Quantum chaotic scattering with a mixed phase space: the three-disk billiard in a magnetic field
We study the classical and semiclassical scattering behavior of electrons in an open three-disk billard in the presence of a homogeneous magnetic field, which is confined to the inner part of the scattering region. As the magnetic field is increased the phase space of the invariant set of the classical scattering trajectories changes from hyperbolic (fully chaotic) to a mixed situation, where KAM tori are present. The "stickiness" of the stable trajectories leads to a much slower decay of the survival probability of trajectories as compared to the hyperbolic case. We show that this effect influences strongly the quantum fluctuations of the scattering amplitude and cross sections.
Eichengrun
M
Physik-Department E13, Technische Universitat Munchen, D-85747 Garching, Germany.
Schirmacher
W
Bregmann
W