On Construction of Quantum Markov Chains on Cayley trees

Luigi Accardi, Farrukh Mukhamedov, Abdessatar Souissi

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number012018
JournalJournal of Physics: Conference Series
Volume697
Issue number1
DOIs
Publication statusPublished - Mar 24 2016
Externally publishedYes
EventInternational Conference on Algebra, Analysis and Quantum Probability - Tashkent, Uzbekistan
Duration: Sep 10 2015Sep 12 2015

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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