Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 24: Poster I
DY 24.16: Poster
Wednesday, March 28, 2007, 16:00–18:00, Poster D
Classical Dynamics of the Time-Dependent Elliptical Billiard — •Florian Lenz1 and Peter Schmelcher1,2 — 1Physikalisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany — 2Theoretische Chemie, Institut für Physikalische Chemie, Universität Heidelberg, 69120 Heidelberg, Germany
We study classically the dynamics of harmonically driven elliptical billiards with the focus lying on escape rates by performing numerical simulations. In the static ellipse, we find algebraic decay laws due to the integrable dynamics of the system. Besides the energy, the product of the angular momenta (PAM) around the foci is preserved. Depending on the sign of the PAM, particles are confined to either librator or rotator orbits. By varying the hole position, the saturation value (SV) of the decay, caused by librator orbits that are not connected with the hole, can be tuned. We apply harmonic oscillations to the boundary to examine the effect of the driving on this SV. Two universal fundamental processes that are able to destroy this SV via changing librator into rotator orbits (they are scattered across the separatrix) are discussed and a simple qualitative model is established that explains the decay and the amplitude-dependent emission rate of the driven system. The analysis of the time-evolution of velocity distributions suggests that the driven ellipse can be used as a cooling device for particles, provided a suitable preparation of the initial ensemble.