Variance of a Trapped Bose-Einstein Condensate

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.