Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

Farrukh Mukhamedov; Soueidy El Gheteb

doi:10.1142/S123016121750010X

Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

Farrukh Mukhamedov, Soueidy El Gheteb

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

Original language	English
Article number	1750010
Journal	Open Systems and Information Dynamics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1142/S123016121750010X
Publication status	Published - Jun 1 2017

Keywords

Cayley tree
Quantum Markov chain
XY-Ising model
uniqueness

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics

Access to Document

10.1142/S123016121750010X

Cite this

@article{ed26bb5629054e689a7e4f26b143afaa,

title = "Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two",

abstract = "In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.",

keywords = "Cayley tree, Quantum Markov chain, XY-Ising model, uniqueness",

author = "Farrukh Mukhamedov and {El Gheteb}, Soueidy",

note = "Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

year = "2017",

month = jun,

day = "1",

doi = "10.1142/S123016121750010X",

language = "English",

volume = "24",

journal = "Open Systems and Information Dynamics",

issn = "1230-1612",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}

TY - JOUR

T1 - Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

AU - Mukhamedov, Farrukh

AU - El Gheteb, Soueidy

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

AB - In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

KW - Cayley tree

KW - Quantum Markov chain

KW - XY-Ising model

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85021779694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021779694&partnerID=8YFLogxK

U2 - 10.1142/S123016121750010X

DO - 10.1142/S123016121750010X

M3 - Article

AN - SCOPUS:85021779694

SN - 1230-1612

VL - 24

JO - Open Systems and Information Dynamics

JF - Open Systems and Information Dynamics

IS - 2

M1 - 1750010

ER -

Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this