Weakly Nonlinear AC Response: Theory and Application

We report a microscopic and general theoretical formalism for electrical response which is appropriate for both DC and AC weakly nonlinear quantum transport. The formalism emphasizes the electron-electron interaction and maintains current conservation and gauge invariance. It makes a formal connection between linear response and scattering matrix theory at the weakly nonlinear level. We derive the dynamic conductance and predict the nonlinear-nonequilibrium charge distribution. The definition of a nonlinear capacitance leads to a remarkable scaling relation which can be measured to give microscopic information about a conductor.