标题： 混沌与湍流的普遍统计结构和标度定律 显示英文标题

标题： The Universal Statistical Structure and Scaling Laws of Chaos and Turbulence

摘要： 湍流是由高雷诺数下流体流动的强非线性动力学所产生的复杂时空结构。 尽管湍流是一种经历了几个世纪研究的普遍现象，但对其全面理解仍然是一个巨大的挑战。 在这里，我们引入了量子混沌和随机矩阵理论（RMT）领域的工具，并对不可压缩和可压缩流体流动的湍流模拟生成的图像数据集进行了详细分析。 聚焦于两个可观测量：数据Gram矩阵和单个图像分布，我们研究了局部和全局特征值统计，并将其与经典混沌、无关联噪声和自然图像进行比较。 我们表明，从RMT的角度来看，湍流Gram矩阵属于与量子混沌而非可积系统相同的普适性类别，数据在其特征值主体中表现出幂律标度，这与无关联的经典混沌、随机数据和自然图像大相径庭。 有趣的是，我们发现单个样本分布仅在完全RMT混沌状态下出现，但在更大的相关长度下偏离混沌，并表现出不同的标度特性。 显示英文摘要

摘要： Turbulence is a complex spatial and temporal structure created by the strong non-linear dynamics of fluid flows at high Reynolds numbers. Despite being an ubiquitous phenomenon that has been studied for centuries, a full understanding of turbulence remained a formidable challenge. Here, we introduce tools from the fields of quantum chaos and Random Matrix Theory (RMT) and present a detailed analysis of image datasets generated from turbulence simulations of incompressible and compressible fluid flows. Focusing on two observables: the data Gram matrix and the single image distribution, we study both the local and global eigenvalue statistics and compare them to classical chaos, uncorrelated noise and natural images. We show that from the RMT perspective, the turbulence Gram matrices lie in the same universality class as quantum chaotic rather than integrable systems, and the data exhibits power-law scalings in the bulk of its eigenvalues which are vastly different from uncorrelated classical chaos, random data, natural images. Interestingly, we find that the single sample distribution only appears as fully RMT chaotic, but deviates from chaos at larger correlation lengths, as well as exhibiting different scaling properties.