Dynamics of manifolds in random media II: long range correlations in the disordered medium

In a previous publication, we investigated the dynamical behaviour of a fluctuating manifold in the framework of a Hartree type approximation. We now extend this calculation to the case of a medium with long range correlations in disorder. In the static limit, we recover solutions known from a replica calculation with hierarchical replica symmetry breaking. In the dynamical formulation this replica symmetry breaking is related to broken ergodicity on an infinite hierarchy of diverging time scales. We give the phase diagram for the model and discuss the dynamical behaviour in the different regimes