Driven periodic structures in random environment

Abstract
We consider a lattice driven in a random environment and analyse its large-scale dynamics in the context of the driven vortex configuration. Using a perturbative coarse-graing procedure, we derive explicitely renormalized equation of motion, including Kardar-Parizi-Zhang nonlinearities and dynamic strain terms. From the generalized Lindemann criterion for the fluctuations of the neighboring sites the temperature shift of the dynamic melting is found to scale proportional to the strength of the disorder and inversly proportional to large driving forces. The presence of dislocations leads to a characteristic anisotropic distortion of the vortex density that is controlled by a Kardar-Parisi-Zhang nonlinearity in the coarse-grained equation of motion. This nonlinearity also implies a screening of the interaction between dislocations and thereby an instability of the vortex lattice to the proliferation of free dislocations.