Fractional field equations for highly improbable events

Free and weakly interacting particles perform approximately Gaussian random walks with collisions. They follow a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. By contrast, the fields of strongly interacting particles extremize more involved effective actions obeyin...

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Bibliographic Details
Published in:Journal of physics. Conference series 2013-01, Vol.442 (1), p.12019-9
Main Author: Kleinert, H
Format: Article
Language:English
Subjects:
Crashes
Earthquakes
Economics
Gaussian
Mathematical analysis
Orbits
Particles (of physics)
Physics
Random walk
Schrodinger equation
Schroedinger equation
Wave equations
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Summary:Free and weakly interacting particles perform approximately Gaussian random walks with collisions. They follow a second-quantized nonlinear Schrödinger 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 Lévy 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.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/442/1/012019