title: Survival probability for open spherical billiards.
abstract: 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-time 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.
authors.affiliation: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
authors.forename: Carl P
authors.initials: CP
authors.lastname: Dettmann
authors.affiliation: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
authors.forename: Mohammed R
authors.initials: MR
authors.lastname: Rahman