On Construction of Quantum Markov Chains on Cayley trees

被引：3

作者：

Accardi, Luigi ^{[1
]}

Mukhamedov, Farrukh ^{[2
]}

Souissi, Abdessatar ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Ctr Interdisciplinare Vito Volterra 2, Via Columbia 2, I-00133 Rome, Italy

[2] Int Islamic Univ Malaysia, Fac Sci, Dept Computat & Theoret Sci, Kuantan 25200, Pahang, Malaysia

[3] Carthage Univ, Marsa Preparatory Inst Sci & Tech Studies, Dept Math, Tunis, Tunisia

来源：

ALGEBRA, ANALYSIS AND QUANTUM PROBABILITY | 2016年 / 697卷

关键词：

BINARY INTERACTIONS; COMPETING TERNARY; GIBBS MEASURES; RANDOM-FIELDS; ISING-MODEL; STATES; PHASE;

D O I：

10.1088/1742-6596/697/1/012018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting.

引用

页数：9

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