Laboratoire de Physique Théorique
Toulouse - UMR 5152

Results on the calculation the long time self diffusion constant of a Brownian particle in a random environment are reviewed. We concentrate on the case of diffusion in a force field generated by a quenched random potential and the case of diffusion in a environment with a quenched, spatially varying, random diffusivity. Mathematical relations between these two problems and exact results in low dimensions are discussed as well as approximative perturbation schemes for these computations. Numerical techniques used in the simulation of these systems are also discussed.