Breakdown of time-dependent mean-field theory for a one-dimensional   condensate of impenetrable bosons
  We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference. 
M. D. Girardeau and E. M. Wright