Phenomenological model for symmetry breaking in a chaotic system

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 at 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.