Undephasing the generalized Gibbs ensemble

Tim Langen

Ph. Chomaz, Francesca Gulminelli, Olivier Juillet

Herbert Spohn

Takaaki Monnai

Integrable quantum many-body systems are considered to equilibrate to generalized Gibbs ensembles (GGEs). A general mechanism of such relaxation to GGE has been shown for unitary evolutions of exactly solvable quadratic bosonic systems in the thermodynamic limit. Here, we explore the role of locality and interaction with surroundings in the relaxation by considering the reduced dynamics of a class of open systems weakly interacting with a reservoir, which is initially prepared in a locally perturbed GGE. The standard derivation of a quantum master equation fails to describe relaxation to GGE in the long-time limit in the presence of the initial perturbation. We investigate a proper quantum master equation that guarantees the relaxation to GGE to avoid this counterintuitive issue and describes the relaxation to the reduced state corresponding to GGE in the thermodynamic limit. In particular, we show that the stationary state of the open system is fully characterized by GGE of the reservoir, which is independent of the initial local perturbation.

J. D. van der Waals

Dries Sels, Michiel Wouters

In this work we investigate the nonequilibrium dynamics of closed quantum systems. In particular we focus on the stationary properties of integrable systems. Here we show how a generalized Gibbs ensemble (GGE) can be constructed as the best approximation to the time-dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core Bose gas. Whereas a correlated GGE properly describes all stationary nonlocal correlations, a simple harmonic GGE is sufficient to completely describe reduced local states.