Issue |
EPL
Volume 139, Number 1, July 2022
|
|
---|---|---|
Article Number | 11001 | |
Number of page(s) | 6 | |
Section | Statistical physics and networks | |
DOI | https://doi.org/10.1209/0295-5075/ac747c | |
Published online | 21 July 2022 |
Isotropic radiative transfer as a phase space process: Lorentz covariant Green's functions and first-passage times
Univ. Grenoble Alpes, CNRS, LPMMC - 38000 Grenoble, France
(a) vincent.rossetto@grenoble.cnrs.fr (corresponding author)
Received: 12 November 2021
Accepted: 30 May 2022
The solutions of the radiative transfer equation, known for the energy density, do not satisfy the fundamental transitivity property for Green's functions expressed by Chapman-Kolmogorov's relation. I show that this property is retrieved by considering the radiance distribution in phase space. Exact solutions are obtained in one and two dimensions as probability density functions of continous-time persistent random walks, the Fokker-Planck equation of which is the radiative transfer equation. The expected property of Lorentz covariance is verified. I also discuss the measured signal from a pulse source in one dimension, which is a first-passage time distribution, and unveil an effective random delay when the pulse is emitted away from the observer.
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