Recurrence of a class of quantum Markov chains on trees

Abdessatar Barhoumi and Abdessatar Souissi

Chaos, Solitons & Fractals, 2022, vol. 164, issue C

Abstract: The problem of recurrence for quantum Markov chains on trees (QMCT), is more subtle than for 1D quantum Markov chains (QMC); it involves infinitely many rays due to the exponential growth of ramifications on the Cayley trees and their relevant constraints. We study criteria for recurrence of QMCT based on the correlations functions and boundary conditions. These represent a bridge between recurrence and phase transitions. Furthermore, we illustrate our results through an Ising model with competing interactions.

Keywords: Quantum Markov chains; Cayley trees; Recurrence; Phase transition (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008232

DOI: 10.1016/j.chaos.2022.112644

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