Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion.

PHYSICAL REVIEW LETTERS(2017)

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Abstract
In this Letter, we present a measurement of the phase-space density distribution (PSDD) of ultracold Rb-87 atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function C-xv(t) builds up on a time scale related to the initial conditions of the ensemble and then decays asymptotically as a power law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte Carlo simulations of two distinct models of anomalous diffusion.
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Key words
diffusion,dynamics,correlation,power-law,position-velocity
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