We study the collective modes of a Bose-Einstein condensate subject to an
optically induced density-dependent gauge potential. The corresponding
interacting gauge theory lacks Galilean invariance, yielding an exotic
superfluid state. The nonlinear dynamics in the presence of a current
nonlinearity and an external harmonic trap are found to give rise to dynamics
which violate Kohn's theorem; where the frequency of the dipole mode strongly
depends on the strength of the mass current in the gas. The linearised spectrum
reveals how the centre of mass and shape oscillations are coupled, whereas in
the strongly nonlinear regime the dynamics is irregular.Comment: General improvements, corrections and references adde
