Quantum Manifestations of Chaotic Scattering

We examine quantum chaotic scattering in the semiclassical regime for the two cases where the classical scattering is hyperbolic and nonhyperbolic. It is shown that in the nonhyperbolic case the energy-dependent S-matrix autocorrelation function C(ɛ) exhibits a cusp-shaped peak at ɛ=0 (where ɛ denotes the energy difference). This indicates that the fine scale fluctuations with energy of the S matrix are characteristically greatly enhanced in the nonhyperbolic case as compared with the hyperbolic case.