Survival Probability for Open Spherical Billiards
Chaotic Dynamics
2017-06-29 v3 Dynamical Systems
Exactly Solvable and Integrable Systems
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-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.
Cite
@article{arxiv.1402.4728,
title = {Survival Probability for Open Spherical Billiards},
author = {Carl P. Dettmann and Mohammed R. Rahman},
journal= {arXiv preprint arXiv:1402.4728},
year = {2017}
}