Accuracy of time-dependent GGE under weak dissipation

TL;DR

This paper demonstrates that the time-dependent GGE accurately describes the open dynamics of a bosonic gas with weak dissipation, validated through tensor network simulations and correlation measurements, and effectively captures transport phenomena.

Contribution

It introduces and validates the use of the t-GGE approach for weakly dissipative integrable systems, extending its applicability to open quantum dynamics.

Findings

t-GGE accurately describes weakly dissipative bosonic gases

Tensor network methods confirm the exactness of t-GGE in adiabatic limit

t-GGE captures transport at the Euler scale in inhomogeneous settings

Abstract

Unitary integrable models typically relax to a stationary Generalized Gibbs Ensemble (GGE), but in experimental realizations dissipation often breaks integrability. In this work, we use the recently introduced time-dependent GGE (t-GGE) approach to describe the open dynamics of a gas of bosons subject to atom losses and gains. We employ tensor network methods to provide numerical evidence of the exactness of the t-GGE in the limit of adiabatic dissipation, and of its accuracy in the regime of weak but finite dissipation. That accuracy is tested for two-point functions via the rapidity distribution, and for more complicated correlations through a non-Gaussianity measure. We combine this description with Generalized Hydrodynamics and we show that it correctly captures transport at the Euler scale. Our results demonstrate that the t-GGE approach is robust in both homogeneous and inhomogeneous settings.