Decay kinetics of ballistic annihilation

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∼${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ and ${\mathit{v}}_{\mathrm{rms}}$∼${\mathit{t}}^{\mathrm{-}\mathrm{\beta }}$, 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 α and β depend strongly on the initial condition, a behavior which is confirmed numerically in one and two dimensions.