Deformed Gaussian orthogonal ensemble analysis of the interacting boson model

A deformed Gaussian orthogonal ensemble (DGOE) which interpolates between the Gaussian orthogonal ensemble and a Poissonian ensemble is constructed. This ensemble is applied to the analysis of the chaotic properties of the low lying collective states of nuclei described by the interacting boson model (IBM). This model undergoes a transition order-chaos-order from the SU(3) limit to the O(6) limit. It is shown that the quantum fluctuations of the IBM Hamiltonian follow the behavior predicted by the DGOE when one goes from one limit to the other.