On mean field theory for ac-driven elastic interfaces exposed to disorder

The analytic description of ac-driven elastic interfaces in random potentials is desirable because the problem is experimentally relevant. This work emphasises on the mean field approximation for the problem at zero temperature. We prove that perturbation theory is regular in all orders by giving an inductive scheme how to find groups of ill-behaved graphs that mutually cancel, leaving a regular expression. In the parameter regimes for which perturbation theory is applicable it agrees with numerical results. Further, we determine the dependence of the Fourier coefficients of the mean velocity on the parameters of the model.