  We report a scattering matrix theory for dynamic and nonlinear transport in
coherent mesoscopic conductors. In general this theory allows predictions of
low frequency linear dynamic conductance, as well as weakly nonlinear DC
conductance. It satisfies the conditions of gauge invariance and electric
current conservation, and can be put into a form suitable for numerical
computation. Using this theory we examine the third order weakly nonlinear DC
conductance of a tunneling diode.
