  We study transport of fermions in a system composed of a short optical
lattice connecting two finite atomic reservoirs at different filling levels.
The average equilibration current through the optical lattice, for strong
lattice-reservoir coupling and finite temperatures, is calculated within the
Landauer formalism using a nonequilibrium Green's functions approach. We
moreover determine quantum and thermal fluctuations in the transport and find
significant shot-to-shot deviations from the average equilibration current. We
show how to control the atomic current by engineering specific optical lattice
potentials without requiring site-by-site manipulations and suggest the
realization of a single level model. Based on this model we discuss the
blocking effect on the atomic current resulting from weak interactions between
the fermions.
