Classically chaotic scattering and nonequilibrium quantum systems (4h)

1) Title: Semiclassics and periodic-orbit quantization of chaotic scattering (1h)

Abstract: This lecture gives the general framework for the study of classically
chaotic quantum scattering in the semiclassical limit. The scattering
resonances associated with each quantum decay mode are defined at complex
energies. It is shown how these resonances can be calculated in terms of
classical periodic orbits.

2) Title: Slowing down of quantum decays in classically chaotic scattering (1h)

Abstract: Using Ruelle’s large-deviation formalism and his topological
pressure function, a semiclassical bound is obtained on the lifetimes of the
quantum decay modes. This bound depends on the chaotic properties of the
corresponding classical dynamics. It is shown that classical chaos leads to a
slowing down of the quantum decays because of the interference between the
competing periodic orbits existing in classically chaotic scattering.

3) Title: Decay of quantum statistical mixtures in classically chaotic scattering

Abstract: It is shown that quantum statistical mixtures have a decay of their
own, besides the decay of pure quantum wavefunctions. In the quasi-classical
limit, the decay of statistical mixtures is controlled by the Pollicott-Ruelle
resonances of classical Liouvillian dynamics. These resonances are defined at
complex frequencies instead of complex energies. The Pollicott-Ruelle
resonances turn out to manifest themselves in several important quantum
scattering phenomena, in particular, in chemical kinetics.

4) Title: Nonequilibrium transients and transport in large quantum systems (1h)

Abstract: The concept of Liouvillian resonances extends from scattering
quantum systems to infinite quantum systems where they control the modes of
decoherence and of relaxation toward equilibrium. In spatially extended
quantum systems, these resonances at complex frequencies can be used in
order to obtain the dispersion relations of the transport properties. The
quantization of the transverse transport properties and driven quantum systems
are also discussed.