Asymptotic realization of the criterion for quantum integrability of a boson system with dynamical symmetry

Abstract

The authors investigate the energy-level statistics in dependence on the boson number and the underlying classical motion for a system of collective states of zero angular momentum in gamma -soft nuclei described in the framework of the O(6) dynamical symmetry of the interacting boson model. This presents a relatively complex test case for relations between classical regular/chaos, dynamical symmetry and energy-level statistics. The classical limit is integrable due to an additional constant of motion Py, but the corresponding quantal energy-level statistics in the range of realistic parametrization is close to Gaussian orthogonal ensemble statistics. However, the boson number NB, which plays the role of Planck constant in semiclassical approximation, appears as a control parameter of quantum chaos, and the energy level statistics asymptotically approaches Poisson statistics with increasing boson number, i.e., with decreasing volume of the unit cell of quantum space.