  We report a theory for analyzing nonlinear DC transport properties of
mesoscopic or nanoscopic normal-superconducting (N-S) systems. Special
attention was paid such that our theory satisfies gauge invariance. At the
linear transport regime and the sub-gap region where the familiar scattering
matrix theory has been developed, we provide confirmation that our theory and
the scattering matrix theory are equivalent. At the nonlinear regime, however,
our theory allows the investigation of a number of important problems: for N-S
hybrid systems we have derived the general nonlinear current-voltage
characteristics in terms of the scattering Green's function, the second order
nonlinear conductance at the weakly nonlinear regime, and nonequilibrium charge
pile-up in the device which defines the electrochemical capacitance
coefficients.
