Effect of phase breaking on the ac response of mesoscopic systems

Recently, there have been a number of interesting experiments on the ac response of mesoscopic systems. An important question in this context concerns the characteristic frequency at which the conductance deviates from the dc value. Depending on the system under consideration, this frequency is determined by the following three parameters: the inverse of the average time an electron spends inside the device, the thermal frequency, and the inverse of the phase-breaking time. The theoretical work in this area has been largely based on the scattering formulation, which neglects phase-breaking processes. The purpose of this paper is to derive a more general formulation that allows us to incorporate phase breaking. This formulation is based on the nonequilibrium-Green's-function formalism and we use double-energy coordinates, which helps establish the relation to scattering theory. We illustrate the effect of phase breaking by two simple examples: a one-dimensional resonant-tunneling device with a single resonant level and a resonant-tunneling device with two resonant levels.