  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.
