Relativistic diffusion of massless particles

TL;DR

This paper explores the relativistic diffusion process for massless particles, deriving its properties, solutions, and connections to quantum mechanics, with applications to astrophysics such as the Sunyaev-Zeldovich effect.

Contribution

It introduces a relativistic diffusion model for massless particles, linking it to quantum mechanics and astrophysical phenomena, and provides explicit solutions and approximations.

Findings

The diffusion process has a log-normal distribution.

The stochastic equations for the Juttner distribution are explicitly solvable.

Relativistic diffusion approximates the Kompaneetz equation for photon diffusion.

Abstract

We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium distribution.We show that for the Juttner equilibrium distribution the relativistic diffusion is a linear approximation to the Kompaneetz equation describing a photon diffusion in an electron gas.The stochastic equation corresponding to the Juttner distribution is explicitly soluble. We relate the relativistic diffusion to imaginary time quantum mechanics. Some astrophysical applications (including the Sunyaev-Zeldovich effect) are briefly discussed.