Weak Non Self-Averaging Behaviour for Diffusion in a Trapping Environment

TL;DR

This paper investigates diffusion in trapping environments modeled by percolating clusters, revealing weak non self-averaging behavior and deviations from standard scaling laws in critical exponents.

Contribution

It demonstrates that diffusion in percolating clusters exhibits weak non self-averaging and non-standard scaling of correlation functions, providing new insights into trapping environments.

Findings

Number of N-step walks follows a log-normal distribution

Variance grows faster than the mean, indicating weak non self-averaging

Critical exponents do not obey standard scaling laws

Abstract

The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a log-normal distribution with a variance growing asymptotically faster than the mean which leads to a weak non self-averaging behaviour. Critical exponents associated with the scaling of the two-points correlation function do not obey standard scaling laws.