Irregular diffusion in the bouncing ball billiard
Abstract
We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers that are very shallow, hence this billiard is a deterministic diffusive version of the well-known bouncing ball problem on a flat vibrating plate. Computer simulations show that the diffusion coefficient of this system is a highly irregular function of the vibration frequency exhibiting pronounced maxima whenever there are resonances between the vibration frequency and the average time of flight of a particle. In addition there exist irregularities on finer scales that are due to higher-order dynamical correlations pointing towards a fractal structure of this curve. We analyze the diffusive dynamics by classifying the attracting sets and by working out a simple random walk approximation for diffusion, which is systematically refined by using a Green-Kubo formula.
Cite
@article{arxiv.nlin/0211023,
title = {Irregular diffusion in the bouncing ball billiard},
author = {L. Matyas and R. Klages},
journal= {arXiv preprint arXiv:nlin/0211023},
year = {2007}
}
Comments
26 pages in Latex, Elsevier style; 11 figures