Anomalous spatial diffusion and multifractality in optical lattices

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.

5 pages, 3 figures

References in corpus (2)

• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Does a Brownian particle equilibrate?

Cited by in corpus (19)

• From the area under the Bessel excursion to anomalous diffusion of cold atoms
• Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
• Infinite densities for Lévy walks
• Scaling Green-Kubo relation and application to three aging systems
• Universal first-passage statistics of aging processes
• Deviations from Boltzmann-Gibbs equilibrium in confined optical lattices
• Large-deviations for spatial diffusion of cold atoms
• Transitions in the ergodicity of subrecoil-laser-cooled gases
• Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion
• Infinite density for cold atoms in shallow optical lattices
• Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs and equipartition: Statistics of confined cold atoms
• Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
• Strong anomalous diffusion of the phase of a chaotic pendulum
• Gas of sub-recoiled laser cooled atoms described by infinite ergodic theory
• Large rare fluctuations in systems with delayed dissipation
• Deviations from generalized Equipartition in Confined, Laser Cooled Atoms
• The available force in long-range interaction complex systems and its statistical physical properties
• Apparent multifractality of self-similar Lévy processes
• Complete Decomposition of Anomalous Diffusion in Variable Speed Generalized Lévy Walks