Dynamics of particles and manifolds in random force fields

¹ Laboratoire de Physique Théorique (Laboratoire Propre du CNRS, associé à l'Ecole Normale Supérieure et à l'Université Paris-Sud.) , Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris, France
² Laboratoire de Physique Théorique des Liquides (Laboratoire associé au CNRS.) 4 Place Jussieu, F-75005 Paris, France
³ Groupe de Physico-Chimie Théorique, ESPCI, 10 rue Vauquelin, F-75231 Paris, France Dipartimento di Scienze Fisiche, Università Federico II, Mostra d'Oltremare Pad. 19, I-80125 Napoli, Italy

Received: 12 December 1996
Accepted: 2 June 1997

Abstract

We study the dynamics of a directed manifold of internal dimension D in a d-dimensional quenched random force field. We obtain an exact solution for and a Hartree approximation for finite d. They yield a Flory-like roughness exponent ζ and a nontrivial anomalous diffusion exponent ν continuously dependent on the ratio of divergence-free (g_T) to potential (g_L) disorder strength. For the particle (D=0) our results agree with previous order RG calculations. The time-translational invariant dynamics for smoothly crosses over to the previously studied ultrametric aging solution in the potential case.