Survival Probability for the Stadium Billiard

Details Survival Probability for the Stadium Billiard Survival Probability for the Stadium Billiard

2008-12-16

arxiv.org/abs/0812.3095v2

Physica D 238, 2395-2403, (2009)

Nonlinear Sciences

Chaotic Dynamics

13 pages, 6 figures

Scientific paper

We consider the open stadium billiard, consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides. Due to the hyperbolic nature of the stadium billiard, the initial decay of trajectories, due to loss through the hole, appears exponential. However, some trajectories (bouncing ball orbits) persist and survive for long times and therefore form the main contribution to the survival probability function at long times. Using both numerical and analytical methods, we concur with previous studies that the long-time survival probability for a reasonably small hole drops like Constant/time; here we obtain an explicit expression for the Constant.

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