Relativistic diffusive motion in random electromagnetic fields

TL;DR

This paper demonstrates that relativistic motion in random electromagnetic fields can be modeled as a relativistic diffusion process, linking microscopic field correlations to macroscopic transport equations and equilibrium states.

Contribution

It establishes a connection between relativistic dynamics in random fields and diffusion processes, providing explicit formulas for the diffusion constant based on field correlations.

Findings

Relativistic dynamics can be approximated by diffusion models.

Diffusion in proper time and laboratory time are related.

Diffusion constant expressed via field correlation function.

Abstract

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).