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
