A Dynamical Mean Field Theory for the Study of Surface Diffusion Constants

TL;DR

This paper develops a combined analytical and numerical dynamical mean field theory to study surface diffusion in lattice-gas models, effectively capturing collective and tracer diffusion behaviors in strongly interacting systems.

Contribution

The paper introduces a novel dynamical mean field theory for surface diffusion that integrates Monte Carlo simulations and analytical approximations, improving understanding of diffusion in complex systems.

Findings

The approach accurately predicts collective diffusion in strongly interacting systems.

Memory effects significantly influence tracer diffusion.

The method outperforms traditional Monte Carlo simulations for collective diffusion.

Abstract

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.