Clustering property for quantum Markov chains on the comb graph-Reference-Cited by-同舟云学术

Clustering property for quantum Markov chains on the comb graph

Published:2023 Issue:4 Volume:8 Page:7865-7880
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Souissi Abdessatar¹²,Soueidy El Gheteb³,Rhaima Mohamed⁴

Affiliation:

1. Department of Management Information Systems, College of Business Management, Qassim University, ArRass, Saudi Arabia

2. Preparatory Institute for Scientific and Technical Studies, University of Carthage, Av. of the Republic, Carthage 1054, Tunisia

3. Department of Mathematics and Informatics, Faculty of Sciences and Technologies, University of Nouakchott, Nouakchott, Mauritania

4. Department of Statistics and Operations Research, College of Sciences, King Saud University, P. O. Box, Riyadh 11451, Saudi Arabia

Abstract

<abstract><p>Quantum Markov chains (QMCs) on graphs and trees were investigated in connection with many important models arising from quantum statistical mechanics and quantum information. These quantum states generate many important properties such as quantum phase transition and clustering properties. In the present paper, we propose a construction of QMCs associated with an $ XX $-Ising model over the comb graph $ \mathbb N\rhd_0 \mathbb Z $. Mainly, we prove that the QMC associated with the disordered phase, enjoys a clustering property.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference47 articles.

1. L. Accardi, Noncommutative Markov chains, Proc. Int. Sch. Math. Phys., 1974,268–295.

2. L. Accardi, A. Frigerio, Markovian cocycles, Proc. R. Ir. Acad., 83 (1983), 251–263.

3. L. Accardi, F. Mukhamedov, A. Souissi, Construction of a new class of quantum Markov fields, Adv. Oper. Theory, 1 (2016), 206–218. https://doi.org/10.22034/aot.1610.1031

4. L. Accardi, F. Mukhamedov, M. Saburov, On quantum Markov chains on Cayley tree Ⅰ: niqueness of the associated chain with $XY$-model on the Cayley tree of order two, Inf. Dimens. Anal., 14 (2011), 443–463. https://doi.org/10.1142/S021902571100447X

5. L. Accardi, F. Mukhamedov, M. Saburov, On quantum Markov chains on Cayley tree Ⅱ: phase transitions for the associated chain with $XY$-model on the Cayley tree of order three, Ann. Henri Poincaré, 12 (2011), 1109–1144. https://doi.org/10.1007/s00023-011-0107-2

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