Three-velocity coalescing ballistic annihilation

TL;DR

This paper introduces a coalescing variant of three-velocity ballistic annihilation, analyzing phase transitions in stationary particle survival probabilities based on initial densities.

Contribution

It extends the classical model by allowing coalescence upon collision and provides explicit calculations of survival probabilities for a symmetric parameter family.

Findings

Identifies a phase transition in stationary particle survival.

Provides explicit formulas for survival probabilities.

Characterizes the impact of coalescence on system dynamics.

Abstract

Three-velocity ballistic annihilation is an interacting system in which stationary, left-, and right-moving particles are placed at random throughout the real line and mutually annihilate upon colliding. We introduce a coalescing variant in which collisions may generate new particles. For a symmetric three-parameter family of such systems, we compute the survival probability of stationary particles at a given initial density. This allows us to describe a phase-transition for stationary particle survival.