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We study the temporal evolution of a small number $N$ of ultra-cold bosonicatoms confined in a ring potential. Assuming that initially the system is in asolitary-wave solution of the corresponding mean-field problem, we identifysignificant differences in the time evolution of the density distribution ofthe atoms when it instead is evaluated with the many-body Schr\"odingerequation. Three characteristic timescales are derived: the first is the periodof rotation of the wave around the ring, the second is associated with a"decay" of the density variation, and the third is associated with periodic"collapses" and "revivals" of the density variations, with a factor of $\sqrtN$ separating each of them. The last two timescales tend to infinity in theappropriate limit of large $N$, in agreement with the mean-field approximation.These findings are based on the assumption of the initial state being amean-field state. We confirm this behavior by comparison to the exact solutionsfor a few-body system stirred by an external potential. We find that the exactsolutions of the driven system exhibit similar dynamical features.

Finite-size effects in the dynamics of few bosons in a ring potential