Survival probability for open spherical billiards

Carl P. Dettmann, Mohammed R. Rahman
2014 Chaos  
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.
doi:10.1063/1.4900776 pmid:25554050 fatcat:kpn7yi46xvht5b2uxff6rtep2i