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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 mesoscopic region and the multiple electrodes connected to it, 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. PACS numbers: 73.63.Kv, 85.35.Ds, 73.23.Hk, 73.40.Gk.

Theory of Nonequilibrium Coherent Transport Through an Interacting Mesoscopic Region Weakly Coupled to Electrodes