Dispersion of particles in periodic media

We discuss the long-time properties of the dispersion of particles in periodic media, using the random walk formalism. Exact asymptotic results are obtained for the average velocity and the diffusion coefficient, expressed in terms of the Green's function of the random walk inside the periodically repeated unit cell. We explicitly calculate the transport coefficients for several specific cases of interest, including a system with dead zones, a simple model for field-induced trapping, and a one-dimensional map leading to deterministic diffusion.