  The correspondence between the steady state theory of current transfer and
scattering theory in a system of coupled tight-binding models of 1-dimensional
wires is explored. For weak interwire coupling both calculations give nearly
identical results, except at singular points associated with band edges. The
effect of decoherence in each of these models is studied using a generalization
of the Liouville-von Neuman equation suitable for steady-state situations. An
example of a single impurity model is studied in details, leading to a lattice
model of scattering off target that affects both potential scattering and
decoherence. For an impurity level lying inside the energy band, the
transmission coefficient diminishes with increasing dephasing rate, while the
opposite holds for impurity energy outside the band. The efficiency of current
transfer in the coupled wire system decreases with increasing dephasing.
