Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number (n)-resolved master equation (ME) approach under the self-consistent Born approximation (SCBA) for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes beyond the scope of the Born-Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise. We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.