Rotating leaks in the stadium billiard

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, ω. It is found that P (t) is very sensitive to ω. For certain ω values P (t) is purely exponential while for other values the power law behaviour at long times persists. We identify three ranges of ω 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).