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 i n an open three-disk billard in the presence of a homogeneous magnetic fiel d, which is confined to the inner part of the scattering region. As the mag netic field is increased the phase space of the invariant set of the classi cal scattering trajectories changes from hyperbolic (fully chaotic) to a mi xed situation, where KAM tori are present. The "stickiness" of the stable t rajectories leads to a much slower decay of the survival probability of tra jectories as compared to the hyperbolic case. We show that this effect infl uences strongly the quantum fluctuations of the scattering amplitude and cr oss sections.