We consider the time dependent dynamics of an atom in a two-color pumped
cavity, longitudinally through a side mirror and transversally via direct
driving of the atomic dipole. The beating of the two driving frequencies leads
to a time dependent effective optical potential that forces the atom into a
non-trivial motion, strongly resembling a discrete random walk behavior between
lattice sites. We provide both numerical and analytical analysis of such a
quasi-random walk behavior