Steady-state quantum kinetic equation

Starting from the Dyson equation in the Keldysh formulation, we derive a kinetic equation for steady-state quantum transport under the simplifying assumption that the inelastic scattering is caused by uncorrelated point scatterers, such as impurities with internal degrees of freedom. This assumption allows us to write a transport equation that involves only the electron density and not the spatial correlations of the wave function. Assuming local thermodynamic equilibrium we then simplify the transport equation to a form which resembles the Büttiker-Landauer formula extended to include a continuous distribution of probes.