Biased diffusion on random structures

We discuss topologically biased diffusion on random structures (e.g. a random comb, a percolation cluster) that are characterized by effective dangling ends. The distribution of lengths L of dangling ends determines the transport behaviour. For a power-law distribution (percolation cluster at p_c) diffusion is ultra-anomalously slow, the mean square displacement of a random walker varies with a power law of logr, while for exponential distributions (p>p_c) a dynamical phase transition occurs: above a critical bias field £c diffusion is anomalous and non-universal. We also consider diffusion in d= 2 percolation clusters at criticality under the influence of a n'we-dependent bias field E(t) = E₀ sin ωt. We discuss the mean displacement <x(t)> of a random walker and investigate strong nonlinear effects in the amplitude A(E₀,ω) of <.x(t)> by computer simulation.