Statistical Analysis Of The Excited-State Quantum Phase Transition

The excited-state quantum phase transition(ESQPT)describes the sudden changes in the properties of the many-body system as a function of the excitation energy.In recent years,the ESQPTs in nuclear system have attracted considerable attention and their preliminary signatures have been revealed in the transitional nuclei.The spectral statistics methods provide valuable tools to analyze the properties of nuclear collective states.In this work,three statistical methods including the nearest level spacing distribution (),the spectral rigidity ?3()and the transition intensities distribution ()have been applied to study the fluctuations in the spectra and 0 transition intensities in different types of ESQPT within the framework of the interacting boson model.The results indicate that the spectra in each phase involved in a given ESQPT would be regular if the whole spectrum is regular,such as the cases in the U(5)-O(6)ESQPTs and the SU(3)-O(6)-U(5)ESQPTs on the AW arc.In contrast,if the whole spectrum in a given ESQPT is chaotic,the spectrum in either the middle-energy phase or the high-energy phase would be chaotic but with the spectrum in the low-energy phase being always regular,such as those happened in the U(5)-SU(3)ESQPTs,the SU(3)-O(6)ESQPTs and the SU(3)-O(6)-U(5)ESQPTs off the AW arc.Therefore,the evolutional law of the collective spectra in the ESQPTs has been identified from the statistical point of view.