非平凡Riemann zeta零点间隔和湍流中类量子混沌的特征
Signatures of quantum-like chaos in spacing intervals of non-trivial Riemann zeta zeros and in turbulent fluid flows
摘要：
相邻Riemann zeta零点（非平凡的）的间隔区间表现出自然界中的动力系统（例如流体流动、心跳模式、股票市场价格指数等）所共有的分形（不规则）波动，并且与不可预测性或混乱有关。这种分形时空涨落的功率谱表现出普遍的逆幂律形式，并表示长程关联，被认为是自组织临界性。由作者开发的湍流流体流动的细胞动力系统模型提供了一个独特的量化的统计正态分布方面的观察到的功率谱，这样的方差表示的统计概率密度。这样一个结果，即涡旋的加性振幅在平方时表示统计概率，这是量子系统（如电子或光子）的亚原子动力学的一个观察特征。因此，自组织临界性是动力系统中类量子混沌的一个特征。模型的概念适用于所有真实世界（观察）和计算（数学模型）的动态系统。对Riemann zeta零间距分形涨落的连续周期图分析表明，其功率谱服从统计正态分布的唯一和普遍的逆幂律形式。因此，黎曼zeta零点表现出类似量子的混沌，零点的间距代表自然界中动力系统固有的类似量子混沌的能量（方差）水平间距。细胞动力系统模型是适用于各种尺度动力系统的一般系统理论。
英文摘要：
The spacing intervals of adjacent Riemann zeta zeros(non-trivial) exhibit fractal(irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated with unpredictability or chaos. The power spectra of such fractal space-time fluctuations exhibit universal inverse power law form and signify long-range correlations, identified as self-organized criticality . A cell dynamical system model developed by the author for turbulent fluid flows provides a unique quantification for the observed power spectra in terms of the statistical normal distribution, such that the variance represents the statistical probability densities. Such a result that the additive amplitudes of eddies when squared, represent the statistical probabilities is an observed feature of the subatomic dynamics of quantum systems such as an electron or photon. Self-organized criticality is therefore a signature of quantum-like chaos in dynamical systems. The model concepts are applicable to all real world(observed) and computed(mathematical model) dynamical systems. Continuous periodogram analyses of the fractal fluctuations of Riemann zeta zero spacing intervals show that the power spectra follow the unique and universal inverse power law form of the statistical normal distribution. The Riemann zeta zeros therefore exhibit quantum-like chaos, the spacing intervals of the zeros representing the energy(variance) level spacings of quantum-like chaos inherent to dynamical systems in nature. The cell dynamical system model is a general systems theory applicable to dynamical systems of all size scales.
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