Spectral statistics of a quantum interval-exchange map.
Curious spectral properties of an ensemble of random unitary matrices appearing naturally in the quantization of a simple interval-exchange map are investigated. It is demonstrated that, under certain conditions on map parameters, local spectral statistics of this ensemble tends to the semi-Poisson distribution with arbitrary integer or half-integer level repulsion at small distances depending on time-reversal symmetry of the map.
Bogomolny
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Laboratoire de Physique Théorique et Modelès Statistiques, Université de Paris-Sud, Bâiment 100, 91405 Orsay Cedex, France.
Schmit
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