Kinetic transport in the two-dimensional periodic Lorentz gas

Details Kinetic transport in the two-dimensional periodic Lorentz gas Kinetic transport in the two-dimensional periodic Lorentz gas

2008-04-03

arxiv.org/abs/0804.0566v1

Nonlinearity 21 (2008) 1413-1422

Physics

Mathematical Physics

10 pages, 5 figures

Scientific paper

10.1088/0951-7715/21/7/001

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.

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