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

PDF (Quantum Markov Chains) - Published Version Restricted to Registered users only Download (320kB) | Request a copy

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

Actions (login required)

View Item