Recurrence of a class of quantum Markov chains on trees. (November 2022)

• Record Type: Journal Article
• Authors: Barhoumi, Abdessatar; Souissi, Abdessatar
• Is Part Of: Chaos, solitons and fractals. Volume 164(2022)
• Publication Date: 2022-11
• Subjects: Quantum Markov chains -- Cayley trees -- Recurrence -- Phase transition; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112644
• Languages: English
• ISSNs: 0960-0779

Abstract

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.