  Nonequilibrium transport properties are determined exactly for an
adiabatically connected single channel quantum wire containing one impurity.
Employing the Luttinger liquid model with interaction parameter $g$, for very
strong interactions $g\lapx 0.2$, and sufficiently low temperatures, we find an
S-shaped current-voltage relation. The unstable branch with negative
differential conductance gives rise to current oscillations and hysteretic
effects. These non perturbative and non linear features appear only out of
equilibrium.
