Semiclassical quantization using diffractive orbits

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in classical mechanics. Semiclassical quantization then requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this Letter we construct the corresponding diffractive zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the zeta function.