Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.