Semiclassical cross section for a classically chaotic scattering system

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Abstract
A semiclassical treatment of the scattering cross section of a classically chaotic scattering problem is presented. In the limit of small h(cross), the authors find several ways in which images of classical fractal structures show up in the semiclassical cross section. First, the fractal arrangement of rainbow singularities emerges. Further, the interference terms in the semiclassical cross section show oscillations on all scales, whose frequency spectra approach fractal structures which are well known from the classical system. This holds for the cross section as a function of the scattering angle for fixed energy as well as for the cross section as a function of energy for fixed scattering angle.

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