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 qnantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.