  We present a systematic theory of dissipation in finite Fermi systems like
nuclei and metallic clusters. This theory is based on the application of
semiclassical methods and random matrix theory to linear response of many-body
systems. The theory is developed in the approximation wherein the many-body
system can be treated as a single particle in an effective, time-dependent
mean-field. We find semiclassical expressions for energy dissipation relevant
in one-body dissipation in heavy nuclei. We also show that this energy
dissipation, related to damping of collective excitations, is irreversible. The
irreversibility is proved by our development of a quantum diffusion equation.
It may be noted that the quantum diffusion equation is derived from the von
Neumann equation and makes no assumption about the initial form of the density
operator. It is shown that, in the semiclassical limit, the quantum diffusion
equation reduces to the classical Smoluchowski equation. Further, we show that
the dissipation is a purely quantal phenomenon as it is related to the
geometric phase acquired by a single-particle wavefunction as the system
evolves in a slow-varying mean-field. It is explicitly shown that the
dissipation rate is related to the nature of dynamics and the spectrum of the
classical Liouvillian operator. Finally, we present an expression for the
viscosity tensor encountered in nuclear fission in terms of periodic orbits of
the single particle in an adiabatically deforming nucleus.
