Statistics of local level spacings in single- and many-body quantum chaos

TL;DR

This paper introduces a new framework for analyzing local level spacings in quantum systems using random matrix theory, revealing universal patterns that distinguish chaotic from regular dynamics across various quantum models.

Contribution

It defines local level spacings and their statistics, establishing universal sequences that identify system symmetries and dynamics, supported by numerical experiments.

Findings

Universal sequences of mean local spacings and ratios identified

Framework distinguishes chaotic and regular quantum dynamics

Numerical validation across diverse quantum systems

Abstract

We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians.