Multimode model for an atomic Bose-Einstein condensate in a ring-shaped optical lattice

We study the population dynamics of a ring-shaped optical lattice with a high number of particles per site and a low, below ten, number of wells. Using a localized on-site basis defined in terms of stationary states, we were able to construct a multiple-mode model depending on relevant hopping and on-site energy parameters. We show that in case of two wells, our model corresponds exactly to the latest improvement of the two-mode model. We derive a formula for the self-trapping period, which turns out to be chiefly ruled by the on-site interaction energy parameter. By comparing to time dependent Gross-Pitaevskii simulations, we show that the multimode model results can be enhanced in a remarkable way over all the regimes by only renormalizing such a parameter. Finally, using a different approach which involves only the ground state density, we derive an effective interaction energy parameter that shows to be in accordance with the renormalized one.