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

被引：24

作者：

Accardi, Luigi ^{[1
]}

Mukhamedov, Farrukh ^{[2
]}

Saburov, Mansoor ^{[2
]}

机构：

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

[2] Int Islamic Univ Malaysia, Fac Sci, Dept Computat & Theoret Sci, Kuantan 25710, Pahang, Malaysia

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2011年 / 14卷 / 03期

关键词：

Quantum Markov chain; Cayley tree; XY-model; uniqueness; GROUND-STATES; RANDOM-FIELDS;

D O I：

10.1142/S021902571100447X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：443 / 463

页数：21

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