Kinetics and scaling in ballistic annihilation

TL;DR

This paper analyzes the decay dynamics of particles undergoing ballistic annihilation, deriving explicit exponents for density and velocity decay, validated by simulations, and discusses universality classes in this non-equilibrium process.

Contribution

It provides explicit analytical expressions for decay exponents in arbitrary dimensions and explores universality classes in ballistic annihilation.

Findings

Analytical exponents match simulation results

Decay behavior characterized across dimensions

Universality classes identified for the process

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.