The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P(S) measuring the chaoticity (regularity) in energy spectra, the Δ₃(L) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P(y) measuring the chaoticity (regularity) in B(E0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)–SU(3) and SU(3)–O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)–O(6) transitional region or those on the ‘Alhassid–Whelan arc’, which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM.

已在相互作用玻色子模型 (IBM) 的框架内通过采用三种统计测量方法研究了激发态量子相变 (ESQPT) 中的光谱涨落和跃迁强度涨落，包括最近邻能级间距分布P ( S ) 测量在能谱的chaoticity（规律性）中，Δ ₃（大号）戴森和梅塔的统计测量光谱的刚性和强度分布P（Ý）测量chaoticity（规律性）乙（Ë0) 过渡。结果表明，如果只有相关的整个光谱是混沌的，则作为激发能量的函数的 ESQPT 可能会发生从规则（或半规则）到高度混沌的转变，这适合 IBM 中的大多数变形情况，包括U(5)–SU(3) 和 SU(3)–O(6) 过渡区域。否则，ESQPT 将表现为从规则（或半规则）到规则的过渡，例如 U(5)-O(6) 过渡区域中的情况或“Alhassid-Whelan 弧”上的情况，这代表了几乎规则的IBM 中连接 U(5) 和 SU(3) 限制的参数区域。