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Münster 1999 – scientific programme

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DY: Dynamik und Statistische Physik

DY 46: Quantenchaos II

DY 46.2: Talk

Thursday, March 25, 1999, 17:15–17:30, R4

Sharp transition in the spectral statistics of a generalized Sinai billiard — •Ulrich Gerland — Institut für Theoretische Festkörperphysik, Universität Karlsruhe, Postfach 6980, 76128 Karlsruhe
We consider a system consisting of a particle moving in a rectangular domain with a repulsive scatterer inside. The scatterer is characterized by a potential that behaves as V(r)∼λ/rα for small radii and periodic boundary conditions are assumed. We present physical arguments and numerical evidence showing that the spectral statistics of the system tends to Poisson statistics in the limit of large particle energy when α<2 and to Wigner-Dyson statistics when α>2 independent of the value of λ. This behaviour is reminiscent of a metal-insulator transition in disordered electronic systems, where the limit of large energy has to be replaced by the limit of large system size. For α=2 we find that the spectral statistics is independent of energy, but depends on λ. We discuss the relation to recent results of Altshuler and Levitov.

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