宇宙的包裹或者为什么Schr“Odinger和Fourier是如此的亲戚？

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摘要翻译：
本文讨论了傅里叶热方程与Schr-Odinger波动方程之间惊人的联系，即如果用时间变量乘以$i=sqrt{-1}$代替热方程中独立的“时间”变量，热方程就变成了Schr-Odinger方程。两种完全不同的物理现象被紧密地联系在一起：材料中的热扩散和原子中粒子的概率振幅。生活中的一个事实是，在流体中随机漂浮的小粒子的运动，即众所周知的布朗运动，是由傅立叶方程调节的，而我们周围物质的概率行为，即量子世界，是由Schr\\“Odinger方程驱动的，但在这里似乎没有已知的随机过程在起作用。通过“时间旋转”，即通常所知的灯芯旋转，形式上的联系表面上的简单性似乎指向了另一个方面。为什么会有这种联系？有什么物理直观的解释吗？有没有实用价值？本文试图对上述问题有所启示。由于Connes、Chamseddine和Mukhanov，非对易几何中最近的体积量子化概念再次指向了量子世界中的随机过程，使Fourier和Schr“Oodinger成为严格的亲戚。
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英文标题：
《Parcels of Universe or why Schr\"odinger and Fourier are so relatives?》
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作者：
Marco Frasca, Alfonso Farina
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
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英文摘要：
  This paper is about the surprising connection between the Fourier heat equation and the Schr\"odinger wave equation. In fact, if the independent "time" variable in the heat equation is replaced by the time variable multiplied by $i=\sqrt{-1}$, the heat equation becomes the Schr\"odinger equation. Two quite different physical phenomena are put in close connection: the heat diffusion in a material and the probability amplitude of particles in an atom. It is a fact of life that the movements of a small particle floating randomly in a fluid, the well-known Brownian motion, is regulated by the Fourier equation while the probabilistic behavior of the matter around us, the quantum world, is driven by the Schr\"odinger equation but no known stochastic process seems at work here. The apparent simplicity of the formal connection by a "time-rotation", a Wick rotation as it is commonly known, seems to point otherwise. Why this connection? Is there any physical intuitive explanation? Is there any practical value? In this paper, the authors attempt to shed some light on the above questions. The recent concept of volume quantization in noncommutative geometry, due to Connes, Chamseddine and Mukhanov, points again to stochastic processes also underlying the quantum world making Fourier and Schr\"oodinger strict relatives.
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PDF链接：
https://arxiv.org/pdf/1804.05204

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关键词：Fourier dinger four DING Fou quantum fact 独立 形式 Schr