On quantum markov chains on cayley tree i: Uniqueness of the associated chain with xy-model on the cayley tree of order two

Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)443-463
Number of pages21
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume14
Issue number3
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

  • Cayley tree
  • Quantum Markov chain
  • XY-model
  • uniqueness

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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