开放式球面台球的生存概率
Survival Probability for Open Spherical Billiards
摘要：
本文研究了在开放的球形台球中长时间生存的概率，推广了以前在圆形台球中的工作。我们提供了关于两个台球配置的计算细节，特别是一个球体与一个圆孔和一个球体与一个方孔。长期生存概率展开式的常数项已被解析地导出。在很长一段时间内消失的条款进行了研究分析和数值，导致与黎曼假设的连接。
英文摘要：
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.
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