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

• Received 20 March 2006

DOI:https://doi.org/10.1103/PhysRevE.74.021109