Chaos and statistical relaxation in quantum systems of interacting particles

TL;DR

This paper introduces a method to analyze the transition to chaos in isolated quantum systems with interacting particles, focusing on eigenstate delocalization and universal relaxation behaviors.

Contribution

It presents a novel approach based on eigenstate delocalization in the energy shell and shows universal relaxation properties regardless of integrability.

Findings

Eigenstate delocalization correlates with chaos transition.

Global eigenstate properties can be similar in integrable and non-integrable systems.

Analytical description of quench dynamics demonstrates universal relaxation.

Abstract

We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that although the fluctuations of energy levels in integrable and non-integrable systems are principally different, global properties of the eigenstates may be quite similar, provided the interaction between particles exceeds some critical value. In this case the quench dynamics can be described analytically, demonstrating the universal statistical relaxation of the systems irrespectively of whether they are integrable or not.