%0 Journal Article
%T Kinetic transport in the two-dimensional periodic Lorentz gas
%A Jens Marklof
%A Andreas Strombergsson
%J Mathematics
%D 2008
%I arXiv
%R 10.1088/0951-7715/21/7/001
%X The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density (Boltzmann-Grad limit), the macroscopic dynamics converges to a stochastic process, whose kinetic transport equation is not the linear Boltzmann equation--in contrast to the Lorentz gas with a disordered scatterer configuration. The present paper focuses on the two-dimensional set-up, and reports an explicit, elementary formula for the collision kernel of the transport equation.
%U http://arxiv.org/abs/0804.0566v1