  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.
