Symmetry Breaking Study with Random Matrix Ensembles

TL;DR

This paper introduces a random matrix model for analyzing symmetry breaking in physical systems, specifically applying it to eigenfrequency data of an anisotropic quartz block to identify intrinsic symmetries.

Contribution

The paper develops a novel random matrix ensemble to model m-fold symmetry coupling and demonstrates its application to real experimental data for symmetry detection.

Findings

Effective modeling of symmetry breaking using random matrices

Identification of intrinsic symmetry in elastomechanical vibrations

Potential for broader application in physical system analysis

Abstract

A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such experimental/theoretical study may supply a powerful means to discern intrinsic symmetry of physical systems.