Driven dynamics of periodic elastic media in disorder

We analyze the large-scale dynamics of vortex lattices and charge-density waves driven in a disordered potential. Using a perturbative coarse-graining procedure, we present an explicit derivation of nonequilibrium terms in the renormalized equation of motion, in particular Kardar-Parisi-Zhang nonlinearities and dynamic strain terms. We demonstrate the absence of glassy features such as diverging linear friction coefficients and transverse critical currents in the drifting state. We discuss the structure of the dynamical phase diagram containing different elastic phases at very small and very large drives, and plastic phases at intermediate velocity.