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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 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

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Abstract

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.

Item Type: Article (Journal)
Additional Information: 5537/6519
Uncontrolled Keywords: Quantum Markov chain; Cayley tree; XY -model; uniqueness.
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: 18 Nov 2011 11:03
Last Modified: 16 Jun 2014 12:21
URI: http://irep.iium.edu.my/id/eprint/6519

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