Time-Dependent Transport through a Mesoscopic Structure

We present a general formulation of the nonlinear, time-dependent current through a small interacting region, where electron energies are changed by time-dependent voltages. An exact solution is obtained for the non-interacting case when the elastic coupling to the leads is independent of energy. Temporal phase coherence in a double-barrier tunneling structure produces ``ringing" in the response of the current to a voltage pulse, which can be observed experimentally in the dc-current by varying the pulse length in a train of voltage pulses. The nonlinear current due to an ac-bias also shows complex time-dependence.