On Construction of Quantum Markov Chains on Cayley trees

Algebra, Analysis and Quantum Probability

Accardi, Luigi^1 ; Mukhamedov, Farrukh^2 ; Souissi, Abdessatar^3

Centro Interdisciplinare Vito Volterra, II Università di Roma Tor Vergata, Via Columbia 2, Roma

00133, Italy^1

Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, Pahang, Kuantan

25200, Malaysia^2

Department of Mathematics, Marsa Preparatory Institute for Scientific and Technical Studies, Carthage University, Tunisia^3

关键词: Arbitrary order;    Cayley trees;    Competing interactions;    New constructions;    Quantum setting;    Transition problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012018/pdf
DOI  :  10.1088/1742-6596/697/1/012018

来源: IOP

【 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.