Anomalous diffusion of cold atoms in an atomic trap
David Kessler, Bar Ilan University
We discuss the problem of diffusion of cold atoms in an atomic trap. In the
semiclassical limit, this problem is equivalent to independent particles
undergoing a weakly biased random walk in momentum space. The tails of the
momentum distribution are determined by the 1/p fall-off of the bias, and have a
power-law decay. This gives rises to anomalous behavior if the exponent of the
power-law is sufficiently small in magnitude. Then, the equilibrium prediction
is that the average kinetic energy is infinite, which is clearly unphysical.
Instead, the system never reaches equilibrium, and the distribution is cut off
at distances of order sqrt(t), rendering all moments finite, but growing in
time. We show how a harmonic oscillator with a randomly varying (positive)
stiffness gives rise to the same phenomenon. Returning to the atomic trap, we
consider the resulting distribution of the atomic positions, which is a cut-off
Levy distribution. Finally, we discuss the comparison to experiment.