Diffusion

Abstract

The classical field of statistical mechanics - the theory of diffusion processes - is still offering considerable challenge when the physical problems to be described by it are more "realistic" than those easily envisioned as simple random walk. In this lecture I shall present our recent results on diffusion processes in two wide classes of physical problems: i) Diffusion in dense quasi-two-dimensional adsorbates on surfaces of the crystals, where the interparticle interactions and the interaction with the host solid cannot be neglected and play a mutually complementary role. These phenomena can be conveniently called the dynamics in d = 2 + 1 dimensions. ii) Diffusion in the crystals containing topological (hue) defects, such as dislocations and disclinations. I shall present our results on use of the combined continuum theory of defects and the path integral approach to description of such diffusion processes. Possibility of generalization of these models for quantum particles will also be outlined.