Symmetry operations and Critical Behaviour in Classical to Quantum Stochastic Processes

TL;DR

This paper explores how symmetry operations influence the critical behavior and relaxation dynamics of quantum extensions of classical stochastic processes, revealing diverse relaxation patterns and scaling properties.

Contribution

It introduces a method to generate quantum analogs of classical Markov chains using symmetry operations and analyzes their relaxation and critical behavior.

Findings

Different quantum extensions exhibit varied relaxation dynamics.

Coherence measures show ambiguous relation to relaxation speed.

Finite size scaling of coherence reveals different critical exponents for short and long times.

Abstract

Recently, a novel construction scheme for generating quantum analogs of classical stochastic processes has been introduced. Here, we use this scheme in order to generate a large class of self-contained quantum extensions of a classical Markov chain process using symmetry operations. We show that the relaxation processes unfold very differently for the different quantum extensions. This is supported by monitoring the coherence, the probability of reaching the equilibrium, the decay of the number of domain walls and the purity. Unexpectedly, we find a rather ambiguous relation between the coherence measure based on the L1-norm and the speed of the relaxation process. Finally we find that the finite size scaling of the coherence measure exists for both short and long times and the value of the critical exponent is different for the short and long time.