Eugene Bogomolny

Statistical properties of quantum barrier billiards

Pseudo-integrable billiards form a special and poorly investigated class of quantum models. The talk is devoted to the investigation of spectral statistics for the simplest example of such systems, namely the barrier billiard consisting of a rectangular billiard with a barrier parallel to a rectangle side. The exact surface-of-section quantization is achieved by the Wiener-Hopf method. The resulting S-matrix is reduced in the semi-classical approximation to a finite unitary matrix whose spectral statistics is the same as the spectral statistics of the barrier billiard. The main result of the research is that spectral properties of barrier billiards are (i) independent on position and height of the barrier and (ii) are well described by the semi-Poisson statistics.