  The study of time-dependent, many-body transport phenomena is increasingly
within reach of ultra-cold atom experiments. We show that the introduction of
spatially inhomogeneous interactions, e.g., generated by optically-controlled
collisions, induce negative differential conductance in the transport of atoms
in 1D optical lattices. Specifically, we simulate the dynamics of interacting
fermionic atoms via a micro-canonical transport formalism within both
mean-field and a higher-order approximation, as well as with time-dependent
DMRG. For weakly repulsive interactions, a quasi steady-state atomic current
develops that is similar to the situation occurring for electronic systems
subject to an external voltage bias. At the mean-field level, we find that this
atomic current is robust against the details of how the interaction is switched
on. Further, a conducting-to-nonconducting transition exists when the
interaction imbalance exceeds some threshold from both our approximate and
time-dependent DMRG simulations. This transition is preceded by the atomic
equivalent of negative differential conductivity observed in transport across
solid-state structures.
