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Ballistic Annihilation

Paul L. Kaprivsky·Clément Sire
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Abstract

Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of Boltzmann equation. The particle density and the rms velocity decay as $c=t^{-α}$ and $ =t^{-β}$, with the exponents depending on the initial velocity distribution and the spatial dimension. For instance, in one dimension for the uniform initial velocity distribution we find $β=0.230472...$. We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.

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Paul L. Kaprivsky, Clément Sire. 2000-05-31. Ballistic Annihilation. https://doi.org/10.1103/physrevlett.86.2494

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