Recurrence of a class of quantum Markov chains on trees

被引：8

作者：

Barhoumi, Abdessatar ^{[1
,3
]}

Souissi, Abdessatar ^{[2
,3
,4
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, POB 400, Al Hasa 31982, Saudi Arabia

[2] Qassim Univ, Coll Business Management, Dept Accounting, Arrass, Saudi Arabia

[3] Univ Carthage, Math Phys Quantum Modeling & Mech Design, LR18ES45,Av Republ, Carthage 1054, Tunisia

[4] Univ Carthage, Preparatory Inst Sci & Tech Studies, Dept Math, Av Republ, Carthage 1054, Tunisia

来源：

CHAOS SOLITONS & FRACTALS | 2022年 / 164卷

关键词：

Quantum Markov chains; Cayley trees; Recurrence; Phase transition; RANDOM-WALKS; BINARY INTERACTIONS; COMPETING TERNARY; GIBBS MEASURES; MODELS; STATES;

D O I：

10.1016/j.chaos.2022.112644

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of recurrence for quantum Markov chains on trees (QMCT), is more subtle than for 1D quantum Markov chains (QMC); it involves infinitely many rays due to the exponential growth of ramifications on the Cayley trees and their relevant constraints. We study criteria for recurrence of QMCT based on the correlations functions and boundary conditions. These represent a bridge between recurrence and phase transitions. Furthermore, we illustrate our results through an Ising model with competing interactions.

引用

页数：6

共 39 条

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[2]

Accardi L., 1974, PROC INT SCH MATH PH, P268

[3]

Accardi L., 1991, Quantum Markov Chains: The recurrence problem, QP III, P63

[4] A Markov-Dobrushin Inequality for Quantum Channels [J].