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Survival probability for open spherical billiards.

Carl P Dettmann1, Mohammed R Rahman1

  • 1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.

Chaos (Woodbury, N.Y.)
|January 3, 2015
PubMed
Summary
This summary is machine-generated.

We analyzed long-time survival probability in open spherical billiards with circular and square holes. Our findings reveal analytical solutions for constant terms and connections to the Riemann hypothesis.

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Area of Science:

  • Mathematical Physics
  • Dynamical Systems

Background:

  • Previous studies focused on circular billiards.
  • Understanding particle behavior in confined spaces is crucial.

Purpose of the Study:

  • Extend survival probability analysis to open spherical billiards.
  • Investigate specific configurations: sphere with circular and square holes.
  • Derive analytical solutions for long-time behavior.

Main Methods:

  • Analytical derivation of constant terms in survival probability expansions.
  • Numerical and analytical investigation of terms vanishing in the long-time limit.

Main Results:

  • Successfully derived analytical expressions for constant terms.
  • Identified terms that decay over time.
  • Established a link between these decaying terms and the Riemann hypothesis.

Conclusions:

  • The study provides a comprehensive analysis of survival probability in open spherical billiards.
  • The findings offer new insights into the mathematical physics of dynamical systems.
  • Connections to the Riemann hypothesis warrant further investigation.