Transport on an annealed disordered lattice

TL;DR

This paper investigates how diffusion behaves on an annealed disordered lattice with dynamic bond reorganization, revealing critical behavior at the percolation threshold and deriving new scaling relations for diffusion properties.

Contribution

It introduces a novel analysis of diffusion on annealed disordered lattices with dynamic bonds, highlighting the role of singly connected bonds and establishing new scaling laws.

Findings

Rearrangement time scales as t_r ∼ τ^α with α ≠ 1.

Critical behavior of crossover time at the percolation threshold.

Scaling relations for diffusion coefficient dependence on renewal rate.

Abstract

We study the diffusion on an annealed disordered lattice with a local dynamical reorganization of bonds. We show that the typical rearrangement time depends on the renewal rate like $t_r \sim \tau^{\alpha}$ with $\alpha \neq 1$. This implies that the crossover time to normal diffusion in a slow rearrangement regime shows a critical behavior at the percolation threshold. New scaling relations for the dependence of the diffusion coefficient on the renewal rate are obtained. The derivation of scaling exponents confirms the crucial role of singly connected bonds in transport properties. These results are checked by numerical simulations in two and three dimensions.