HP Labs Technical Reports
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Discrete Symmetries and Spectral Statistics
Keating, J.P.
HPLBRIMS9628
Keyword(s): quantum chaos; discrete symmetries; spectral statistics; random matrix theory
Abstract: We calculate the 2point spectral statistics associated with a given irreducible representation (i.e. symmetry class) for timereversal 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 timereversal invariance breaking (e.g. magnetic) fields.
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