Anomalous spatial diffusion and multifractality in optical lattices

Andreas Dechant, Eric Lutz

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Article number230601
JournalPhysical review letters
Issue number23
Publication statusPublished - 2012 Jun 8
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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