Quantum chaos for exact and brokenKquantum number in the interacting-boson model

We show that the exact K quantum number in the SU(3) limit of the interacting-boson model has a strong effect on the fluctuation properties: Pure sequences of a single K value have Δ₃ statistic close to the Gaussian overlap ensemble prediction while mixed sequences with combined K values are removed far from the Gaussian overlap ensemble because of K degeneracy, exceeding even the Poisson-ensemble prediction. Applying the extended interacting boson model to the realistic case of ¹⁶⁴Er nucleus, we have demonstrated that weak breaking of the K quantum number introduces a very rapid change in fluctuation properties towards those of a pure sequence.