Classical and quantum dynamics of time-dependent billiards

• Applicant: Professor Dr. Peter Schmelcher
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 48246955

We investigate the nonlinear classical and quantum dynamics of time-dependent billiards with the focus on escape and emission rates as well as transport properties. The fundamental dynamical mechanisms of driven billiards will be identified and analyzed in detail. Our studies aim at the control and preparation of ensembles of particles emitted from or transported through driven billiards and/or at suggesting the driven billiards as tunable sources of particles. To this end we explore a significant number of setups including different billiard geometries (ellipse, oval, stadium) and driving laws of their boundaries (harmonic single frequency, multi-frequency and stochastic) as well as hard versus soft-wall potentials. The quantum physics will be investigated by developing and applying wave packet propagation methods combined with complex absorbing potentials. It is foreseeable that novel phenomena due to the driving will enhance the understanding of the dynamics of driven systems in general. The primary focus is on the case of non-interacting particles but interacting few-particle billiards will be considered too, first classically and as a long-term perspective also quantum mechanically. A close contact to experimental groups exists and will be put forward in the course of the evolution of the project.

• DFG Programme: Research Grants