  Static and dynamic properties of Bose-Einstein condensates in annular traps
are investigated by solving the many-boson Schr\"odinger equation numerically
accurately using the multiconfigurational time-dependent Hartree for bosons
method. We concentrate on weakly-interacting bosons exhibiting low depletion.
Analysis of the mean-field position variance, which accounts for the shape of
the density only, and the many-body position variance, which incorporates a
tiny amount of excitations through the reduced two-particle density matrix,
shows that the former behaves essentially as a quasi-one-dimensional quantity
whereas the latter as a two-dimensional quantity. This brings another dimension
to the physics of bosons in ring-shaped traps.
