Spectral properties of quantum $N$-body systems versus chaotic   properties of their mean field approximations
  We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum $N$-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed. 
Patrizia Castiglione, Giovanni Jona-Lasinio, and Carlo Presilla