PENUMBRA DIFFRACTION IN THE QUANTIZATION OF DISPERSING BILLIARDS

Diffraction corrections to the semiclassical spectral density of dispe rsing (Sinai) billiards, due to orbits which are almost tangent to the concave part of the boundary, are studied here for the first time. We show that most periodic orbits needed for quantization must be correc ted. For orbits which just miss tangency, the corrections are of the s ame magnitude as the semiclassical contributions themselves. For orbit s which glance at an extreme forward direction, the new theory replace s the semiclassical term that approaches 0 at tangency with a finite o ne. These corrections are one of the most significant modifications of the trace formula considered so far.