Phys. Rev. E 56, 1135–1141 (1997)Solution of the time-dependent Boltzmann equationReceived 12 March 1997; published in the issue dated July 1997 The time-dependent Boltzmann equation, which describes the propagation of radiation from a point source in a random medium, is solved exactly in Fourier space. An explicit expression in real space is given in two and four dimensions. In three dimensions an accurate interpolation formula is found. The average intensity at a large distance r from the source has two peaks, a ballistic peak at time t=r/c and a diffusion peak at t≃r2/D (with c the velocity and D the diffusion coefficient). We find that forward scattering adds a tail to the ballistic peak in two and three dimensions, ∝(ct-r)-1/2 and ∝-ln(ct-r), respectively. Expressions in the literature do not contain this tail. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.56.1135
DOI:
10.1103/PhysRevE.56.1135
PACS:
42.25.Bs, 05.60.+w, 42.68.Ay, 95.30.Jx
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