Kinetics of ballistic annihilation and branching

TL;DR

This paper analyzes a one-dimensional ballistic annihilation and branching model, revealing a phase transition at q=1/2 where the system's dynamics shift from coarsening to rapid relaxation.

Contribution

It provides an analytical solution in mean-field approximation and numerical simulations for a novel model combining annihilation and branching in ballistic particles.

Findings

At q=1/2, a dynamical phase transition occurs.

For q<1/2, slow coarsening dynamics dominate.

For q>1/2, the system quickly reaches a stationary state.

Abstract

We consider a one-dimensional model consisting of an assembly of two-velocity particles moving freely between collisions. When two particles meet, they instantaneously annihilate each other and disappear from the system. Moreover each moving particle can spontaneously generate an offspring having the same velocity as its mother with probability 1-q. This model is solved analytically in mean-field approximation and studied by numerical simulations. It is found that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the slow dynamics of the system is governed by the coarsening of clusters of particles having the same velocities, while for q>1/2 the system relaxes rapidly towards its stationary state characterized by a distribution of small cluster sizes.