Decay kinetics of ballistic annihilation.

@article{BenNaim1993DecayKO,
  title={Decay kinetics of ballistic annihilation.},
  author={Ben-Naim and Redner and Leyvraz},
  journal={Physical review letters},
  year={1993},
  volume={70 12},
  pages={
          1890-1893
        }
}
We study the kinetics of ballistic annihilation, A+A→0, with continuous initial particle velocity distributions. The concentration and the rms velocity are found to decay as c∼t -α and υ rms ∼t -β , respectively, with the relation α+β=1 holding in any spatial dimension. A «mean-field» Boltzmann equation for the evolution of the velocity distribution predicts that a and β depend strongly on the initial condition, a behavior which is confirmed numerically in one and two dimensions 

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