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

¹ James Franck Institute and Department of Physics, University of Chicago - Chicago, IL 60637, USA
² Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie - Paris VI 4 Place Jussieu, 75252 Paris Cedex 05, France

Received: 26 August 2013
Accepted: 4 December 2013

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 dissipationless 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 transition at some critical bath coupling strength. The apparent dissipationless dynamics then correspond to the relaxation towards the new ground state.