Correlations between spectra with different symmetry: any chance to be observed?

TL;DR

This paper investigates whether correlations exist between spectra with different symmetries in quantum chaology, finding no correlation in the universal regime but potential correlations in classical timescales for continuous symmetries.

Contribution

The study challenges the standard assumption by analyzing spectral correlations across different symmetries, revealing conditions under which correlations may or may not occur.

Findings

No correlation in the universal regime.

Potential correlations up to classical times for continuous symmetries.

Spectra of different symmetries are expressed via the same periodic orbits.

Abstract

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular, because in semiclassics spectra of different symmetry are expressed in terms of the same set of periodic orbits. We reexamine this question and find absence of correlation in the universal regime. In the case of continuous symmetry the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time.