On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree

Mukhamedov, Farrukh and Saburov, Mansoor (2011) On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree. Australian Journal of Basic and Applied Sciences, 5 (3). pp. 20-27. ISSN 1991-8178

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Abstract

In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a dynamical system it is proved existence of exactly three fixed points and absence of periodic points. Moreover, it is established finiteness and infiniteness of the trajectory of the system.

Item Type:	Article (Journal)
Additional Information:	5537/1610
Uncontrolled Keywords:	Cayley tree, quantum Markov chain, Ising model, stability of the dynamical system
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:	05 Sep 2011 15:11
Last Modified:	28 Dec 2012 14:31
URI:	http://irep.iium.edu.my/id/eprint/1610

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