It is a common assumption that time reversal invariance or some other anti-unitary symmetry for a classically chaotic system implies GOE-type spectral fluctuations for the corresponding quantum system. Based on previous work on structural invariance, we show that a time-reversal invariant system for certain point symmetries displays the GUE statistics typical of systems with broken time-reversal symmetry; specifically a billiard having only three-fold symmetry shows this unexpected behaviour.
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Leyvraz et al. (1996) studied this question.
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