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Discrete Symmetries and Spectral Statistics

Keating, J.P.


Keyword(s): quantum chaos; discrete symmetries; spectral statistics; random matrix theory

Abstract: We calculate the 2-point spectral statistics associated with a given irreducible representation (i.e. symmetry class) for time-reversal invariant systems possessing discrete symmetries using semiclassical periodic orbit theory. When the representation in question is real or pseudoreal, our results conform to those of the Gaussian Orthogonal Ensemble (GOE) of random matrices. When it is complex, we find instead Gaussian Unitary Ensemble (GUE) behaviour. This provides a direct semiclassical explanation for the recent observation by Leyvraz et al. (1996) of GUE correlations in the desymmetrized spectra of certain symmetric billiards in the absence of any time-reversal invariance breaking (e.g. magnetic) fields.

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