Eur. Phys. J. B 37, 205-212 (2004)
https://doi.org/10.1140/epjb/e2004-00048-6

Bulk mediated surface diffusion: finite bulk case

¹ Grupo de Física Estadística, Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Argentina
² Facultad de Matemáticas, Astronomía y Física, Universidad Nacional de Córdoba 5000 Córdoba, Argentina
³ Departament de Física, Universitat de les Illes Balears and IMEDEA, 07122 Palma de Mallorca, Spain

Corresponding author: ^a wio@imedea.uib.es

Received: 7 November 2003
Revised: 18 December 2003
Published online: 15 March 2004

Abstract

Within the framework of a Master Equation scheme, we address the dynamics of adsorbed molecules (a fundamental issue in surface physics) and study the diffusion of particles in a finite cubic lattice whose boundaries are at the z = 1 and the z = L planes where , while the x and y directions are unbounded. As we are interested in the effective diffusion process at the interface z = 1, we calculate analytically the conditional probability for finding the particle on the z = 1 plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement. These results show that: there exists an optimal number of layers that maximizes  on the interface; for a small number the layers the long-time effective diffusivity on the interface is normal, crossing over abruptly towards a subdiffusive behavior as the number of layers increases. 02.50.Ey Stochastic processes 05.10.Ln Monte Carlo methods 46.65.+g Random phenomena and media