title: Anomalous spatial diffusion and multifractality in optical lattices.
abstract: The transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We 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.
authors.affiliation: Department of Physics, University of Augsburg, D-86135 Augsburg, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Dechant
authors.forename: Eric
authors.initials: E
authors.lastname: Lutz