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  • Letter
  • Open Access

Accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation

Shay I. Heizler*, Menahem Krief*, and Michael Assaf

  • Racah Institute of Physics, The Hebrew University, 9190401 Jerusalem, Israel

  • *These authors contributed equally to this work.
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Phys. Rev. Research 6, L012023 – Published 31 January, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012023

Abstract

We resolve a long-standing question regarding the suitable effective diffusion coefficient of the spherical-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions for homogeneous media, to include general-collisional properties, including birth-death events and linearly anisotropic scattering. This is done by introducing an exact scaling law relating the Green's function of the pure-scattering case with the general-collision case, which is verified using deterministic and Monte Carlo simulations. Importantly, the effective diffusion coefficient is identified by inspecting the transport solution at long times.

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References (48)

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Phys. Rev. Research 6, L012023– Published 31 January, 2024
  • Received 21 July 2023
  • Accepted 28 December 2023
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