Theory of nonequilibrium coherent transport through an interacting mesoscopic region weakly coupled to electrodes

We develop a theory for the nonequilibrium coherent transport through a mesoscopic region, based on the nonequilibrium Green function technique. The theory requires the weak coupling between the central rnesoscopic region and the multiple electrodes, but allows arbitrary hopping and interaction in the central region. An equation determining the nonequilibrium distribution in the central interacting region is derived and plays an important role in the theory. The theory is applied to two special cases for demonstrations, revealing the novel effects associated with the combination of phase coherence, Coulomb interaction, and nonequilibrium distribution.