Quantum rate equations for electron transport through an interacting system in the sequential tunneling regime

We present a set of modified quantum rate equations, with the help of the nonequilibrium Green's function and slave-particle techniques along with the correct quantization, for description of the quantum transport through an interacting mesoscopic region connected with two leads, in the sequential tunneling regime. The assumption that only leading order of $|V|^2$ ($V$ is the tunneling coupling between the interacting central region and the leads) has been taken into account in deriving these equations implies that the quantum rate equations are only valid in the case of weak coupling between the central region and the leads. For demonstrations, we consider two special cases in the central region, a single interacting quantum dot (SQD) with weak spin-flip scattering and a weakly coupled double quantum dots (CQD), as examples. In the limit of zero temperature and large bias voltage, the resulting equations are identical to the previous results derived from the many-body Schr\"odinger equation. The numerical simulations reveal: 1) the dependence of the spin-flip scattering on the temperature and bias voltage in the SQD; and 2) the possible negative differential conductance and negative tunnel magnetoresistance in the CQD, depending on the hopping between the two quantum dots.