一类驱动SU系统的分形蝴蝶Floquet谱的生成（2）：本征态统计
Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems: Eigenstate Statistics
摘要：
一类受驱动SU（2）系统的Floquet谱显示出具有多重分形性质的蝴蝶图案。在这项工作中的Floquet本征态统计的这种关键的光谱行为的含义进行了研究。遵循理解时间无关系统能量本征态在Anderson转变点上的分形行为的方法，我们分析了多重分形Floquet谱的Floquet本征态的分布轮廓、平均值以及Floquet本征态的反参与比对数的方差。结果表明，Floquet本征态也具有分形行为，但与时间无关的Anderson跃迁模型有明显的不同。这促使我们提出了一种新的类型的随机酉矩阵合奏，称为“幂律随机带状酉矩阵”合奏，照亮Floquet本征态统计的临界驱动系统。基于所提出的随机矩阵模型的计算结果与我们的动力学算例在有无时间反演对称性的情况下的计算结果一致。
英文摘要：
The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior, but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose a new type of random unitary matrix ensemble, called "power-law random banded unitary matrix" ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
