Mesoscopic transport at finite frequencies

Abstract

We derive a set of equations that describe electrical transport in mesoscopic systems, at finite frequencies. The electron-electron interactions are treated at the level of a self-consistent field. It is shown that the static limit corresponds to frequencies ω smaller than the inverse passage time ${\mathrm{\tau }}_{\mathit{L}}^{\mathrm{-}1}$ through the system. In this limit, the conductance is not affected by the complicated self-consistent field due to the current flow, in agreement with earlier results. However, for frequencies greater than ${\mathrm{\tau }}_{\mathit{L}}^{\mathrm{-}1}$ the transport equations for current, charge, and potential become strongly coupled and it is no longer possible to ignore the self-consistent field in the calculation of conductance.