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An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Spectral statistics of a pseudo-integrable map

Author: Eugene Bogomolny (UMR Universit Paris-Sud)

Abstract

Different curious spectral properties of a quantum interval exchange map are discussed. In particular, it is demonstrated that when the matrix dimension obeys a certain congruence property the spectral statistics of the map coincides with the semi-Poisson statistics with integer and half integer level repulsion. Special attention is given to the general case where the spectral statistics is calculated by the transfer matrix approach.