Semiclassical approximations to diffractive effects in the annulus billiard

The semiclassical theory formulated by Bogomolny [E. B. Bogomolny, Nonlinearity 5, 805 (1992)] employs a transfer operator constructed from classical trajectories that connect points on a suitably chosen Poincarésurface of section. In this paper we study the two-dimensional annulus billiard, and modify Bogomolny's transfer operator to include diffractive paths. The penumbra contributions [H. Primack et al., Phys. Rev. Lett. 76, 1615 (1996)], …