Bulk Mediated Surface Diffusion: Non Markovian Desorption with Finite First Moment

TL;DR

This paper investigates the surface diffusion of molecules with non-Markovian desorption dynamics, providing analytical solutions and validating them with Monte Carlo simulations to understand the effective diffusion process at interfaces.

Contribution

It introduces an analytical framework for non-Markovian desorption in surface diffusion, extending traditional Markovian models and validating results with simulations.

Findings

Analytical expressions for surface dispersion over time.

Excellent agreement between theory and Monte Carlo simulations.

Insights into non-Markovian effects on surface diffusion dynamics.

Abstract

Here we address a fundamental issue in surface physics: the dynamics of adsorbed molecules. We study this problem when the particle's desorption is characterized by a non Markovian process, while the particle's adsorption and its motion in the bulk are governed by a Markovian dynamics. We study the diffusion of particles in a semi-infinite cubic lattice, and focus on the effective diffusion process at the interface $z = 1$. We calculate analytically the conditional probability to find the particle on the $z=1$ plane as well as the surface dispersion as functions of time. The comparison of these results with Monte Carlo simulations show an excellent agreement.