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 t here exists a correspondence between the spectral properties of the ex act 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 th e second quantization of the mean field, which generates the exact dyn amics of the quantum N-body system, and the first qnantization of clas sical canonical coordinates. The limit of infinite density and the the rmodynamic limit are then briefly discussed.