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Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems

A. M. Selvam
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Abstract

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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A. M. Selvam. 2004-08-19. Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems. https://arxiv.org/abs/physics/0408089

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