Rotating Leaks in the Stadium Billiard

TL;DR

This paper studies how rotating leaks affect particle escape probabilities in stadium billiards, revealing that leak motion can switch decay behavior between exponential and power law, influenced by interactions with special orbits.

Contribution

It introduces the concept of a rotating leak in stadium billiards and demonstrates how its velocity alters decay dynamics through interactions with MUPOs.

Findings

Decay behavior depends on leak rotation speed.

Certain velocities produce purely exponential decay.

Interactions with MUPOs explain the different responses.

Abstract

The open stadium billiard has a survival probability, $P(t)$, that depends on the rate of escape of particles through the leak. It is known that the decay of $P(t)$ is exponential early in time while for long times the decay follows a power law. In this work we investigate an open stadium billiard in which the leak is free to rotate around the boundary of the stadium at a constant velocity, $\omega$. It is found that $P(t)$ is very sensitive to $\omega$. For certain $\omega$ values $P(t)$ is purely exponential while for other values the power law behaviour at long times persists. We identify three ranges of $\omega$ values corresponding to three different responses of $P(t)$. It is shown that these variations in $P(t)$ are due to the interaction of the moving leak with Marginally Unstable Periodic Orbits (MUPOs).