Prethermal memory loss as a dynamical phase transition in dissipative quantum chains

We study the relaxation dynamics of tilted (Wannier-Stark-type) quantum
chains coupled to thermal environments. We find that for a large set of
pure initial states, the entropy evolves in a non-monotonous fashion.
Starting from zero, it first approaches its maximal possible value, before
decreasing to its equilibrium value defined by the bath temperature. Since
the maximum entropy state is unique, reaching the peak implies that the
system has lost memory of its precise initial state, long before reaching
thermal equilibrium. This behaviour is confirmed by the observation that
expectation values computed for different initial conditions converge at
the peak time to subsequently follow the same dynamics. Moreover, by
applying finite-size scaling, we argue that this prethermal memory loss
corresponds to a phase transition with respect to time. The effect is
confirmed experimentally in Artur Widera’s group in Kaiserslautern for a
large spin in contact with a bath given by a Bose condensate.

References:
[1] Prethermal memory loss and universal non-equilibrium dynamics in
interacting quantum systems coupled to thermal baths,
Ling-Na Wu and André Eckardt, Phys. Rev. B, 101, 220302(R) (2020)
[2] Dynamical phase transition in an open quantum system, in preparation,
Ling-Na Wu, Alexander Schnell and André Eckardt in collaboration with
Artur Widera's group.