Weak-coupling approximations in non-Markovian transport

We study the transport properties of the Fano-Anderson model with non-Markovian effects, which are introduced by making one tunneling-rate energy dependent. We show that the non-Markovian master equation may fail if these effects are strong. We evaluate the stationary current, the zero-frequency current noise, and the occupation dynamics of the resonant level by means of a quantum master-equation approach within different approximation schemes and compare the results to the exact solution obtained by the scattering theory and Green's functions.