ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO-Reference-Cited by-同舟云学术

ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO

Published:2011-09 Issue:03 Volume:14 Page:443-463
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

ACCARDI LUIGI¹,MUKHAMEDOV FARRUKH²,SABUROV MANSOOR²

Affiliation:

1. Centro Interdisciplinare Vito Volterra, II Università di Roma "Tor Vergata", Via Columbia 2, 00133 Roma, Italy

2. Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box 141, 25710, Kuantan, Pahang, Malaysia

Abstract

In this paper we study forward quantum Markov chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction, we investigate QMC associated with XY-model on a Cayley tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021902571100447X

Reference36 articles.

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4. QUANTUM MARKOV FIELDS

5. Non-homogeneous quantum Markov states and quantum Markov fields

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