Stability of a Vortex in a Trapped Bose-Einstein Condensate

In the large-condensate (Thomas-Fermi) limit, an analytical solution of the Bogoliubov equations and a time-dependent variational analysis both show that a vortex in a trapped Bose-Einstein condensate has a formally unstable normal mode with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, this solution becomes stable above an angular velocity $\Omega_m$ that characterizes the onset of metastability with respect to small transverse displacements of the vortex from the central axis.