Coulomb effects in open quantum dots within the random-phase approximation

The effect of electron-electron interactions on coherent transport in quantum dot systems is theoretically investigated by adapting the well-known random-phase approximation (RPA) to the nonequilibrium GreenKeldysh formalism for open mesoscopic systems. The contour-ordered polarization operator is computed in terms of the Green functions of the noninteracting system. We apply the proposed RPA-Keldysh scheme for studying Coulomb-modified Fano lines and dephasing effects in interferometers with side-coupled many-level dots. Our method allows us to treat on equal footing the decoherence induced by the intradot interaction and that by the Coulomb coupling to a nearby system. In the case of a single interferometer, we show that the intradot Coulomb interaction leads to a reduction of-the Fano line amplitude. From the analysis of the interaction self-energy, it follows that this effect originates in inelastic scattering processes in which electron-hole pairs are involved. The interplay between the interdot and the intradot interactions in decoherence is discussed for two nearby identical T-shaped interferometers. We also show that the intradot interaction does not prevent the observation of controlled dephasing due to a nearby charge detector, as long as the latter is subjected to a sufficiently large bias.