Effective diffusion constant in a two dimensional medium of charged point scatterers

TL;DR

This paper derives exact expressions for the effective diffusion constant of a tracer in a 2D medium with charged point scatterers, revealing conditions under which diffusion vanishes, with implications for understanding transport in charged disordered systems.

Contribution

It provides the first exact results for the effective diffusion constant in a 2D system with charged scatterers, including both Yukawa and Coulomb interactions, under various configurations.

Findings

Diffusion constant obeys Vogel-Fulcher-Tammann law with Yukawa potential.

Exact results for Coulomb scatterers in equilibrium configurations.

Diffusion vanishes under certain conditions, indicating localization.

Abstract

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.