Bio-Informatics IV. QP-PQ: Quantum Probability and White Noise Analysis, 28 . World Scientific, Singapore, pp. 267-278. ISBN 13 978-981-4343-75-6 |
| spellingShingle | QA Mathematics Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor On phase transitions in Quantum Markov Chains on Cayley tree |
| title | On phase transitions in Quantum Markov Chains on Cayley tree |
| title_full | On phase transitions in Quantum Markov Chains on Cayley tree |
| title_fullStr | On phase transitions in Quantum Markov Chains on Cayley tree |
| title_full_unstemmed | On phase transitions in Quantum Markov Chains on Cayley tree |
| title_short | On phase transitions in Quantum Markov Chains on Cayley tree |
| title_sort | on phase transitions in quantum markov chains on cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/12133/ http://irep.iium.edu.my/12133/1/acmfms-quantumBio-Info-IV_2.pdf |