arXiv:1004.3623 · Infinite Dimensional Analysis Quantum Probability and Related Topics

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 Maksutovich Mukhamedov, Mansoor Khajibaevich Saburov

Published Sep 1, 2011• 33 citations

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.

DOI: 10.1142/s021902571100447x

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