  We investigate the nonstationary electronic transport in noninteracting
nanostructures driven by a finite bias and time-dependent signals applied at
their contacts to the leads. The systems are modelled by a tight-binding
Hamiltonian and the transient currents are computed from the non-equilibrium
Green-Keldysh formalism. The numerical implementation is not restricted to weak
coupling to the leads and does not imply the wide-band limit assumption for the
spectral width of the leads. As an application of the method we study in detail
the transient behavior and the charge dynamics in single and double quantum
dots connected to leads by a step-like potential, but the method allows as well
the consideration of non-periodic potentials or short pulses. We show that when
the higher energy levels of the isolated system are located within the bias
window of the leads the transient current approaches the steady state in a
non-oscillatory smooth fashion. At moderate coupling to the leads and fixed
bias the transient acquires a step-like structure, the length of the steps
increasing with the system size. The number of levels inside a finite bias
window can be tuned by a constant gate potential. We find also that the
transient behavior depends on the specific way of coupling the leads to the
mesoscopic system.
