Universal scaling of spectral fluctuation transitions for interacting chaotic systems

TL;DR

This paper studies how spectral fluctuations in interacting chaotic systems transition from Poisson to random matrix statistics, revealing a universal behavior characterized by a single scaling parameter.

Contribution

It introduces a new random matrix ensemble that models the universal transition in spectral statistics of interacting chaotic systems.

Findings

The transition from Poisson to RMT statistics is highly sensitive and universal.

The new ensemble accurately models spectral transitions with excellent agreement.

Perturbation theory effectively describes the transition dynamics.

Abstract

The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random matrix ensemble modeling this dynamical symmetry breaking transition which turns out to be universal and depends on a single scaling parameter only. Coupled kicked rotors, a dynamical systems paradigm for such transitions, are compared with this ensemble and excellent agreement is found for the nearest-neighbor-spacing distribution. It turns out that this transition is described quite accurately using perturbation theory.