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

(1h)

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.

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

(1h)

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.