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 $\zeta$ and a non trivial anomalous diffusion exponent $\nu$ 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 ${\epsilon }^2$ 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.

5 pages, Latex file

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