Spontaneous symmetry breaking in thermalization and anti-thermalization

TL;DR

This paper explores how spontaneous symmetry breaking influences the thermalization process in a degenerate quantum system, revealing conditions under which the system's steady state depends on initial states or becomes independent, especially near zero temperature.

Contribution

It demonstrates the role of symmetry breaking in quantum thermalization and shows how initial state dependence can persist or vanish depending on system-bath interactions.

Findings

Steady state can be independent of initial conditions due to symmetry breaking.

Initial state dependence persists when degeneracy is not fully lifted.

Behavior varies with the manner of approaching zero temperature and degeneracy lifting.

Abstract

The phenomenon of spontaneous symmetry breaking is investigated in the dynamic thermalization of a degenerate quantum system. A three-level system interacting with a heat bath is carefully studied to this end. It is shown that the three-level system with degenerate ground states might have different behaviors depending on the details of the interaction with the heat bath when the temperature approaches zero. If we introduce an external field to break the degeneracy of the ground states and let it approach zero after letting the temperature approach zero, then two possibilities will arise: the steady state is a definite one of the degenerate states independent of the initial state, or the steady state is dependent on the initial state in a complicated way. The first possibility corresponds to a spontaneous symmetry breaking of the system and the second one implies that the heat bath could not totally erase the initial information in certain cases.