Quantum thermalization and the route to ergodicity

TL;DR

This paper investigates how coupled quantum chaotic systems approach thermalization and ergodicity, revealing regimes where spectral chaos does not imply thermalization, and revising the energy shell concept independently of semiclassical methods.

Contribution

It introduces a minimal model for quantum thermalization, contrasting spectral chaos with ergodicity measures, and revises the energy shell concept independently of semiclassical assumptions.

Findings

Identification of a coupling regime with spectral chaos but lacking ETH thermalization

Revised energy shell concept consistent with quantum but independent of semiclassical theory

Contrast between RMT predictions and actual thermalization behavior

Abstract

We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix Theory (RMT) and the Eigenstates Thermalization Hypothesis (ETH). We highlight a coupling regime of disparity between the spectral statistics that indicates chaos, and ergodicity measures that indicate lack of ETH thermalization. The analysis involves a revision of the energy shell concept, in a way that is consistent but independent of the semiclassical perspective.