分形时空涨落：动力学系统中类量子混沌的一个特征
Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems
摘要：
自然界中的动力系统，如流体流动、心跳模式、降雨变化、股票市场价格波动等，在空间和时间的所有尺度上都表现出自相似的分形波动。分形涨落的功率谱分析呈现出逆幂律形式，表明长程时空相关性，被认为是自组织临界性。作者提出了一种广义系统理论，它预言观测到的自组织临界性是类量子混沌的特征。该模型表明：（1）分形涨落是由一个整体对数螺旋轨迹和内部结构的准周期Penrose镶嵌图案引起的。对这种对数螺旋轨迹的常规功率谱分析将显示出相位逐渐增加的连续涡旋。(2)动力系统分形涨落的功率谱分析表明，分形涨落的统计正态分布具有普遍的逆幂律形式。这样的结果表明，涡旋的加性振幅，当平方（即方差）表示概率时，这是量子系统（如电子或光子）的亚原子动力学所表现出的特性。此外，长程时空相关性或非定域连接，如宏观动力系统所表现出的，也是量子系统的特征。因此，自然界中所有尺度的动力系统都具有的自相似分形涨落是类量子混沌的一个特征。应用该模型的概念表明，人类Y染色体DNA中碱基A、C、G、T的频率分布具有长程空间相关性。
英文摘要：
Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal fluctuations exhibit inverse power law form indicating long-range space-time correlations, identified as self-organized criticality. The author has proposed a general systems theory, which predicts the observed self-organized criticality as signatures of quantumlike chaos. The model shows that (1) the fractal fluctuations result from an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. Conventional power spectral analysis of such a logarithmic spiral trajectory will show a continuum of eddies with progressive increase in phase. (2) Power spectral analyses of fractal fluctuations of dynamical systems exhibit the universal inverse power law form of the statistical normal distribution. Such a result indicates that the additive amplitudes of eddies, when squared (namely the variance) represent the probabilities, a characteristic exhibited by the subatomic dynamics of quantum systems such as the electron or photon. Further, long-range space-time correlations or non-local connections such as that exhibited by macroscale dynamical systems characterize quantum systems also. Therefore selfsimilar fractal fluctuations generic to dynamical systems of all scales in nature is a signature of quantumlike chaos. The model concepts are applied to show that the frequency distribution of bases A, C, G, T in Human Chromosome Y DNA exhibit long-range spatial correlations.
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