Friday, November 22, 2002, 16:00
WHGA Auditorium
Prof. F. Steiner, Univ. Ulm
Abstract:
In classical physics chaos can be characterized by the long-time
behaviour of the dynamics, the most obvious property being a
sensitive dependence on initial conditions due to the nonlinear
nature of Newton's equations. In contrast the Schroedinger
equation is linear, and thus the quantum mechanical time evolution
is almost periodic, which implies that there is no "quantum chaos"
that manifests itself in the long-time behaviour. In the talk it
will be shown that there exist, however, unique fingerprints of
classical chaos in spectra and wave functions of the corresponding
quantum systems, which justify to speak of universal signatures
of quantum chaos. Prominent examples are the quantum ergodicity
theorem for wave functions and the conjectures describing the
statistical properties of energy levels by the results of random
matrix theory. To prove these conjectures is a great challenge to
physicists and mathematicians who participate in the European
Commission Research Training Network "Mathematical Aspects of
Quantum Chaos".