Scattering from a classically chaotic repellor

Abstract

We report a study of the classical scattering of a point particle from three hard circular discs in a plane, which we propose as a model of an idealized unimolecular fragmentation. The system possesses a fractal and chaotic metastable classical state. On the basis of a coding of the system dynamics, we develop a method to construct the invariant probability measure and to calculate the particle escape rate, the Hausdorff dimension, the Kolmogorov–Sinai entropy per unit time and the mean largest Lyapunov exponent of the repellor. The relations between these characteristics of the system dynamics are discussed. In particular, we show that, in general, chaos inhibits escaping from the metastable state. The theory is compared with numerical simulations. We also introduce the classical tools necessary for the semiclassical quantization of the dynamics; the latter is discussed in the following paper.