Diffusion on a random lattice: Weak-disorder expansion in arbitrary dimension

Abstract

We consider a random-hopping model on a regular lattice. We describe a method of calculating the drift velocity, the diffusion tensor, and the conductivity. The method works for symmetric as well as for nonsymmetric hopping rates. We can use this way to obtain systematic weak-disorder expansions. In the symmetric case we compare the results of the expansion with those of the effective-medium approximation. In the nonsymmetric case, the expansion shows that the upper critical dimension is 2. At $d=2\mathrm{}$, we conjecture logarithmic corrections in the velocity.