  Transport of cold atoms in shallow optical lattices is characterized by slow,
nonstationary momentum relaxation. We here develop a projector operator method
able to derive in this case a generalized Smoluchowski equation for the
position variable. We show that this explicitly non-Markovian equation can be
written as a systematic expansion involving higher-order derivatives. We use
the latter to compute arbitrary moments of the spatial distribution and analyze
their multifractal properties.
