Exact dynamics and thermalization of an open bosonic quantum system in presence of a quantum phase transition induced by the environment

TL;DR

This paper derives an exact, non-Markovian description of a bosonic system coupled to an environment, revealing a quantum phase transition at a critical coupling that leads to dissipationless relaxation to a new ground state.

Contribution

It provides an exact solution for the out-of-equilibrium dynamics of a bosonic mode coupled to a bath, capturing quantum phase transitions without relying on master equations.

Findings

Identifies a quantum phase transition at a critical bath coupling strength.

Shows that dissipationless dynamics correspond to relaxation towards a new ground state.

Provides an exact Wigner function solution for the system.

Abstract

We derive the exact out-of-equilibrium Wigner function of a bosonic mode linearly coupled to a bosonic bath of arbitrary spectral density. Our solution does not rely on any master equation approach and it therefore also correctly describes a bosonic mode which is initially entangled with its environment. It has been recently suggested that non-Markovian quantum effects lead to dissi- pationless dynamics in the case of a strong coupling to a bath whose spectral density has a support bounded from below. We show in this work that such a system undergoes a quantum phase transi- tion at some critical bath coupling strength. The apparent dissipationless dynamics then correspond to the relaxation towards the new ground-state.