Stability of a Vortex in a Trapped Bose-Einstein Condensate

Based on the method of matched asymptotic expansion and on a time-dependent variational analysis, we study the dynamics of a vortex in the large-condensate (Thomas-Fermi) limit. Both methods as well as an analytical solution of the Bogoliubov equations show that a vortex in a trapped Bose-Einstein condensate has formally unstable normal mode(s) with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, the solution becomes stable above an angular velocity $\Omega_m$ characterizing the onset of metastability with respect to small transverse displacements of the vortex from the central axis.