Exact Results for a Three-Body Reaction-Diffusion System

TL;DR

This paper presents an exact solution for a three-body reaction-diffusion system, revealing non-mean-field decay behavior similar to two-body systems, with implications for understanding complex particle interactions.

Contribution

It provides the first exact analytical results for a three-body annihilation reaction-diffusion system under symmetrical initial conditions.

Findings

Particle density decays as ~1/√t, indicating non-mean-field behavior.

Exact solutions match numerical simulations for specific initial conditions.

System behavior is similar to two-body annihilation but with distinct decay rates.

Abstract

A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to that found in two-body annihilation, and both systems show non-mean-field, ~1/t**(1/2) instead of ~1/t, decrease of particle density for large times.