Relativistic diffusive transport

TL;DR

This paper explores relativistic diffusion and transport equations, showing how solutions relate through proper time integration, and analyzes stochastic processes with analytic solutions involving Bessel diffusion, emphasizing Lorentz covariance.

Contribution

It introduces a Lorentz covariant framework for relativistic diffusion and transport equations, linking solutions via proper time and analyzing Bessel diffusion processes.

Findings

Solution of transport equation derived from diffusion equation via proper time integration

Relativistic transport equations relate to Bessel diffusion with analytic solutions

Discussion of equilibrium approaches in a moving frame

Abstract

We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the proper time. We study the stochastic processes solving the relativistic diffusion equation and the relativistic transport equation. We show that the relativistic transport equation for massive particles in the light cone coordinates and for massless particles in spatial momentum coordinates are related to the (generalized) Bessel diffusion which has an analytic solution. The solution describes a particle moving in a fixed direction whose frequency distribution is the Bessel process. An approach to an equilibrium in a moving frame is discussed. We formulate the equilibrating diffusion and transport processes in a Lorentz covariant way.