Perturbative Treatment of Symmetry Breaking Within Random Matrix Theory

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.