Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully   Dynamical Number-Conserving Approach
  We consider a Bose-Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion in our fully-time-dependent, second-order description acts to damp this growth, leading to oscillations in the (non)condensate population and the coherence of the system. 
T. P. Billam and S. A. Gardiner
cond-mat.quant-gas