Non-generic spectral statistics in the quantized stadium billiard

We consider the effect of a continuous family of neutral (bouncing ball) orbits on the energy spectrum of the quantized stadium billiard. Using a semiclassical approximation we derive analytic expressions for standard two-point spectral measures. The corrections due to the bouncing ball orbits account for some of the non-generic features observed in the analysis of the spectrum of a stadium cavity which was recently measured. Once the bouncing ball contributions are subtracted, the spectrum is shown to be well reproduced by the semi-classical trace formula based on unstable periodic orbits. We also study special patterns in the spectrum which are due to other non-generic features such as edge effects and 'whispering gallery' trajectories.