On phase transitions in Quantum Markov Chains on Cayley tree

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

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Abstract

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.

Item Type:	Book Chapter
Additional Information:	5537/12133
Uncontrolled Keywords:	quantum Markov Chain; Cayley tree; phase transition
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	06 Jan 2012 16:24
Last Modified:	28 Dec 2012 14:52
URI:	http://irep.iium.edu.my/id/eprint/12133

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