Kinetics and scaling in ballistic annihilation

Abstract

We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out in arbitrary dimension. These predictions are in excellent agreement with the complementary results of extensive Monte Carlo and Molecular Dynamics simulations. We finally discuss the definition of universality classes indexed by a continuous parameter for this far from equilibrium dynamics with no conservation laws.