Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates
arXiv:1106.5764 · doi:10.1016/j.physleta.2011.06.061
Abstract
We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.
8 pages, 3 figures, to appear in Phys. Lett. A