Anomalous kinetics of attractive $A+B \to 0$ reactions

TL;DR

This paper studies the unusual reaction kinetics of an attractive $A+B o 0$ process in one dimension, revealing new scaling laws and a distinct universality class due to local attraction effects.

Contribution

It introduces a novel universality class for $A+B o 0$ reactions with local attraction, with analytical and numerical evidence for unique scaling exponents.

Findings

Particle density scales as $t^{-1/3}$

Domain size grows as $t^{1/3}$

Distances between particles scale as $t^{2/3}$

Abstract

We investigate the kinetics of $A+B \to 0$ reaction with the local attractive interaction between opposite species in one spatial dimension. The attractive interaction leads to isotropic diffusions inside segregated single species domains, and accelerates the reactions of opposite species at the domain boundaries. At equal initial densities of $A$ and $B$, we analytically and numerically show that the density of particles ($\rho$), the size of domains ($\ell$), the distance between the closest neighbor of same species ($\ell_{AA}$), and the distance between adjacent opposite species ($\ell_{AB}$) scale in time as $\rho \sim t^{-1/3}$, $\ell_{AA} \sim t^{1/3}$, and $\ell \sim \ell_{AB} \sim t^{2/3}$ respectively. These dynamical exponents form a new universality class distinguished from the class of uniformly driven systems of hard-core particles.