素数分布和湍流中的类量子混沌
Quantum-like Chaos in Prime Number Distribution and in Turbulent Fluid Flows
摘要：
最近的研究表明素数的分布和量子力学定律之间有着密切的联系，量子力学定律支配着量子系统（如电子或光子）的亚原子动力学。数论概念与从微观亚原子动力学到宏观湍流流体流动（如大气流动）的所有尺度的动力学系统的定量描述有着内在的联系。现在人们认识到，Cantorian分形时空涵盖了自然界中所有的动力系统。作者提出的细胞动力学系统模型表明，湍流的连续动力学是由遵循类量子力学规律的宽带连续谱涡旋组成的。该模型的概念，使显示连续实数场包含独特的结构，即素数，这是类似于在湍流流体流动中的涡流连续的主导涡流。本文证明了素数的频谱服从类量子力学定律。
英文摘要：
Recent studies indicate a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. Number theoretical concepts are intrinsically related to the quantitative description of dynamical systems of all scales ranging from the microscopic subatomic dynamics to macroscale turbulent fluid flows such as the atmospheric flows. It is now recognised that Cantorian fractal spacetime characterise all dynamical systems in nature. A cell dynamical system model developed by the author shows that the continuum dynamics of turbulent fluid flows consist of a broadband continuum spectrum of eddies which follow quantumlike mechanical laws. The model concepts enable to show that the continuum real number field contains unique structures, namely prime numbers which are analogous to the dominant eddies in the eddy continuum in turbulent fluid flows. In this paper it is shown that the prime number frequency spectrum follows quantumlike mechanical laws.
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