  We investigate the phase coherence of a trapped Bose-Einstein condensate that
undergoes a dynamical superfluid-insulator transition in the presence of a
one-dimensional optical lattice. We study the evolution of the condensate after
a sudden displacement of the harmonic trapping potential by solving the
Gross-Pitaevskii equation, and comparing the results with the prediction of two
effective 1D models. We show that, owing to the 3D nature of the system, the
breakdown of the superfluid current above a critical displacement is not
associated to a sharp transition, but there exists a range of displacements for
which the condensate can recover a certain degree of coherence. We also discuss
the implications on the interference pattern after the ballistic expansion as
measured in recent experiments at LENS.
