scattering and nonequilibrium quantum systems (4h)
1) Title: Semiclassics and periodic-orbit quantization of chaotic
Abstract: This lecture gives the general framework for the study of
chaotic quantum scattering in the semiclassical limit. The scattering
resonances associated with each quantum decay mode are defined at
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
Abstract: Using Ruelle’s large-deviation formalism and his topological
pressure function, a semiclassical bound is obtained on the lifetimes
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
competing periodic orbits existing in classically chaotic scattering.
3) Title: Decay of quantum statistical mixtures in classically chaotic
Abstract: It is shown that quantum statistical mixtures have a decay of
own, besides the decay of pure quantum wavefunctions. In the
limit, the decay of statistical mixtures is controlled by the
resonances of classical Liouvillian dynamics. These resonances are
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
Abstract: The concept of Liouvillian resonances extends from scattering
quantum systems to infinite quantum systems where they control the
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.
quantization of the transverse transport properties and driven quantum
are also discussed.