Normal and anomalous diffusion in random potential landscapes

TL;DR

This paper explores the conditions under which anomalous diffusion occurs in random potential landscapes, establishing a link between microscopic energy distributions and macroscopic transport properties, and clarifying when subdiffusion or superdiffusion can arise.

Contribution

It introduces a relation connecting effective diffusion and conductivity in random systems, revealing the specific conditions for subdiffusion and ruling out superdiffusion in such models.

Findings

Subdiffusion occurs if the mean Boltzmann factor diverges or percolation threshold is at unity.

Superdiffusion cannot occur in the studied models under any conditions.

The relation aids in understanding anomalous diffusion sources in random potential systems.

Abstract

A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous diffusion in random potential models. We show that subdiffusion is only possible either if the mean Boltzmann factor in the corresponding potential diverges or if the percolation concentration in the system is equal to unity (or both), and that superdiffusion is impossible in our system under any condition. We show also other useful applications of this relation.