%0 Journal Article
%T Survival Probability for Open Spherical Billiards
%A Carl P. Dettmann
%A Mohammed R. Rahman
%J Physics
%D 2014
%I arXiv
%R 10.1063/1.4900776
%X We study the survival probability for long times in an open spherical billiard, extending previous work on the circular billiard. We provide details of calculations regarding two billiard configurations, specifically a sphere with a circular hole and a sphere with a square hole. The constant terms of the long-term survival probability expansions have been derived analytically. Terms that vanish in the long time limit are investigated analytically and numerically, leading to connections with the Riemann hypothesis.
%U http://arxiv.org/abs/1402.4728v3