Correlations in Ballistic Processes

TL;DR

This paper studies how velocity correlations affect long-term behavior in ballistic reaction processes, revealing deviations from mean-field predictions especially in aggregation scenarios.

Contribution

It analytically accounts for velocity correlations in ballistic reactions, providing new decay exponents differing from traditional mean-field results.

Findings

Density decays as n ~ t^(-2d/(d+3)) in the reaction-controlled limit.

Velocity correlations significantly influence the decay dynamics.

Analytical approach improves understanding of long-time behavior in ballistic reactions.

Abstract

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 $\xi=2d/(d+3)$ in the reaction-controlled limit in $d$ dimensions, in contrast with well-known mean-field prediction $\xi=2d/(d+2)$.