8 - Chaotic scattering

Summary

Scattering processes have played an important role in different sciences since the discovery of the atomic nucleus by directing a particle beam onto a thin layer of a solid and evaluating its deflection. Scattering methods are now widely used in the investigation of material structures. Other phenomena, such as, for example, the motion of a comet, or the reflection of light on a set of mirrors, are also scattering processes (cf. Section 1.2.4). Perhaps the simplest example is provided by the motion of a particle under the effect of a force bounded to a finite region in space. In general, a scattering process is the dynamics of a conservative system that starts and ends with a very simple (usually uniform rectilinear) motion, typically far away from the region where interactions are strong (the scattering region). The well known classical examples of scattering all exhibit regular motion. The moral of Chapter 7 is, however, also valid in these cases: even the slightest perturbation makes the dynamics chaotic. Chaotic scattering is, therefore, typical.

Because of the simplicity of the initial and final states, chaotic behaviour can only extend to a finite domain of phase space, and it can only be transient. Chaotic scattering is therefore the manifestation of transient chaos in conservative systems. Consequently, it is related to the chaotic saddle (see Chapter 6) of a volume-preserving (σ ≡ 0 or J ≡ 1) dynamics.