Continuously varying exponents in $A+B\to 0$ reaction with long-ranged attractive interaction

Abstract

We investigate the kinetics of the $A+B\to 0$ reaction with long-range attractive interaction $V(r)\sim -r^{-2\sigma }$ between $A$ and $B$ or with the drift velocity $v\sim r^{-\sigma }$ in one dimension, where $r$ is the closest distance between $A$ and $B$. It is analytically show that the dynamical exponents for density of particles ($\rho$) and the size of domains ($\ell$) continuously vary with $\sigma$ when $\sigma <{\sigma }_c=/1/2$, while that for the distance between adjacent opposite species (${\ell }_{AB}$) varies when $\sigma <{\sigma }_c^{AB}=7/6$. Beyond ${\sigma }_c^{AB}$, diffusive motions dominate the kinetics, so that the dynamical behavior for diffusive systems is completely recovered. These anomalous behaviors with the two crossover values of $\sigma$ are supported by numerical simulations and the argument of effective repulsion between the opposite species domains.

arXiv comment5 pages, 4 figures

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Cited by in corpus (2)

• Annihilation of single-species charged particles based on the Dyson gas dynamics
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