  In this paper, we study the emergence of a Landauer transport regime from the
quantum-mechanical dynamics of free electrons in a disordered tight-binding
chain, which is coupled to finite leads with open boundaries. Both partitioned
and partition-free initial conditions are analyzed and seen to give rise, for
large enough leads, to the same spatially uniform quasi-steady-state current,
which agrees with the Landauer value. The quasi-steady-state regime is preceded
by a transient regime, which last for a time proportional to the length of the
disordered sample, and followed by recursions, after a time that is
proportional to the lead size. These theoretical predictions may be of interest
to future experiments on transport of fermionic ultra-cold atoms across optical
lattices. We also observe finite-size current oscillations, superimposed on the
quasi-steady-state, whose behavior depends crucially on the conditions
initially imposed on the system. Finally, we show how a time-resolved Kubo
formula is able to reproduce this Landauer transport regime, as the leads grow
bigger.
