Linearized Kompaneetz equation as a relativistic diffusion

TL;DR

This paper demonstrates that the linearized Kompaneetz equation for photon diffusion aligns with a relativistic diffusion model, connecting it to quantum mechanics and proposing nonlinear extensions with astrophysical relevance.

Contribution

It establishes a link between the linearized Kompaneetz equation and relativistic diffusion, introducing potential nonlinear generalizations and applications in astrophysics.

Findings

Linearized Kompaneetz equation matches relativistic diffusion models.

Relates relativistic diffusion to imaginary time quantum mechanics.

Proposes nonlinear extensions with astrophysical applications.

Abstract

We show that Kompaneetz equation describing photon diffusion in an environment of an electron gas, when linearized around its equilibrium distribution, coincides with the relativistic diffusion discussed in recent publications. The model of the relativistic diffusion is related to soluble models of imaginary time quantum mechanics. We suggest some non-linear generalizations of the relativistic diffusion equation and their astrophysical applications (in particular to the Sunyaev-Zeldovich effect).