Chaos
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).