Dephasing in two decoupled one-dimensional Bose-Einstein condensates and   the subexponential decay of the interwell coherence
  We provide a simple physical picture of the loss of coherence between two coherently split one-dimensional Bose-Einstein condensates. The source of the dephasing is identified with nonlinear corrections to the elementary excitation energies in either of the two independent condensates. We retrieve the result by Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on the subexponential decay of the cocherence for the large time, however, the scaling of the characteristic decoherence time differs. 
I.E. Mazets, J. Schmiedmayer