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DOE OSTI · 21362179

Stochastic models for relativistic diffusion

Baeumer, Boris·Meerschaert, Mark M·Naber, Mark
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Abstract

The diffusion equation is related to the Schroedinger equation by analytic continuation. The formula E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4} leads to a relativistic Schroedinger equation, and analytic continuation yields a relativistic diffusion equation that involves fractional calculus. This paper develops stochastic models for relativistic diffusion and equivalent differential equations with no fractional derivatives. Connections to anomalous diffusion are also discussed, along with alternative models.

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97 MATHEMATICS AND COMPUTINGDIFFERENTIAL EQUATIONSDIFFUSION EQUATIONSENERGY RANGEEQUATIONSMATHEMATICAL SOLUTIONSPARTIAL DIFFERENTIAL EQUATIONSRELATIVISTIC RANGESCHROEDINGER EQUATIONSTOCHASTIC PROCESSESWAVE EQUATIONS

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Baeumer, Boris, Meerschaert, Mark M, Naber, Mark. 2010-07-15. Stochastic models for relativistic diffusion. https://doi.org/10.1103/physreve.82.011132

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