A continuum theory for vacancy-mediated diffusion, such as the vacancy-driven motion of tracers in crystals, was considered. Attention was restricted to ultra-low vacancy densities, so that a tracer experienced only a single vacancy over the time-scale of interest. Results were obtained for all spatial dimensions, and revealed the strongly non-Gaussian nature of tracer fluctuations. In integer dimensions, the results were in complete agreement with previous exact lattice calculations. The results had the advantage of being valid for arbitrary dimensions, thus revealing their analytical structure more clearly.

Continuum Theory of Vacancy-Mediated Diffusion. T.J.Newman: Physical Review B, 1999, 59[21], 13754-63