Nonequilibrium Transport-Equation For Nonlocal Impurity Self-Energy Within With Keldysh Formalism

We derive a relationship between the nonequilibrium particle distribution function and the scattering distribution function with nonlocal self-energy due to random impurity scattering. Using this relationship, we obtain a transport equation for mesoscopic devices that contains both known and random elastic scatterers. We show that for arbitrary applied bias, our equation resembles Buttiker's equation for coherent transport with continuous voltage probes.