  A Bose-Einstein condensate in a tilted double-well potential under the
influence of time-periodic potential differences is investigated in the regime
where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some
parameters near stable regions, even averaging over several condensate
oscillations does not remove the differences between mean-field and N-particle
results. While introducing decoherence via piecewise deterministic processes
reduces those differences, they are due to the emergence of mesoscopic
entangled states in the chaotic regime.
