  A model is developed describing the energy distribution of quasi-particles in
a quasi-one dimensional, normal metal wire, where the transport is diffusive,
connected between equilibrium reservoirs. When an ac bias is applied to the
wire by means of the reservoirs, the statistics of the charge carriers is
influence by the formed non-equilibrium. The proposed model is derived from
Green function formalism. The quasi-particle energy distribution is calculated
with a quantum diffusion equation including a collision term accounting for
inelastic scattering. The ac bias, due to high frequency irradiation, drives
the wire out of equilibrium. For coherent transport the photon absorption
processes create multiple photon steps in the energy distribution, where the
number of steps is dependent on the relation between the amplitude of the field
eV and the photon energy \omega. Furthermore we observe that for the slow field
regime, \omega \tau_D < 1, the photon absorption is highly time-dependent. In
the fast field regime \omega \tau_D > 1 this time-dependency disappears and the
photon steps in the distribution have a fixed value. When the wire is extended,
the transport becomes incoherent due to interaction processes, like
electron-electron interaction and electron-phonon interaction. These
interactions give rise to a redistribution of the quasi-particles with respect
to the energy. We focused on the fast field regime and concluded that the
strong interaction limit for both mechanisms gives the expected result. Strong
electron-phonon interaction forces the distribution function on every position
in the wire to become a Fermi function with the bath temperature, while strong
electron-electron interaction causes an effective temperature profile across
the wire and the distribution function on every position in the wire is a Fermi
function with an effective temperature.
