Out-of-equilibrium Eigenstate Thermalization Hypothesis

TL;DR

This paper introduces a new statistical ansatz inspired by ETH to describe the thermalization process of out-of-equilibrium quantum states, highlighting the role of cross-correlations and universality in relaxation dynamics.

Contribution

It proposes a novel ansatz for non-equilibrium initial states in the energy basis, extending ETH concepts to out-of-equilibrium quantum thermalization.

Findings

Verified the scaling behavior numerically.

Identified exponentially small cross-correlations.

Discovered emergent universality in high-frequency behavior.

Abstract

Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. In this work, we propose a statistical ansatz for the matrix elements of non-equilibrium initial states in the energy eigenbasis, in order to describe such evolution. The approach is inspired by the Eigenstate Thermalisation Hypothesis (ETH) but the proposed ansatz exhibits different scaling. Importantly, we point out the exponentially small cross-correlations between the observable and the initial state matrix elements that determine relaxation dynamics toward equilibrium. We numerically verify scaling and cross-correlation, point out the emergent universality of the high-frequency behavior, and outline possible generalizations.