Dresden 2003 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Brownian motion

DY 21.2: Talk

Tuesday, March 25, 2003, 10:15–10:30, G\"OR/229

Irregular diffusion in the bouncing ball billiard — •Rainer Klages and Laszlo Matyas — Max-Planck-Institut für Physik komplexer Systeme,Nöthnitzer Str. 38, 01187 Dresden

We call a system a bouncing ball billiard if it consists of a particle that is subject to a constant vertical force and bounces inelastically on a one-dimensional 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.

[1] L.Matyas, R.Klages, preprint nlin.CD/0211023 (2002)