Finite-size effects in the dynamics of few bosons in a ring potential
arXiv:1706.00859 · doi:10.1088/1361-6455/aaa05c
Abstract
We study the temporal evolution of a small number of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schrödinger equation. Three characteristic timescales are derived: the first is the period of 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 separating each of them. The last two timescales tend to infinity in the appropriate limit of large , in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.
To appear in Journal of Physics B
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