Phenomenological model for symmetry breaking in chaotic system

TL;DR

This paper introduces a phenomenological model describing how symmetry breaking affects the energy spectrum of chaotic systems, linking spectral statistics to symmetry interactions and validating predictions with experimental data.

Contribution

It proposes a novel superposition-based model for symmetry breaking in chaotic systems and derives relations between level densities and interactions, supported by numerical and experimental validation.

Findings

Model accurately predicts spectral statistics during symmetry breaking

Derived relations match numerical calculations

Experimental results confirm model predictions

Abstract

We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the fractional level densities of the sequences and the symmetry breaking interaction is deduced by comparing the asymptotic expression of the level-number variance with the corresponding expression obtained using the perturbation theory. This relation is supported by a comparison with previous numerical calculations. The predictions of the model for the nearest-neighbor-spacing distribution and the spectral rigidity are in agreement with the results of an acoustic resonance experiment.