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Non-equilibrium transport through a model quantum dot: Hartree-Fock approximation and beyond

The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree-Fock (HF) approximation, the transmission probability and the non-linear $I$-$V$ characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard-Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact $I$-$V$ characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model.