On phase transitions in Quantum Markov Chains on Cayley tree

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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Main Authors: Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Book Chapter
Language:English
Published: World Scientific 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/12133/
http://irep.iium.edu.my/12133/1/acmfms-quantumBio-Info-IV_2.pdf
id iium-12133
recordtype eprints
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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
On phase transitions in Quantum Markov Chains on Cayley tree
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.
author2 Accardi, Luigi
author_facet Accardi, Luigi
Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
format Book Chapter
author Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Accardi, Luigi
title On phase transitions in Quantum Markov Chains on Cayley tree
title_short 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_sort on phase transitions in quantum markov chains on cayley tree
publisher World Scientific
publishDate 2011
url http://irep.iium.edu.my/12133/
http://irep.iium.edu.my/12133/1/acmfms-quantumBio-Info-IV_2.pdf
first_indexed 2023-09-18T20:21:22Z
last_indexed 2023-09-18T20:21:22Z
_version_ 1777408129329266688

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