Dipole diffusion in a random electrical potential

TL;DR

This paper investigates the diffusion behavior of a dipole in a random electrical potential, deriving an effective model in the adiabatic limit and analyzing the diffusion constant and transition phenomena.

Contribution

It introduces an effective Langevin equation for dipole diffusion in a random potential, revealing static-determined dynamical transitions and anomalous diffusion characteristics.

Findings

Analytic expressions for the diffusion constant near the adiabatic limit.

Identification of a finite temperature dynamical transition.

Numerical validation of anomalous diffusion exponents at low temperatures.

Abstract

We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the dynamics of its position), one can reduce the coupled stochastic equations to an effective Langevin equation for a particle diffusing in an effective potential with a spatially varying and anisotropic local diffusivity $\kappa_{ij}$. Analytic results, close to the adiabatic limit, for the diffusion constant $\kappa_e$ are found in one dimension and a finite temperature dynamical transition is found. The system is also studied numerically. In particular, we study the anomalous diffusion exponent in the low temperature regime. Our findings strongly support the conclusion that the location of the dynamical transition and the anomalous diffusion exponents are determined by purely static considerations, i.e. they are independent of the relative values of the diffusion constants of the particle position and its dipole moment.