Provable quantum thermalization without statistical averages

TL;DR

This paper introduces a rigorous, system-agnostic method to predict quantum thermalization in many-body systems using out-of-time-ordered correlators, avoiding the need for statistical averages or detailed eigenstate knowledge.

Contribution

The authors develop a novel geometric framework linking quantum thermalization to correlator saturation, applicable to almost all pure states without large-time or eigenstate information.

Findings

Predicts thermalization using few-body correlators in large systems.

Connects thermalization to high-dimensional subspace alignment.

Provides a practical approach for experimental and theoretical studies.

Abstract

We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body observables. In contrast to previous rigorous results on thermalization with semiclassical counterparts, our method is not limited to statistical averages of observables, such as time averages in ergodicity or state averages in mixing. Moreover, consistent with such approaches, we retain the advantage of not requiring a detailed knowledge of energy eigenstate structure or thermodynamically large times, which can become intractable for systems with more than a handful of particles. Our approach is centered on a geometric result that connects thermalization to the alignment of high dimensional subspaces in a Hilbert space, which is determined by the saturation of "controllably nonlocal" out-of-time-ordered correlators. This formalism reduces the problem of establishing pure state quantum thermalization at finite times in almost all complex many-body states to a theoretically or experimentally accessible study of few-body correlators, even in thermodynamically large systems.