Wave-function entropy and dynamical symmetry breaking in the interacting boson model

The degree of chaos in the simplest interacting boson model (IBM-1) is compared with what we call the "dynamical symmetry content" of the system. The latter is represented by the information entropy of the eigenfunctions with respect to bases associated with dynamical symmetries of the IBM-1, and expresses thus the localization of actual eigenfunctions in these symmetry bases. The wave-function entropy is shown to be a sensitive tool for monitoring the processes of a single dynamical symmetry breaking or transitions between two and more symmetries. For the IBM-1 Hamiltonians studied here, the known features related to chaos, namely, the dependence of chaotic measures on the Hamiltonian parameters (position in the Casten triangle) and on the angular momentum, turn out to be correlated with the behavior of the wave-function entropy.