Order and Chaos in a generalized Interacting Boson Model

The spectra of a rotationaly invariant random Hamiltonian for a system of $N$ particles on 2 $j$ levels is examined. In the interacting boson model, $j$=0,2, and in the vibron model, $j$=0,1. Here a broader range of $j$ is considered. In spite of the random nature of the interaction, regular spectral structures emerge, such as rotational bands, spin-0 and maximum spin ground states, and smooth yrast lines. Signatures of rotational bands are present in both the structure of the spectra near the ground state and in the $B(E2)$ values. These spectral features are usually associated with collective states, yet the usual signatures of quantum chaos are present in the wave functions of the ground state and low lying states. An explanation is framed based on the statistical mechanics of a quantum gas.