Spontaneous Emission in Chaotic Cavities

The spontaneous emission rate $\gamma$ of a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing $N$ wave channels, the distribution of $\gamma$ is given by $P\left(\gamma \right)\propto {\gamma }^{N/2-1}(\gamma +{\gamma }_0{)}^{-N-1\mathrm{}}$, where ${\gamma }_0$ is the free-space rate. For small $N$ the most probable value of $\gamma$ is much smaller than the mean value ${\gamma }_0$.