  We study effects of relaxation/decoherence processes on quantum transport of
non-interacting Fermi particles across the tight-binding chain, where we
distinguish between relaxation processes in the contacts (external decoherence)
and those in the chain (internal decoherence). It is argued that relaxation
processes in the contacts can essentially modify the resonant transmission as
compared to the Landauer theory. We also address quantum transport in
disordered chains. It is shown that external decoherence reduces conductance
fluctuations but does not alter the Anderson localization length. This is in
strong contrast with the effect of internal decoherence which is found to
suppress the Anderson localization.
