Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled   Bose-Einstein Condensates
  We predict a dynammical classical superfluid-insulator transition (CSIT) in a Bose-Einstein condensate (BEC) trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly-coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the BEC center of mass oscillates with the relative phases of neighbouring condensates locked at the same (oscillating) value. For large displacements, the BEC remains localized on the side of the harmonic trap. This is caused by a randomization of the relative phases, while the coherence of each individual condensate in the array is preserved. The CSIT is attributed to a discrete modulational instability, occurring when the BEC center of mass velocity is larger than a critical value, proportional to the tunneling rate between adjacent sites. 
A. Smerzi, A. Trombettoni, P.G. Kevrekidis and A.R. Bishop