Non-Universal Decay Kinetics in Ballistic Annihilation,

E. Ben-Naim and S. Redner F. Leyvraz

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 $c\sim t^{-\alpha}$ and $v\sim t^{-\beta}$ respectively, with the relation $\alpha+\beta=1$ holding in any spatial dimension. A ``mean-field'' Boltzmann equation for the evolution of the velocity distribution predicts that $\alpha$ and $\beta$ depend strongly on the initial condition. This non-universal behavior is confirmed numerically in one and two dimensions.


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