Time-dependent transport in interacting and non-interacting mesoscopic   systems
  We consider a mesoscopic region coupled to two leads under the influence of external time-dependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel- barrier heights, or to the gates which define the mesoscopic region. We derive, with the Keldysh nonequilibrium Green function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitrary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current is simply the integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, in close analogy to the time-independent result of Meir and Wingreen (PRL {\bf 68}, 2512 (1992)). Analytical and numerical results for the exactly solvable non-interacting resonant-tunneling system are presented. 
Antti-Pekka Jauho, Ned S.Wingreen, and Yigal Meir