FINITE-SIZE-SCALING ANALYSIS OF BIASED DIFFUSION ON FRACTALS

Diffusion on a T fractal lattice under the influence of topological bi asing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormal ization group approach on infinite system as a consequence of logarith mic diffusion. Within the scheme, logarithmic diffusion is proved on t he basis of an analysis of various temporal scales such as first passa ge time moments and survival probability characteristic time. This con firms and puts on firmer basis previous renormalization group results. A careful study of the asymptotic occupation probabilities of differe nt kinds of lattice points allows to elucidate the mechanism of trappi ng into dangling ends, which is responsible of the logarithmic time de pendence of average displacement.