Quantum dynamics of bosons in a double-well potential: Josephson   oscillations, self-trapping and ultralong tunneling times
  The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations. 
A. N. Salgueiro, A. F. R. de Toledo Piza, G. B. Lemos, R. Drumond, M.   C. Nemes and M. Weidemueller