Statistical Analysis Of Energy Spectrum In The Interaction Boson Model

The interacting boson model,which provides the direct correspondence between nuclear shape and dynamical symmetry,offers an often-used framework to study both shape phase tran-sition and quantum chaos in many-body systems.In this work,we have studied the evolutions of spectral fluctuations with excitation energy in the U(5)-SU(3)and SU(3)-O(6)transitions as well as the AW arc in the IBM based on two statistical schemes,the nearest-neighbor level spacing distribution P(S)and spectral rigidity ?₃(L).The calculated results indicate that the energy-dependence of the spectral fluctuations in different situations may be different but their features are closely related to the corresponding mean-field structures.Specifically,most of the changes in spectral fluctuations may be triggered near the stationary points.In particular,the effects of these stationary points in the deformed area of the phase diagram may be exhibited as the excited-state quantum phase transitions(ESQPTs).Therefore,the present results may not only provide important complements to the chaotic map of the IBM but also justify that the ESQPTs can be driven by the effects of the stationary points from a statistical point of view.In addition,the results also reveal the possible statistical signature of the approximate degeneracy near the AW arc,thus providing a statistical way to understand the related SU(3)quasidynami-cal symmetry in the IBM.The present study confirms again that the adopted statistical measures can be not only applied to reveal quantum chaos but also taken as the effective tools to analyze the evolutions of the excited state properties in a system.