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Chaotic Billiards
(2000)

The frictionless motion of a particle on a plane billiard table The frictionless motion of a particle on a plane billiard table bounded by a closed curve provides a very simple example of a conservative classical system with non-trivial, chaotic dynamics. The limiting cases of strictly regular ("integrable") and strictly irregular ("ergodic") systems can be illustrated, as well as the typical case which shows an intricate mixture of regular and irregular behavior. Irregular orbits are characterized by an extremely sensitivity with respect to the initial conditions. Such billiard systems are exemplarily suited for educational purposes as models for simple systems with complicated dynamics as well as for far-reaching fundamental investigations.

Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states is obtained and used to calculate the absorption spectrum in the region of high static fields.