ON THE TRANSITION TO CHAOTIC SCATTERING

A classical scattering system is chaotic if it possesses a fractal set of trapped unstable orbits, resulting in singular deflection functions. A scattering system is regular if it supports only a countable set of trapped unstable orbits. Its deflection functions are piecewise smooth with at most a countable number of scattering singularities caused by the trapped orbits. Despite the simple structure of the deflection functions, the Poincare scattering mapping (PSM) may be regular, hyperbolic or display mixed dynamics. Thus, the degree of chaoticity of the PSM serves as a finer scale for the discussion of the transition to chaotic scattering in the classical domain. In the quantum domain we show that the properties of the PSM determine the statistics of the eigenphases of the S-matrix, and that, if the PSM is hyperbolic, the eigenphases follow the statistics predicted by random matrix theory.