Current bistability and hysteresis in strongly correlated quantum wires
  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. 
R. Egger, H. Grabert, A. Koutouza, H. Saleur and F. Siano