Finite Size Scaling Analysis of Biased Diffusion on Fractals

Abstract

Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on infinite system as a consequence of logarithmic diffusion. Within the scheme, logarithmic diffusion is proved on the basis of an analysis of various temporal scales such as first passage time moments and survival probability characteristic time. This confirms and puts on firmer basis previous renormalization group results. A careful study of the asymptotic occupation probabilities of different kinds of lattice points allows to elucidate the mechanism of trapping into dangling ends, which is responsible of the logarithmic time dependence of average displacement.