  There had been consensus on what the accurate ac quantum transport theory was
until some recent works challenged the conventional wisdom. Basing on the
non-equilibrium Green's function formalism for time-dependent quantum
transport, we derive an expression for the dynamic admittance that satisfies
gauge invariance and current continuity, and clarify the key concept in the
field. The validity of our now formalism is verified by first-principles
calculation of the transient current through a carbon-nanotube-based device
under the time-dependent bias voltage. Moreover, the previously well-accepted
expression for dynamic admittance is recovered only when the device is a
perfect conductor at a specific potential.
