The average jump rate and diffusion in disordered systems

The average jump rate for particles undergoing diffusion in disordered systems is calculated for arbitrary concentrations of particles. The disorder model considered is a combination of site-energy and barrier-energy disorder. Uniform and Gaussian distribution functions are used as examples. The average jump rate does not show Arrhenius behaviour in general, but can in particular cases. The tracer diffusion coefficient is deduced from the average jump rate in the low-concentration limit for the site-energy disorder model for which there are no spatial correlations in successive jumps. For models where spatial correlations do occur, expressions for the diffusion coefficient and the average jump rate can be used to obtain information about the correlations.