Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2

Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2. Mathematical Notes, 90 (2). pp. 8-20. ISSN 0001-4346

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Abstract

We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain i.e., we show that the state is independent of the boundary conditions.

Item Type:	Article (Journal)
Additional Information:	5537/1614
Uncontrolled Keywords:	quantum Markov chain, Cayley tree, XY -model, Gibbs state, phase transition, quasiconditional expectation, graph, dynamical system, quasilocal algebra
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	06 Sep 2011 15:21
Last Modified:	28 Jun 2013 09:24
URI:	http://irep.iium.edu.my/id/eprint/1614

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