Analytic study of a model of biased diffusion on a random comblike structure

An analytic study of a model of biased diffusion on a random comblike structure in which a bias field exists along the backbone is presented. The asymptotic behaviour at large time of the average probability of presence of the particle at its initial site is calculated directly in an exact manner. As for the particle position and dispersion, they are first computed in a periodized system of arbitrary period N. The corresponding quantities for the random system are then obtained by taking the limit N → ∞. The general features of the results strongly depend on the distribution of the lengths of the branches. While for an exponential distribution transport properties are normal, anomalous drift and diffusion may take place for a power law distribution when long branches are present with sufficiently high weights.