The Two Dimensional Lorentz Gas in the Kinetic Limit: Theoretical and Numerical Results

The Lorentz gas is a model for the motion of electrons in a metal, where the motion is dominated by collisions of the electrons with immobile atomic nuclei, the scatterers. The motion depends on the distribution of scatterers, and we focus here on modifications of periodic scatterer distributions in two dimensions, and in the low density, or Boltzmann Grad, limit. Some theoretical results are complemented with numerical illustrations including modified periodic scatterer distributions, and scatterer distributions given by a quasi-crystal and by the zero set of a Gaussian analytic function.