Fractional field equations for highly improbable events

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Kleinert, H.^1,2

Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D14195 Berlin, Germany^1

ICRANeT, Piazzale della Republica 1, 10-65122 Pescara, Italy^2

关键词: Dinger equation;    Fractional fields;    Fractional wave equation;    Gaussian random walk;    Heavy-tails;    Interacting particles;    Particle orbit;    Rogue waves;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012019/pdf
DOI  :  10.1088/1742-6596/442/1/012019

学科分类：力学，机械学

来源: IOP

【 摘 要 】

Free and weakly interacting particles perform approximately Gaussian random walks with collisions. They follow a second-quantized nonlinear Schrodinger equation, or relativistic versions of it. By contrast, the fields of strongly interacting particles extremize more involved effective actions obeying fractional wave equations with anomalous dimensions. Their particle orbits perform universal Le´vy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.