Biased diffusion on random structures

Abstract

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 logt, while for exponential distributions p ^c) a dynamical phase transition occurs: above a critical bias field E, diffusion is anomalous and non-universal. We also consider diffusion in d = 2 percolation clusters at criticality under the influence of a time-dependent bias field E(t) = E ₀ sin ωt. We discuss the mean displacement ⟨x(t)⟩ of a random walker and investigate strong nonlinear effects in the amplitude A(E ₀, ω) of ⟨x(t)⟩ by computer simulation.