Chaos due to symmetry-breaking in deformed Poisson ensemble

TL;DR

This paper investigates how breaking symmetries in a Hamiltonian affects its spectral properties, introducing a deformed Poisson ensemble to model the transition from integrable to chaotic behavior, supported by theoretical and numerical analysis.

Contribution

It introduces a deformed Poisson ensemble that maps coupling terms to symmetries and predicts a chaotic limit based on the maximum entropy principle, verified numerically.

Findings

Spectral properties interpolate between Poisson and Wigner-Dyson ensembles.

Chaotic limit predicted by maximum entropy principle is confirmed numerically.

Spectral and survival probability analyses support the theoretical predictions.

Abstract

The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal terms of a Hamiltonian evolve as one or more symmetries of an integrable system are explicitly broken. We introduce a deformed Poisson ensemble to demonstrate an exact mapping of the coupling terms to the underlying symmetries of a Hamiltonian. From the maximum entropy principle we predict a chaotic limit which is numerically verified from the spectral properties and the survival probability calculations.