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

We formulate the problem of electron transport through an interacting quantum dot system in the framework of the self-consistent perturbation theory of the nonequilibrium Green's function and show that the current conservation through the central region is automatically guaranteed owing to the gauge-invariant properties of the resulting Green's functions and the generalized Ward identity. By using a generating functional for the statistics of the nonequilibrium system, we obtain general formulas for calculating the current and the current fluctuations in the presence of arbitrary time-dependent potentials. As an illustration of application, we study the interaction effects on the finite-frequency noise for electron resonant tunneling through an Anderson impurity and obtain an analytical expression for the finite-frequency current noise within the Hartree approximation, which is an extension of the results obtained by Hershfield on zero-frequency shot noise.