Anomalous spatial diffusion and multifractality in optical lattices

TL;DR

This paper develops a generalized non-Markovian diffusion equation for cold atoms in optical lattices, revealing anomalous diffusion and multifractality in their spatial distribution through a systematic expansion approach.

Contribution

It introduces a projector operator method to derive a generalized Smoluchowski equation capturing nonstationary, non-Markovian transport phenomena in optical lattices, including multifractal analysis.

Findings

Identification of anomalous, nonstationary diffusion behavior

Derivation of a systematic expansion for higher-order derivatives

Analysis of multifractal properties of spatial distribution

Abstract

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.