Survival probability time distribution in dielectric cavities

We study the survival probability time distribution (SPTD) in dielectric cavities. In a circular dielectric cavity the SPTD has an algebraic long time behavior, $\sim t^{-2}$ in both TM and TE cases, but shows different short time behaviors due to the existence of the Brewster angle in TE case where the short time behavior is exponential. The SPTD for a stadium-shaped cavity decays exponentially, and the exponent shows a relation of $\gamma \sim n^{-2}$, $n$ is the refractive index, and the proportional coefficient is obtained from a simple model of the steady probability distribution. We also discuss about the SPTD for a quadrupolar deformed cavity and show that the long time behavior can be algebraic or exponential depending on the location of islands.