On dynamical system relating to quantum Markov chain associated with Ising model on cayley tree

Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)20-27
Number of pages8
JournalAustralian Journal of Basic and Applied Sciences
Volume5
Issue number3
Publication statusPublished - Mar 2011
Externally publishedYes

Keywords

  • Cayley tree
  • Ising model
  • Quantum Markov chain
  • Stability of the dynamical system

ASJC Scopus subject areas

  • General

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