  In this work, the spectral properties of a singly-charged vortex in a In this
work, the spectral properties of a singly-charged vortex in a Bose-Einstein
condensate confined in a highly anisotropic (disk-shaped) harmonic trap are
investigated. Special emphasis is given on the analysis of the so-called
anomalous (negative energy) mode of the Bogoliubov spectrum. We use analytical
and numerical techniques to illustrate the connection of the anomalous mode to
the precession dynamics of the vortex in the trap. Effects due to inhomogeneous
interatomic interactions and dissipative perturbations motivated by finite
temperature considerations are explored. We find that both of these effects may
give rise to oscillatory instabilities of the vortex, which are suitably
diagnosed through the perturbation-induced evolution of the anomalous mode, and
being monitored by direct numerical simulations.
