Multiple Collective Vibrations and Nonlinear Dynamics in Mean-Field Approaches

Abstract

We study the connection between the Fourier transforms of one- and two-body observations and the excitation of multiple vibrations. We show that one-body observables give information on the excitation of a single vibration while two-body operators are needed to measure the excitation of double vibrations. Therefore, while mean-field approaches correctly predict the excitation of a single vibration, the study of multiple vibrations requires the estimation of many-body observables which goes beyond the mean-field approximation. These findings are illustrated in an algebraical model.