Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-09-17
J. Phys. A., 37, 10459 (2004)
Physics
Condensed Matter
Disordered Systems and Neural Networks
22 pages, 6 figures, IOP (J. Phys. A. style)
Scientific paper
10.1088/0305-4470/37/44/001
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.
Dean David S.
Drummond Ian T.
Horgan Ronald R.
Lefèvre Alexandre
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