Universal fragmentation in annihilation reactions with constrained kinetics

TL;DR

This paper introduces a reaction model with constrained particle dynamics that leads to a universal fragmentation state, diverging from the typical emptying behavior in low-dimensional annihilation reactions.

Contribution

It presents a minimal, exactly solvable model demonstrating universal fragmentation in reaction-diffusion systems with conserved center of mass.

Findings

Particles form independent clusters at late times

Universal asymptotic density is derived

Exact results for large reaction rates are provided

Abstract

In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a reciprocal bottleneck on particle dynamics where single-particle motion conserves the center of mass. We show that such a constrained reaction-diffusion dynamics does not approach an empty state but freezes at late times in a state with fragmented particle clusters, and that the late-time dynamics and asymptotic density are universal. Our setup thus constitutes a minimal model for the fragmentation of a one-dimensional lattice into independent particle clusters, and we provide exact results for the final density in the large-reaction rate limit. We suggest that the universal reaction dynamics could be observable in experiments with cold atoms or in the Auger recombination of exciton gases.