Several people at this department ( Abteilung fuer Theoretische Quantendynamic) are studying chaotic systems and the classical chaos research involves Kai Hansen, Achim Kohler and Stephan Guettler, and from a more quantum mechanical point of view Gernot Alber, Jan Michael Rost, and others.

Classical/Semiclassical chaos projects

Diamagnetic Kepler problem

One project involves the understanding of the classical structure and semiclassical calculations of the problem of a Hydrogen atom in a strong magnetic field (diamagnetic Kepler Problem). We describe the periodic orbits with help of symbolic dynamics and are using the techinque of pruning front to describe the system in the case where it is not a complete repellor. The zeta-function formalism is used to find resonanses in the quantum mechanical system.

Involved people: Kai Hansen, Stephan Guettler and Gregor Tanner

Publications: K.T. Hansen, Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem, Phys. Rev. E, 51, 1838 (1995).

Gaussian scattering

We study the scattering problem of a particle moving in a two dimensional plane under influence of a number of attracting Gaussian potentials.

Involved people: Kai Hansen and Achim Kohler.

Billiard Systems

We work on different billiard system and describe these with help of symbolic dynamics.

Involved people: Kai Hansen.

Publications: K.T. Hansen, {\em CHAOS} {\bf 2}, 71 (1992). K.T. Hansen, Symbolic dynamics I, Finite dispersive billiards, Nonlinearity, 6, 753 (1993). K.T. Hansen, Symbolic dynamics II, Bifurcations in billiards and smooth potentials, Nonlinearity, 6, 771 (1993). K.T. Hansen and P. Cvitanovic, Symbolic Dynamics and Markov Partitions for the Stadium Billiard, submitted to J Stat Phys, (1994).