CONTINUUM DERRIDA APPROACH TO DRIFT AND DIFFUSIVITY IN RANDOM-MEDIA

By means of rather general arguments, based on an approach due to Derr ida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random media in whi ch the motion of the particles is controlled by molecular diffusion an d a local how field with known statistical properties. The power of th e Derrida method is that it uses the equilibrium probability distribut ion, which exists for each finite sample, to compute asymptotic behavi our at large times in the infinite medium. In certain cases, where thi s equilibrium situation is associated with a vanishing microcurrent, o ur results demonstrate the equality of the renormalization processes f or the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop orde r in perturbation theory in certain models. The technique can also be applied to media in which the diffusivity exhibits spatial fluctuation s. We derive a simple relationship between the effective diffusivity i n this case and that for an associated gradient drift problem that pro vides an interesting constraint on previously conjectured results.