  We propose a simple quantum mechanical model describing the time dependent
diffusion current between two fermion reservoirs that were initially
disconnected and characterized by different densities or chemical potentials.
The exact, analytical solution of the model yields the transient behavior of
the coupled fermion systems evolving to a final steady state, whereas the
long-time behavior is determined by a power law rather than by exponential
decay. Similar results are obtained for the entropy production which is
proportional to the diffusion current.
