Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency ω on the chemical potential μ, this is no longer true for a general potential V(r)rp. Our calculations suggest that for p>2, the precession frequency scales with μ as ω∼μ-2/p. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov-de Gennes) stability analysis by identifying the relevant precession mode dependence on μ but also through direct numerical computations of the vortex evolution in the large-μ, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.