Non-Markovian Equilibration Controlled by Symmetry Breaking

TL;DR

This paper investigates how symmetry breaking influences non-Markovian dynamics in quantum systems, revealing that breaking symmetries causes the loss of non-Markovian features within a finite time, with scaling behaviors depending on the type of symmetry broken.

Contribution

It provides a numerical and theoretical analysis of the finite-time effects of symmetry breaking on non-Markovian dynamics and proposes a universal scaling law for the characteristic time t_{g}.

Findings

Symmetry breaking causes non-Markovian features to disappear after a finite time t_{g}.

The scaling of t_{g} with symmetry breaking strength varies with the type of symmetry.

The spectrum of the total Hamiltonian explains the differences in scaling behaviors.

Abstract

We study the effects of symmetry breaking on non-Markovian dynamics in various system-bath arrangements. It is shown that by breaking certain symmetries features signaling non-Markovian time evolution disappear within a finite time t_{g}. We demonstrate numerically that the scaling of t_{g} with the symmetry breaking strength is different for various types of symmetry. We provide a mathematical explanation for these differences related to the spectrum of the total system-bath Hamiltonian and provide arguments that the scaling properties of t_{g} should be universal.