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通过矩阵永久式——临界现象、分形、量子计算、#P 复杂度实现自然复杂性的统一

Unification of the Nature's Complexities via a Matrix Permanent-Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity.

作者信息

Kocharovsky Vitaly, Kocharovsky Vladimir, Tarasov Sergey

机构信息

Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA.

Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, Russia.

出版信息

Entropy (Basel). 2020 Mar 12;22(3):322. doi: 10.3390/e22030322.

DOI:10.3390/e22030322
PMID:33286096
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7516781/
Abstract

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.

摘要

我们揭示了矩阵的积和式与临界现象、分形结构和混沌中所表现出的大自然主要复杂性、多体物理中的量子信息过程、数学中的数论复杂性以及计算复杂性理论中的#P完全问题之间的解析关系。它们源于将临界现象的伊辛模型简化为积和式，以及基于以下四点的积和式的四种积分表示：(i) 类分形魏尔斯特拉斯函数；(ii) 复变量多项式；(iii) 拉普拉斯积分；(iv) 麦克马洪主定理。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/519f/7516781/c523e183d1b2/entropy-22-00322-g015.jpg
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