These
lectures will serve as an introduction to the quantum
mechanics of classically chaotic systems, and provide the background
needed for a good understanding of the lectures of the other speakers.
The
topics to be discussed include: Ergodic properties of classical
dynamical
systems; Classical statistical mechanics - transport phenomena,
Green-Kubo
formalism; Quantum systems and quantum statistical mechanics - Wigner
and
Husimi distribution functions, Green-Kubo formalism for quantum
systems;
The origins of "quantum chaos", Loschmidt echo; Ehrenfest and
Heisenberg
time scales; Energy level spacings - Random Matrix Theory (RMT) and
associated ensembles; The B-G-S conjecture and approaches to a proof;
Statistical properties of wave functions; Quantum ergodicity;
Semi-classics; The Gutzwiller trace formula; Quantum statistical
mechanics
and transport theory, useful model systems, diffusive - ballistic
crossover, localization, interactions with the environment,
decoherence.