Dimension and escape rate of chaotic scattering from classical and semiclassical cross section data

Abstract

A new method is presented to extract information concerning the strange repeller underlying chaotic potential scattering based on classical and quantum mechanical scattering cross section data in the semiclassical limit. In particular, the authors show that both the fractal dimension and the escape rate of the classical system can be deduced from quantum measurements. The method can be applied in the limit of small wavelengths of the incoming projectile compared with the size of the target. As input, the differential quantum cross section is needed for the angle and/or the energy with such good resolution that fast interference oscillations are well resolved.