Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) -- that the power spectrum is merely determined by the spectral form factor -- breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.

中文翻译：

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随机对角矩阵和可积台球中的功率谱和形状因子

由围绕表现出规则经典动力学的量子系统中功率谱的普遍行为的争议引发，我们专注于随机对角矩阵 (RDM) 模型，通常与泊松谱普遍性类相关联，并研究功率谱和形状因数受到 RDM 光谱两侧截断的影响。在对这两种统计量进行了非微扰描述后，我们进行了详细的渐近分析，以明确证明传统假设（位于争议的核心）——功率谱仅由频谱形状因子决定——分解为截断的光谱。这一观察结果具有重要意义，因为我们进一步认为具有可积经典动力学的有界量子系统是由严重截断而不是完整的 RDM 光谱描述的。半圆形和无理矩形台球的高精度数值模拟为这些结论提供了独立的支持。