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

Source: [Continuously varying exponents in $A+B \\to 0$ reaction with long-ranged attractive interaction](<https://www.sota2.com/research/paper/68fa274c2c2a3760193c1c2d>)

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Data updated: 2025-10-24T11:55:51.777Z

Authors: Sungchul Kwon, S. Y. Yoon, Yup Kim

Published: 2006-03-20T06:40:58.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0603493>)

[PDF](<https://arxiv.org/pdf/cond-mat/0603493.pdf>)