The Large Scale Energy Landscapes of Randomly Pinned Objects

We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the Functional Renormalisation Group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.