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Second-order post-Hartree-Fock perturbation theory for the electron current

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties. We find that the nonequilibrium leads to enhancement of electronic correlations.