Chaotic Scattering in the Gaussian Potential

Abstract

It is well known that general classical Hamiltonian dynamical systems have as a rule chaotic behaviour. By such a term one usually understands a sensitive dependence on initial conditions which manifests itself in the topology of phase space. For the most studied case of bounded motions this behaviour is detected, for example, by analysing the Poincaré surfaces of section and by calculating Lyapunov characteristic exponents. The question then naturally arises of what are the effects of this complexity on the unbounded motions, i.e., on scattering phenomena. The signature of chaotic dynamics in these scattering regions of phase space has been the object of several papers appeared mainly in the last decade. Although it has been approached from different points of view it is true that both the number of case studies and the agreement over the quantitative characterization of the phenomenon is much less extensive than the corresponding situation for bounded motion.