  We study a special dynamical regime of a Bose-Einstein condensate in a
ring-shaped lattice where the populations in each site remain constant during
the time evolution. The states in this regime are characterized by equal
occupation numbers in alternate wells and non-trivial phases, while the phase
differences between neighboring sites evolve in time yielding persistent
currents that oscillate around the lattice. We show that the velocity
circulation around the ring lattice alternates between two values determined by
the number of wells and with a specific time period that is only driven by the
onsite interaction energy parameter. In contrast to the self-trapping regime
present in optical lattices, the occupation number at each site does not show
any oscillation and the particle imbalance does not possess a lower bound for
the phenomenon to occur. These findings are predicted with a multimode model
and confirmed by full three-dimensional Gross-Pitaevskii simulations using an
effective onsite interaction energy parameter.
