论文标题
随机对角线矩阵和可整合台球的功率谱和外形
Power spectrum and form factor in random diagonal matrices and integrable billiards
论文作者
论文摘要
围绕具有常规经典动力学的量子系统中的电源谱的普遍行为引起的争议，我们专注于一个随机对角线矩阵（RDM）的模型，通常与Poisson频谱普遍性类别相关，并检查功率谱和形式如何受到RDM Spectra的双向截面的影响。在对两个统计数据进行了非扰动描述之后，我们进行了详细的渐近分析，以明确证明传统假设（躺在争议的核心）是如何仅由频谱形式确定的功率谱 - 截断的光谱分解。该观察结果具有重要的后果，因为我们进一步认为，具有整合经典动力学的有界量子系统由严重截短而不是完整的RDM光谱描述。半圆形和非理性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。
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.
