道琼斯指数和湍流中的类量子混沌特征
Signatures of Quantum-like Chaos in Dow Jones Index and Turbulent Fluid Flows
摘要：
道琼斯指数时间序列在从天、月到年的所有时间尺度上都表现出不规则或分形的波动。非线性涨落是自相似的，表现为时间涨落功率谱的逆幂律形式。分形涨落功率谱的逆幂律形式是自然界中所有动力系统所共有的，它被认为是自组织临界性.作者发展了一种通用系统理论，用以普遍量化动力系统中观测到的自组织临界性.该模型预测分形涨落的功率谱遵循统计正态分布的普遍而唯一的逆幂律形式，并被识别为类量子混沌的签名。连续周期图功率谱分析的标准化的每日，每月和每年的道琼斯指数在过去的100年表明，功率谱遵循普遍的逆幂律形式的统计正态分布与模型预测。因此，道琼斯指数表现出自组织临界性，这是从天到年的所有时间尺度上的量子混沌的特征。所有的数据集表现出接近模型预测值的周期性。道琼斯指数的明显噪声，不规则的分形波动有助于形成强大的自相似几何结构，这表明市场经济在100年内具有惊人的弹性。
英文摘要：
Dow Jones Index time series exhibit irregular or fractal fluctuations on all time scales from days, months to years. The nonlinear fluctuations are selfsimilar as exhibited in inverse power law form for power spectra of temporal fluctuations. Inverse power law form for power spectra of fractal fluctuations is generic to all dynamical systems in nature and is identified as self-organized criticality.The author has developed a general systems theory for universal quantification of the observed self-organized criticality in dynamical systems. The model predicts that the power spectra of fractal fluctuations follow the universal and unique inverse power law form of the statistical normal distribution and is identified as a signature of quantum-like chaos. Continuous periodogram power spectral analyses of normalised daily, monthly and annual Dow Jones Index for the past 100-years show that the power spectra follow the universal inverse power law form of the statistical normal distribution in agreement with model prediction. Dow Jones Index therefore exhibits self-organized criticality which is a signature of quantum-like chaos on all time scales from days to years. All the data sets exhibit periodicities close to model predicted values. The apparently noisy, irregular fractal fluctuations of the Dow Jones Index contribute to the formation of robust selfsimilar geometrical structures which indicate the surprising resilience of market economy over a period of 100 years.
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