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Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena Fractals Quantum Computing ♯P-Complexity

机译：通过矩阵永久关键现象分形量子计算P复杂性统一性质的复杂性

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We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem.

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期刊名称 Entropy
作者
Vitaly Kocharovsky; Vladimir Kocharovsky; Sergey Tarasov;
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年(卷),期 2020(22),3
年度 2020
页码 322
总页数 44
原文格式 PDF
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中图分类
关键词
♯P-complexity; NP-complexity; critical phenomena; fractals; quantum computing; matrix permanent; MacMahon master theorem; Toeplitz determinant;

机译：♯P复杂性;NP复杂性;关键现象;分形;量子计算;矩阵永久;Macmahon大师定理;Toeplitz决定因素;

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专利

1. On Complexity of Computing the Permanent of a Rectangular Matrix [J] . Tsutomu KAWABATA, Jun TARUI IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences . 1999,第5期

机译：计算矩形矩阵永久性的复杂性
2. D. SORNETTE, Critical Phenomena in Natural Sciences. Chaos, Fractals, Self Organization and Disorder: Concepts and Tools, Springer Verlag, Berlin 2000, 2004 [J] . Rivista Internazionale di Scienze Sociali . 2007,第2期

机译：D. SORNETTE，自然科学中的关键现象。混沌，分形，自我组织和混乱：概念和工具，施普林格出版社，柏林，2000年，2004年
3. The fractal nature of nature: power laws, ecological complexity and biodiversity [J] . Brown JH., Gupta VK., Li BL., Philosophical Transactions of the Royal Society of London, Series B. Biological Sciences . 2002,第1421期

机译：自然的分形性质：幂律，生态复杂性和生物多样性
4. HOW FAR CAN A PRAGMATIST GO INTO QUANTUM THEORY? A CRITICAL VIEW OF OUR CURRENT UNDERSTANDING OF QUANTUM PHENOMENA [C] . A. S. SANZ International Workshop on High-Energy Physics . 2015

机译：实用主义者进入量子理论有多远？我们目前对量子现象的理解的批判性观点
5. Quantum complexity: Quantum mutual information, complex networks, and emergent phenomena in quantum cellular automata. [D] . Vargas, David L. 2016

机译：量子复杂性：量子相互信息，复杂网络和量子细胞自动机中的新兴现象。
6. The fractal nature of nature: power laws ecological complexity and biodiversity. [O] . James H Brown, Vijay K Gupta, Bai-Lian Li, 2002

机译：自然的分形性质：幂律生态复杂性和生物多样性。
7. Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity [O] . Vitaly Kocharovsky, Vladimir Kocharovsky, Sergey Tarasov 2020

机译：通过矩阵永久关键现象，分形，量子计算，P复杂性统一性质的复杂性
8. Are Earthquakes, Fractals, and 1/F Noise Self-Organized Critical Phenomena. [R] . Bak, P., Tang, C., Wiesenfeld, K. 1988

机译：是地震，分形和1 / F噪声自组织的关键现象。

Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena Fractals Quantum Computing ♯P-Complexity

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