Apparent superluminal velocities and random walk in the velocity space

TL;DR

This paper proposes that modeling acceleration in relativistic jets as a random walk in velocity space effectively captures the diffusion process, demonstrated through a simple toy model across different regimes.

Contribution

It introduces a novel approach of using random walk and diffusion in velocity space to describe relativistic jet acceleration, bridging non-relativistic and relativistic regimes.

Findings

Diffusion in velocity space can model jet acceleration.

The toy model illustrates key features in both regimes.

The approach offers a new perspective on relativistic jet dynamics.

Abstract

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes.