Astrid de Wijn:
Vertical chaos and horizontal diffusion in the bouncing-ball billiard
Abstract:
The bouncing-ball billiard is an interesting, low-dimensional system
in which transport properties of real physical systems can be studied
theoretically. We study the bouncing-ball billiard, which was first
introduced in ref. [3], with non-convex
scatterers with small slopes. We show that there is a time-scale
separation between the horizontal and vertical motion, which is
controlled by the slope of the billiard. We apply the theory of
time-scale separation developed in ref. [2]. If the vertical motion
is chaotic, the horizontal motion is diffusive, but if the vertical
motion is (quasi-)periodic, there is no diffusion. We confirm the results
with numerical simulations. Hence, the order-chaos transition in the
vertical degrees of freedom translates into a
localisation-delocalisation transition for the horizontal motion.
[1] Astrid S. de Wijn and Holger Kantz, Physical Review E 75 046214
(2007).
[2] Anja Riegert, Niluefer Baba, Katrin Gelfert, Wolfram Just, Holger Kantz,
Phys. Rev. Lett. 94 054103 (2005).
[3] Laszlo Mátyás and
Rainer Klages, Physica D 187 165 (2004).