Correlations in Ballistic Processes

We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the reaction-controlled limit when particles undergo mostly elastic collisions and therefore are always near equilibrium, the correlations are accounted analytically. For ballistic aggregation, for instance, the density decays as $n\sim t^{-\xi }$ with $\xi =2d\mathrm{/}(d+3)$ in the reaction-controlled limit in $d$ dimensions, in contrast with well-known mean-field prediction $\xi =2d\mathrm{/}(d+2)$.