Bulk mediated surface diffusion: non Markovian desorption with finite first moment

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