Perturbative Treatment of Symmetry Breaking Within Random Matrix Theory

TL;DR

This paper applies perturbative methods within Random Matrix Theory to analyze symmetry breaking in quartz crystals, revealing discrepancies with experimental data and suggesting missing eigenfrequencies as a resolution, with implications for nuclear isospin violation.

Contribution

It demonstrates the applicability of perturbative symmetry breaking analysis in RMT to experimental spectral data and compares different symmetry cases, highlighting the need to consider missing eigenfrequencies.

Findings

Spectral rigidity is better modeled by threefold symmetry.

Discrepancies at large L suggest missing eigenfrequencies.

Perturbative approach helps interpret symmetry breaking in experimental spectra.

Abstract

We discuss the applicability, within the Random Matrix Theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both twofold and threefold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequecies is considered to be missing in the sample. Our findings are relevant to isospin violation study in nuclei.