Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems

TL;DR

This paper investigates the eigenstate thermalization hypothesis and random matrix theory universality in few-body quantum chaotic systems, using semiclassical analysis and numerical simulations to reveal their interplay and applicability.

Contribution

It demonstrates the applicability of ETH in few-body systems and establishes the universal RMT description of observables within a microcanonical energy window.

Findings

ETH holds in certain regimes of few-body systems.

Universal RMT behavior emerges for observables in energy windows.

Results bridge quantum chaos and thermalization theories.

Abstract

In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems with chaotic classical limits and the emergence of random matrix theory universality. More specifically, we focus on: 1) the applicability of the eigenstate thermalization hypothesis in few-body systems and the dependence of its form on the effective Planck constant and 2) the existence of a universal random matrix theory description of observables when truncated to a small microcanonical energy window. Our results provide new insights into the established field of few-body quantum chaos and help bridge it to modern perspectives, such as the general eigenstate thermalization hypothesis (ETH).