Diffusion von einzelnen Teilchen und Gittergasen auf ungeordneten Gittern

In this PhD thesis diffusion of single particles and of lattice gases on arbitrary dimensional lattices is studied. Transitions of particles are allowed only between nearestneighbour sites with disordered transition rates. In the case of lattice gas diffusion, transitions to occupied sites are forbidden. No furt her interactions between lattice gas particles are taken into account. The aim of this thesis is a general analytical description of the single-particle and collective or chemical diffusion coefficient for different kinds of disorder models. For this purpose an effective medium theory for single-particle diffusion and symmetric transition rates is generalized by introducing weighted symmetrized rates. Monte Carlo simulations are performed to examine the validity of the approximations. An exact result is found for the diffusion coefficient of single particles on a linear choin. A first-passage time method is used to derive the diffusion coefficient. It is equivalent to a linear response theory. A phenomenological theory for the collective diffusion coefficient, introduced for example by metal physicists, is identified as an exact expression for an infinite dimensional lattice. The generalized eflective medium theory is consistent with the results in one and infinite dimensions and summarizes all known exact results for the studied problems. It becomes exact in the limits of very low and very large particle concentrations on linear chains for arbitrary disorder models and is identical to a mean-field solution for intermediate concentrations in the random-trap model. For arbitrary concentrations it becomes a better approximation with increasing dimension of the lattice. Mussawisade and the author applied the generalized effective medium theory to a model suggested by Limoge and Bocquet to describe the Arrhenian temperature dependence of single-particle diffusion in amorphous substances. In more detail single-particle and collective diffusion for the random-trap and the Miller-Abrahams model, of which both are based on disordered site energies, are investigated. Because of the disordered site energies they show a complicated behaviour of the collective diffusion coefficient as a function of particle concentration. Of special interest is the exponential distribution of site energies where collective diffusion is found even in the absence of a single-particle diffusion coefficient. The main effects that determine the behaviour of the collective diffusion are saturation of lattice sites with very deep site energies at low particle concentrations and blocking effects by occupied sites at large concentrations