Münster 1999 – scientific programme
Parts | Days | Selection | Search | Downloads | Help
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.