  In this paper we deal with further recent developments, strictly connected to
the recent result obtained by Basile, Nota, Pezzotti and Pulvirenti. We
consider the Lorentz gas out of equilibrium in a weak coupling regime. Each
obstacle of the Lorentz gas generates a smooth radially symmetric potential
with compact support. We prove that the macroscopic current in the stationary
state is given by the Fick's law of diffusion. The diffusion coefficient is
given by the Green-Kubo formula associated to the generator of the diffusion
process dictated by the linear Landau equation.
