Condensates beyond mean field theory: quantum backreaction as   decoherence
  We propose an experiment to measure the slow log(N) convergence to mean-field theory (MFT) around a dynamical instability. Using a density matrix formalism, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break-time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state. 
Amichay Vardi and James R. Anglin