From subdiffusion to superdiffusion of particles on solid surfaces

TL;DR

This study explores diverse diffusion behaviors of particles on surfaces using Langevin dynamics, revealing how potential type and damping influence superdiffusion, subdiffusion, and other diffusion regimes.

Contribution

It provides a combined numerical and analytical analysis of diffusion regimes on surfaces with periodic or random potentials, highlighting the emergence of complex behaviors from simple Langevin equations.

Findings

Superdiffusion occurs at low damping and is often transient.

Subdiffusion is linked to high damping and can be metastable.

Rich diffusion behaviors naturally arise from Langevin dynamics with Maxwell-Boltzmann statistics.

Abstract

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.