Linear-response formulation for mesoscopic systems with arbitrary interactions

In this paper we derive a linear-response equation starting from the nonequilibrium Green-function formalism that can be used to calculate the current in mesoscopic systems described by arbitrary self-energy functions. Current conservation is ensured regardless of the approximation used for the self-energy. We also obtain explicit expressions for the transmission T̃ \~ᵢⱼ from terminal j to terminal i and present a simple illustrative example calculating T̃ \~ᵢⱼ for a short single-moded electron waveguide with electron-phonon interactions. An important difference between the present formulation and usual linear-response theory is that the electrochemical potential difference is treated as the driving force; however, we do not neglect the self-consistent fields that appear in an interacting system when a small bias is applied. This work generalizes our earlier results (which were derived for phonon scattering in the self-consistent Born approximation) to arbitrary interactions.