  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.

Quantum Physics