  Based on the nonequilibrium Green's function (NEGF), we develop a quantum
nonlinear theory to study time-dependent ac transport properties in the low
frequency and nonlinear bias voltage regimes. By expanding NEGF in terms of
time to the linear order in Wigner representation, we can explicitly include
the time-dependent self-consistent Coulomb interaction induced by external ac
bias. Hence this theory automatically satisfies two basic requirements, i.e.,
current conservation and gauge invariance. Within this theory, the nonlinear ac
current can be evaluated at arbitrarily large bias voltages under the low
frequency limit. In addition, we obtain the expression of time-dependent
current under the wide band limit and derive the relation between the nonlinear
electrochemical capacitance and the bias voltage, which are very useful in
predicting the dynamical properties of nanoelectronic devices. This quantum
theory can be directly combined with density functional theory to investigate
time-dependent ac transport from first-principles calculation.
