MEAN-FIELD OUT OF CHAOS

The microscopic dynamics of a quantum many-body system is analyzed under the assumption that numerous complicated intermediate states in exact operator equations of motion are of chaotic nature and can be averaged out. The averaging procedure, preserving all kinematical constraints, is defined by the invariance with respect to phase transformations. The situation with no significant collective correlations is considered in detail. As a result, the mean-field theory (MFT) emerges accumulating the smooth component of the total random dynamics. The obtained version of the MFT differs from the Hartree-Fock approximation in taking into account the average effect of fluctuations. The mean-field representation is suggested to be a natural basis for estimating the degree of complexity of generic complicated wave functions.