  The ground state of a rotating Bose-Einstein condensate trapped in a
two-dimensional anharmonic--anisotropic potential is analyzed numerically at
the limit of an infinite number of particles. We find that the density breaks
up along the $x$ direction in position space and along the $p_y$ direction in
momentum space together with the acquisition of angular momentum. Side by side,
the anisotropies of the many-particle position variances along the $x$ and $y$
directions and of the many-particle momentum variances along the $p_y$ and
$p_x$ directions become opposite when computed at the many-body and mean-field
levels of theory. All in all, the rotating bosons are found to possess unique
correlations at the limit of an infinite number of particles, both in position
and momentum spaces, although their many-body and mean-field energies per
particle and densities per particle coincide and the condensate fraction is
100\%. Implications are briefly discussed.
