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Continuously varying exponents in $A+B to 0$ reaction with long-ranged attractive interacti.pdf

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Continuouslyvaryingexponentsin$ABto0$reactionwithlong-rangedattractiveinteracti

a r X i v : c o n d - m a t / 0 6 0 3 4 9 3 v 1 [ c o n d - m a t .s t a t - m e c h ] 2 0 M a r 2 0 0 6 Continuously varying exponents in A + B → 0 reaction with long-ranged attractive interaction Sungchul Kwon, S. Y. Yoon, and Yup Kim Department of Physics and Research Institute of Basic Sciences, Kyung Hee University, Seoul 130-701, Korea (Dated: February 6, 2008) We investigate the kinetics of the A + B → 0 reaction with long-range attractive interaction V (r) ～ ?r?2σ between A and B or with the drift velocity v ～ r?σ 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 (ρ) and the size of domains (?) continuously vary with σ when σ σc = /1/2, while that for the distance between adjacent opposite species (?AB) varies when σ σ AB c = 7/6. Beyond σABc , 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 σ are supported by numerical simulations and the argument of effective repulsion between the opposite species domains. PACS numbers: 05.70.Ln,05.40.-a The irreversible two-species reaction A + B → 0 has been intensively and widely investigated as a basic model for various phenomena in physics [1, 2], chemistry [3], and biology [4]. When an A and a B particle meet on the same site, they instantly and irreversibly combine to form an inert species. Until now the studies for the re- action have been focused on understanding the effect of the fluctuations of the initial particle density or the global bias of particle motions on the kinetics without careful consideration of the interactions between A and B even for charged particles [1, 5, 6, 7, 8, 9, 10, 11]. However, in situations where the kinetics of reaction is affected by certain attractive interactions between A and B such as the Coulomb interaction, the interactions should be much more im