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

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.