Kinetics of the $A+B \to 0$ reaction with mass-dependent fragmentation

Abstract

We investigate the kinetics of uniformly driven $A+B \to 0$ reaction with mass-dependent fragmentation in one dimension. In this model, the fragmented mass $m$ of a site with mass $n_i$ is given as $m=n^λ_i$, and it is driven to the one direction. When opposite species masses occupy the same site, mass reaction takes place instantaneously. Since the fragmented mass $m$ of $λ<1$ is less than mass $n_i$ of a site, the exponent $λ$ controls the attractive interaction between particles at the same site. The $λ=0$ case corresponds to hard-core (HC) particle system. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths except the domain length $\ell$ are the same as that of the uniformly driven HC particle system. The scaling behavior of $\ell$ is $\ell \sim t^{2/3}$. The kinetics of the reaction is independent of $λ$ as long as $λ<1$. The $λ$-independent kinetics results from the $λ$-independent collective motions of single species domains.