Physics (Internal)

Anomalous Diffusion of Cold Atoms: Bessel Excursions and Levy Walks

This event is part of the Biophysics/Condensed Matter Seminar Series.

Abstract: The semiclassical theory of atoms undergoing Sisyphean cooling maps onto the problem of particles in a heat bath with a nonlinear friction force that falls as 1/p for large momentum p. At long times, this leads to a power-law distribution of momenta, which is cut off at order sqrt(t). This power-law momentum distribution implies an anomalous spatial distribution of particles. This latter distribution corresponds a specific kind of Levy walk, where the jump length is correlated to the time duration of the jump. This correlation is given by the distribution of the area under a Bessel excursion, a Bessel process that describes first returns to the origin at a given time. The Bessel process itself corresponds to the random fluctuations of the radius of a random walk in arbitrary dimension. We use all this to derive the time-dependence of the mean-squared displacement of the particles, which exhibits transitions as the strength of the cooling is varied.