  We consider a non-interacting one-dimensional gas accelerated by a constant
and uniform external field. The energy absorbed from the field is transferred
via elastic collisions to a bath of scattering obstacles. At gas-obstacle
encounters the particles of the gas acquire a fixed kinetic energy. The
approach to the resulting stationary state is studied within the Boltzmann
kinetic theory. It is shown that the long time behavior is governed by the
hydrodynamic mode of diffusion superposed on a convective flow. The diffusion
coefficient is analytically calculated for any value of the field showing a
minimum at intermediate field intensities. It is checked that the properly
generalized Green-Kubo formula applies in the non-equilibrium stationary state.
