2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132035The present work is based on the nonequilibrium perturbative formalism. There the self-energies are derived up to the forth-order. In consequence, it proves that the nonequilibrium (real-time) perturbative expansion can be connected with the Matsubara imaginary-time perturbative expansion for equilibrium. As the numerical results, the Kondo resonance still disappears for bias voltage exceeding the Kondo temperatures, as observed in experiments of two terminal systems.Some conclusions and typos are corrected;the derived expressions and numerical results are unchangedMesoscale and Nanoscale PhysicsStrongly Correlated Electronstext