Open University, Milton Keynes, MK7 6AA, England, United Kingdom

Dissipation is the irreversible transfer of energy into a reservoir, having a large number of degrees of freedom. I will consider the case where the reservoir is a system of nearly independent fermions. This includes dissipation by electrical conduction and dissipation in the dynamics of the nucleus. The lectures will demonstrate that this is a rich subject for investigation, with significant problems outstanding.

**Lecture 1**:
Physical applications, and the standard approach (the Kubo
formula). Energy diffusion as an alternative approach to
dissipation. Classical-quantum correspondence. Limitations
of the Kubo formula approach.

Complex quantum systems. Random matrix theory, and universality hypotheses. Dimensionless parameters describing response of complex systems. Parametric random matrix models. Matrix element sum-rules, and semiclassical estimates. Some parametric statistics.

**Lecture 2**:
Estimates for energy diffusion constant in
Landau-Zener and Kubo formula regimes.
Predictions of various anomalous effects. Numerical experiments
testing these predictions. Theoretical arguments reconciling
random matrix and semiclassical predictions.

Much of the material is covered in *Parametric Random Matrices:
Static and Dynamic Applications* , M. Wilkinson, in `*Supersymmetry and Trace Formulae*, eds. I. V. Lerner,
J. P. Keating and D. E. Khmelnitskii, New York: Plenum,
p.369-399, (1999). Several new results will be discussed.