  A scissors mode of a rotating Bose-Einstein condensate is investigated both
theoretically and experimentally. The condensate is confined in an
axi-symmetric harmonic trap, superimposed with a small rotating deformation.
For angular velocities larger than $\omega_\perp/\sqrt2 $, where $\omega_\perp$
is the radial trap frequency, the frequency of the scissors mode is predicted
to vanish like the square root of the deformation, due to the tendency of the
system to exhibit spontaneous rotational symmetry breaking. Measurements of the
frequency confirm the predictions of theory. Accompanying characteristic
oscillations of the internal shape of the condensate are also calculated and
observed experimentally.

Statistical Mechanics