Dynamics of particles and manifolds in a quenched random force field

TL;DR

This paper investigates the complex dynamics of particles and manifolds in a high-dimensional quenched random force field, providing exact and approximate solutions that reveal how disorder types influence roughness and diffusion behaviors.

Contribution

It offers an exact solution for infinite dimensions and a Hartree approximation for finite dimensions, elucidating the impact of disorder ratios on dynamical exponents.

Findings

Derived a Flory-like roughness exponent $z$

Identified a non-trivial anomalous diffusion exponent $$

Showed crossover from time-translational invariance to aging dynamics

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.