Diffusion in random media as a problem of interacting Bose and Fermi fields

Diffusion on a percolative lattice is formulated as a theory of interacting Bose-Fermi fields. The effective medium approximation (EMA) of Odagaki and Lax (1981) is obtained directly from the functional integral and is used to provide an EMA approximation for the diffusion constant and the DC conductivity. Simple corrections to the usual EMA produce exponents near the percolation threshold that agree with the best available data for d=2 and 3. This agreement reveals a strong connection between the dynamics of percolative diffusion and percolation itself.