  The nonstationary and steady-state transport through a mesoscopic sample
connected to particle reservoirs via time-dependent barriers is investigated
within the reduced density operator method. The generalized Master equation is
solved via the Crank-Nicolson algorithm by taking into account the memory
kernel which embodies the non-Markovian effects that are commonly disregarded.
We propose a physically reasonable model for the lead-sample coupling which
takes into account the match between the energy of the incident electrons and
the levels of the isolated sample, as well as their overlap at the contacts.
Using a tight-binding description of the system we investigate the effects
induced in the transient current by the spectral structure of the sample and by
the localization properties of its eigenfunctions. In strong magnetic fields
the transient currents propagate along edge states. The behavior of populations
and coherences is discussed, as well as their connection to the tunneling
processes that are relevant for transport.
