Defects, order, and hysteresis in driven charge-density waves

We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of channels of dislocations. These results are in qualitative accord with recent dynamical x-ray scattering experiments by Ringland et al. [Phys. Rev. Lett. 82, 1923 (1999)] and transport experiments by Lemay et al. [Phys. Rev. Lett. 83, 2793 (1999)].