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

Farrukh Mukhamedov; Mansoor Saburov

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

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	20-27
Number of pages	8
Journal	Australian Journal of Basic and Applied Sciences
Volume	5
Issue number	3
Publication status	Published - Mar 2011
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General

Cite this

@article{57c30c2323aa45b89f516fb43d3b731f,

title = "On dynamical system relating to quantum Markov chain associated with Ising model on cayley tree",

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.",

keywords = "Cayley tree, Ising model, Quantum Markov chain, Stability of the dynamical system",

author = "Farrukh Mukhamedov and Mansoor Saburov",

year = "2011",

month = mar,

language = "English",

volume = "5",

pages = "20--27",

journal = "Australian Journal of Basic and Applied Sciences",

issn = "1991-8178",

publisher = "INSInet Publications",

number = "3",

}

TY - JOUR

T1 - On dynamical system relating to quantum Markov chain associated with Ising model on cayley tree

AU - Mukhamedov, Farrukh

AU - Saburov, Mansoor

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - Cayley tree

KW - Ising model

KW - Quantum Markov chain

KW - Stability of the dynamical system

UR - http://www.scopus.com/inward/record.url?scp=79955090093&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955090093&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79955090093

SN - 1991-8178

VL - 5

SP - 20

EP - 27

JO - Australian Journal of Basic and Applied Sciences

JF - Australian Journal of Basic and Applied Sciences

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this