Finite Size Scaling Analysis of Biased Diffusion on Fractals

TL;DR

This paper investigates biased diffusion on fractal lattices using finite size scaling, confirming logarithmic diffusion behavior and elucidating trapping mechanisms affecting particle displacement.

Contribution

It introduces a finite size scaling approach to analyze biased diffusion on fractals, avoiding issues of divergence in traditional renormalization methods, and clarifies trapping effects.

Findings

Logarithmic diffusion confirmed on T fractals.

Finite size scaling avoids singularities in analysis.

Trapping into dangling ends causes logarithmic displacement.

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.