Finite frequency current fluctuations and the self-consistent perturbation theory for electron transport through quantum dot

We have formulated the problem of electron transport through interacting quantum dot system in the framework of self-consistent perturbation theory, and show that the current conservation condition is guaranteed due to the gauge invariant properties of the Green’s functions and the generalized Ward identity. By using a generating functional for the statistics of the nonequilibrium system, we have obtained general formulae for calculating the current and the current fluctuations in the presence of arbitrary time-dependent potentials. As demonstration of application, we have studied the interaction effects on the finite frequency noise for electron resonant tunneling through an Anderson impurity, and obtained an analytical equation for the interaction effect on the finite frequency current noise within the Hartree approximation, which is an extension of the previous results obtained by Hershfield on zero frequency shot noise.