Gaussian ensemble for quantum integrable dynamics

TL;DR

This paper introduces a Gaussian ensemble to describe long-time dynamics in quantum integrable systems, extending the GGE by including fluctuations and capturing quantum and finite-size corrections.

Contribution

It develops a Gaussian ensemble framework that generalizes the GGE, applicable across classical and quantum regimes, and valid for systems with non-local interactions.

Findings

Asymptotically exact in the classical limit

Captures quantum corrections near the classical limit

Valid for finite size and non-local interactions

Abstract

We propose a Gaussian ensemble as a description of the long-time dynamics of isolated quantum integrable systems. Our approach extends the Generalized Gibbs Ensemble (GGE) by incorporating fluctuations of integrals of motion. It is asymptotically exact in the classical limit irrespective of the system size and, under appropriate conditions, in the thermodynamic limit irrespective of the value of Planck's constant. Moreover, it captures quantum corrections near the classical limit, finite size corrections near the thermodynamic limit, and is valid in the presence of non-local interactions. The Gaussian ensemble bridges the gap between classical integrable systems, where a generalized microcanonical ensemble is exact even for few degrees of freedom and GGE, which requires thermodynamic limit. We illustrate our results with examples of increasing complexity.