Analysis of symmetry breaking in quartz blocks using superstatistical random matrix theory

TL;DR

This paper investigates the gradual symmetry breaking in quartz blocks' acoustic resonances using superstatistical random matrix theory, proposing a new approach to model the transition more effectively.

Contribution

It introduces the application of inverse-chi-square superstatistics to describe the entire symmetry breaking process in acoustic resonances.

Findings

Superstatistics effectively models the symmetry transition.

Inverse-chi-square superstatistics fits the data well.

Compared with previous models, it offers a unified description.

Abstract

We study the symmetry breaking of acoustic resonances measured by Ellegaard et al., Phys. Rev. Lett. 77, 4918 (1996), in quartz blocks. The observed resonance spectra show a gradual transition from a superposition of two uncoupled components, one for each symmetry realization, to a single component well represented by a Gaussian orthogonal ensemble (GOE) of random matrices. We discuss the applicability of superstatistical random-matrix theory to the final stages of the symmetry breaking transition. A comparison is made between different formula of the superstatistics and a pervious work [Abd El-Hady et al, J. Phys. A: Math. Theor. 35, 2361 (2002)], which describes the same data by introducing a third GOE component. Our results suggest that the inverse-chi-square superstatistics could be used for studying the whole symmetry breaking process.