Traffic jams and hysteresis in driven one-dimensional systems

The driven underdamped chain of anharmonically interacting atoms in the sinusoidal external potential is studied. It is shown that due to the interatomic interaction the system exhibits hysteresis for any nonzero rate of changing of the dc driving force. Before the transition to the running state the system passes through the traffic-jam inhomogeneous state. The system behavior is explained with the help of two simple models, the discrete lattice-gas model with two states of atoms, and the continuum mean-field model based on the Fokker-Planck equation.