We study D-dimensional elastic manifolds driven by ac-forces in a
disordered environment using a perturbation expansion in the disorder strength
and the mean-field approximation. We find, that for D≤4 perturbation
theory produces non-regular terms that grow unboundedly in time. The origin of
these non-regular terms is explained. By using a graphical representation we
argue that the perturbation expansion is regular to all orders for D>4.
Moreover, for the corresponding mean-field problem we prove that ill-behaved
diagrams can be resummed in a way, that their unbounded parts mutually cancel.
Our analytical results are supported by numerical investigations. Furthermore,
we conjecture the scaling of the Fourier coefficients of the mean velocity with
the amplitude of the driving force h.Comment: 23 pages, substantial changes, replaced with the published versio