Ballistic Annihilation

Details Ballistic Annihilation Ballistic Annihilation

2000-05-31

arxiv.org/abs/cond-mat/0005539v1

Phys. Rev. Lett. 86, 2494 (2001)

Physics

Condensed Matter

Statistical Mechanics

4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.86.2494

Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of Boltzmann equation. The particle density and the rms velocity decay as $c=t^{-\alpha}$ and $=t^{-\beta}$, 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 $\beta=0.230472...$. 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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