Chaotic scattering and diffusion in the Lorentz gas

Abstract

A chaotic-scattering theory of diffusion in the Lorentz gas is presented. The scattering process is considered on disk scatterers of increasing sizes. In this way, chaotic and fractal properties of the scattering process are related to diffusion. A formula is obtained that gives the diffusion coefficient in terms of the Lyapunov exponent and the Hausdorff codimension of the fractal repeller of orbits trapped in the scatterer. Numerical results are presented that support our theoretical results.