Multidimensional diffusion in random potentials.

Abstract

It is shown that, in the long-time limit, d-dimensional diffusion in a Gaussian random potential has the logarithm of the average population ln 〈P〉 growing as ${t}^{(2\mathrm{\ensuremath{-}}d/2)}$. The dimension d=4 is critical. For d\ensuremath{\ge}4, 〈P〉 only grows as a power of t. Numerical simulations have confirmed this result.