  In this paper, we develop a nonequilibrium theory for transient electron
transport dynamics in nanostructures based on the Feynman-Vernon influence
functional approach. We extend our previous work on the exact master equation
describing the non-Markovian electron dynamics in the double dot [Phys. Rev.
B78, 235311 (2008)] to the nanostructures in which the energy levels of the
central region, the couplings to the leads and the external biases applied to
leads are all time-dependent. We then derive nonperturbatively the exact
transient current in terms of the reduced density matrix within the same
framework. This provides an exact non-linear response theory for quantum
transport processes with back-reaction effect from the contacts, including the
non-Markovian quantum relaxation and dephasing, being fully taken into account.
The nonequilibrium steady-state transport theory based on the Schwinger-Keldysh
nonequilibrium Green function technique can be recovered as a long time limit.
For a simple application, we present the analytical and numerical results of
transient dynamics for the resonance tunneling nanoscale device with a
Lorentzian-type spectral density and ac bias voltages, where the non-Markovian
memory structure and non-linear response to the bias voltages in transport
processes are demonstrated.
