  The ground state of a Bose-Einstein condensate in a two-dimensional trap
potential is analyzed numerically at the infinite-particle limit. It is shown
that the anisotropy of the many-particle position variance along the $x$ and
$y$ axes can be opposite when computed at the many-body and mean-field levels
of theory. This is despite the system being $100\%$ condensed, and the
respective energies per particle and densities per particle to coincide.
