On the Periodic Lorentz Gas and the Lorentz Kinetic Equation
arXiv:math/0703812 · doi:10.5802/afst.1200
Abstract
We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence to the linear Boltzmann equation has been proved by Gallavotti [Phys. Rev. (2) 185 (1969), p. 308].