Correlated random walks with random hopping rates

Abstract

A concentration c of particles undergo correlated random walks on a lattice. The random walks are constrained by only allowing the lattice sites to be singly occupied. This leads to the particles being 'dynamically' correlated. In addition to the dynamic correlations the hopping rates of the particles are disordered. The random hopping rates give rise to 'static' correlations. The resultant model is a many-body problem with disorder. Of principal interest are the new correlations that arise between a disordered random walk and a correlated random walk (CRW) and the effect these correlations have on the self-diffusion constant. The CRW is represented by a nonlinear master equation from which the diffusion constant is obtained by means of classical many-body Green functions. The dynamic correlations are represented by a two-particle Green function. The disorder is studied by means of the bond coherent potential approximation (BCPA). The disorder gives rise to a vertex correction to the two-particle Green function. The vertex correction is obtained by using the BCPA.