The correspondence between the steady-state theory of current transfer and scattering theory in a system of coupled tight-binding models of one-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 detail, 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.
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