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On construction of quantum Markov chains on Cayley trees

Accardi, Luigi and Mukhamedov, Farrukh and Souissi, Abdessatar (2016) On construction of quantum Markov chains on Cayley trees. In: International Conference Algebra, Analysis and Quantum Probability, 10-12 Sep 2015, Tashkent, Uzbekistan.

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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

Item Type: Conference or Workshop Item (Invited Papers)
Additional Information: 5537/50161
Uncontrolled Keywords: Markov chain, Cayley tree
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 15 Apr 2016 08:47
Last Modified: 11 May 2017 09:38
URI: http://irep.iium.edu.my/id/eprint/50161

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