Semiclassical approach to discrete symmetries in quantum chaos

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We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated with irreducible representations of the corresponding symmetry group. We show that for (spinless) time-reversal invariant systems, the statistics inside these subspectra depends on the type of irreducible representation. For real representations the spectral statistics agrees with those of the Gaussian orthogonal ensemble of random matrix theory (RMT), whereas complex representations correspond to the Gaussian unitary ensemble (GUE). For systems without time-reversal invariance, all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.

Original languageEnglish
Article number205102
Number of pages24
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
Early online date8 May 2012
Publication statusPublished - 25 May 2012


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