On construction of quantum Markov chains on Cayley trees
The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this constr...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English English |
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Institute of Physics Publishing
2016
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/50161/ http://irep.iium.edu.my/50161/3/50161.pdf http://irep.iium.edu.my/50161/6/50161_on%20construction%20of%20quantum%20Markov%20chains_scopus.pdf |
| _version_ | 1848783587299557376 |
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| author | Accardi, Luigi Mukhamedov, Farrukh Souissi, Abdessatar |
| author_facet | Accardi, Luigi Mukhamedov, Farrukh Souissi, Abdessatar |
| author_sort | Accardi, Luigi |
| building | IIUM Repository |
| collection | Online Access |
| description | The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting |
| first_indexed | 2025-11-14T16:23:43Z |
| format | Proceeding Paper |
| id | iium-50161 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:23:43Z |
| publishDate | 2016 |
| publisher | Institute of Physics Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-501612017-05-11T01:38:10Z http://irep.iium.edu.my/50161/ On construction of quantum Markov chains on Cayley trees Accardi, Luigi Mukhamedov, Farrukh Souissi, Abdessatar QA Mathematics The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting Institute of Physics Publishing 2016-03 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/50161/3/50161.pdf application/pdf en http://irep.iium.edu.my/50161/6/50161_on%20construction%20of%20quantum%20Markov%20chains_scopus.pdf Accardi, Luigi and Mukhamedov, Farrukh and Souissi, Abdessatar (2016) On construction of quantum Markov chains on Cayley trees. In: International Conference Algebra, Analysis and Quantum Probability, 10-12 Sep 2015, Tashkent, Uzbekistan. http://iopscience.iop.org/article/10.1088/1742-6596/697/1/012018 10.1088/1742-6596/697/1/012018 |
| spellingShingle | QA Mathematics Accardi, Luigi Mukhamedov, Farrukh Souissi, Abdessatar On construction of quantum Markov chains on Cayley trees |
| title | On construction of quantum Markov chains on
Cayley trees |
| title_full | On construction of quantum Markov chains on
Cayley trees |
| title_fullStr | On construction of quantum Markov chains on
Cayley trees |
| title_full_unstemmed | On construction of quantum Markov chains on
Cayley trees |
| title_short | On construction of quantum Markov chains on
Cayley trees |
| title_sort | on construction of quantum markov chains on
cayley trees |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/50161/ http://irep.iium.edu.my/50161/ http://irep.iium.edu.my/50161/ http://irep.iium.edu.my/50161/3/50161.pdf http://irep.iium.edu.my/50161/6/50161_on%20construction%20of%20quantum%20Markov%20chains_scopus.pdf |