Diffusion on random comblike structures: field-induced trapping effects

An analytic study of diffusion in random comblike structures in which field-induced trapping effects enter into play is presented. In order to mimic at best a percolation cluster above pc, the distribution of the lengths of the branches is taken as exponential. The branches act as traps of efficiency growing with the applied bias. The asymptotic behaviour at large time of the probability of presence of the particle at its initial site and on the backbone, and of its position and dispersion are computed in an exact manner. As a result, when the field exceeds a certain critical value, anomalous behaviours emerge, characterized by exponents depending continuously on the field.