Anisotropic thermally activated diffusion in percolation systems

TL;DR

This paper investigates anisotropic thermally activated diffusion in a 2D percolation system, revealing temperature-dependent behaviors and characteristic frequencies with direction-specific activation energies.

Contribution

It introduces a model for anisotropic diffusion considering temperature effects and calculates characteristic frequencies with distinct activation energies in each direction.

Findings

Static diffusion exhibits Arrhenius behavior at low temperatures.

Characteristic frequency $\omega_c$ also follows Arrhenius behavior.

Different activation energies are observed in each spatial direction.

Abstract

We present a study of static and frequency-dependent diffusion with anisotropic thermally activated transition rates in a two-dimensional bond percolation system. The approach accounts for temperature effects on diffusion coefficients in disordered anisotropic systems. Static diffusion shows an Arrhenius behavior for low temperatures with an activation energy given by the highest energy barrier of the system. From the frequency-dependent diffusion coefficients we calculate a characteristic frequency $\omega_{c}\sim 1/t_{c}$, related to the time $t_c$ needed to overcome a characteristic barrier. We find that $\omega_c$ follows an Arrhenius behavior with different activation energies in each direction.