Dynamics of particles and manifolds in a quenched random force field

Details Dynamics of particles and manifolds in a quenched random force field Dynamics of particles and manifolds in a quenched random force field

1996-12-09

arxiv.org/abs/cond-mat/9612079v1

Europhys. Lett. vol 39 p 111 (1997)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, Latex file

Scientific paper

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.

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