Deriving Landauer's result by using the master equation approach

We revisit the problem of two-terminal transport of non-interacting Fermi particles in a mesoscopic device. First, we generalize the transport problem by including into consideration relaxation processes in contacts (which are characterized by the contact self-thermalization rate $\gamma$) and then solve it by using the master equation approach. In the limit $\gamma\rightarrow0$ the obtained results are shown to reproduce those of the Landauer theory. Thus, the presented analysis proves correspondence between the Landauer and master-equation approaches to quantum transport, -- the problem which waited its solution for decades