On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree

Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree. Annales Henri Poincare, 12 (6). pp. 1109-1144. ISSN 1424-0637

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Abstract

In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K_{x,y}}.

Item Type:	Article (Journal)
Additional Information:	5537/1817
Uncontrolled Keywords:	Physics, Mathematical and Computational Physics, Dynamical Systems and Ergodic Theory, Quantum Physics, Mathematical Methods in Physics, Relativity and Cosmology Elementary Particles and Quantum Field Theory
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:	07 Sep 2011 10:28
Last Modified:	11 Jun 2014 11:29
URI:	http://irep.iium.edu.my/id/eprint/1817

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