Anomalous transport in disordered media
Disordered and fractal structures play an important role in composite electrolytes, heterogeneous catalysis, and mixed alkali conductors. Here we study how these structures influence the diffusive motion of Brownian particles for various types of jump rates between neighbouring sites, including constant rates and rates chosen from a power law distribution. We discuss the meansquare displacement of the particles and the frequency-dependent conductivity. The transport behaviour is very rich when in addition strong bias fields are applied. Here the paradox of “ultra-anomalously” slow motion can occur where the motion is dramatically slowed down with increasing field strength.