Stochastic models for relativistic diffusion

Abstract

The diffusion equation is related to the Schrödinger equation by analytic continuation. The formula $E^2=p^2{c}^2+m^2{c}^4$ leads to a relativistic Schrödinger 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. DOI: http://dx.doi.org/10.1103/PhysRevE.82.011132 © 2010 The American Physical Society