A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography

TL;DR

This paper proposes a set of sufficient conditions for the strong eigenstate thermalization hypothesis (ETH) applicable to chaotic systems, including holographic theories, using inequalities involving long-time thermal correlators.

Contribution

It introduces a novel framework of inequalities as sufficient conditions for strong ETH, extending analytic understanding to broad classes of chaotic theories including holography.

Findings

Toy models satisfying the conditions under certain assumptions.

Conditions relate to long-time averages of thermal correlators.

Comments on applicability to realistic holographic models.

Abstract

The strong eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration. Although it is expected to be hold in a wide class of highly chaotic theories, there are only a few analytic examples demonstrating the strong ETH in special cases, often through methods related to integrability. In this paper, we explore sufficient conditions for the strong ETH that may apply to a broad range of chaotic theories. These conditions are expressed as inequalities involving the long-time averages of real-time thermal correlators. Specifically, as an illustration, we consider simple toy examples which satisfy these conditions under certain technical assumptions. This toy models have same properties as holographic theories at least in the perturbation in large $N$. We give a few comments for more realistic holographic models.