Title: Derivation of the Fick's law for the Lorentz model in a low
density regime
In this talk we consider the Lorentz model in a slab with two mass
reservoirs at the boundaries. We show that, in a low density regime,
there exists a unique stationary solution for the microscopic dynamics
which converges to the stationary solution of the heat equation,
namely to the linear profile of the density. In the same regime the
macroscopic current in the stationary state is given by the Fick's
law, with the diffusion coefficient determined by the Green-Kubo
formula. The results presented are obtained in collaboration with
G. Basile, F. Pezzotti and M. Pulvirenti.