Dynamics of particles and manifolds in a quenched random force field

Abstract

We study the dynamics of a directed manifold of internal dimension D in a d-dimensional random force field. We obtain an exact solution for $d \to \infty$ and a Hartree approximation for finite d. They yield a Flory-like roughness exponent $ζ$ and a non trivial anomalous diffusion exponent $ν$ continuously dependent on the ratio $g_{T}/g_{L}$ of divergence-free ($g_{T}$) to potential ($g_{L}$) disorder strength. For the particle (D=0) our results agree with previous order $ε^2$ RG calculations. The time-translational invariant dynamics for $g_{T} >0$ smoothly crosses over to the previously studied ultrametric aging solution in the potential case.