Abstract
We show some inaccuracies in recent arguments claiming that in the long-time limit the initially correlated A+B→0 diffusion-limited reaction can be faster than the A+A→0 one. With the errors corrected, these arguments seem to confirm the former theory of Toussant and Wilczek according to which the global rate of both reactions should ultimately be the same. This hypothesis is also supported by our numerical simulations of a two-dimensional lattice system.
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References
D. Griffeath and A. Bramson, Asymptotics for interacting particle systems onZ d,Z. Wahrsch. Verw. Gebiete 53:183 (1980).
T. Ohtsuki, Field-theoretical approach to scaling behavior of diffusion-controlled recombination,Phys. Rev. A 43:6917 (1991).
M. Bramson and J. L. Lebowitz, Asymptotic behavior of densities for two-particle annihilating random walks,J. Stat. Phys. 62:297 (1991).
K. Lindenberg, B. J. West, and R. Kopelman, Diffusion-limited A+B→0 reaction: Correlated initial condition,Phys. Rev. A 42:890 (1990).
K. Lindenberg, W. S. Shen, and R. Kopelman, Scaling properties of diffusion-limited reactions of fractal and Euclidean geometries,J. Stat. Phys. 65:890 (1991).
D. Toussant and F. Wilczek, Particle-antiparticle annihilation diffusive motion,J. Chem. Phys. 78:2642 (1983).
C. R. Doering and D. ben-Avraham, Interparticle distribution functions and rate equations for diffusion-limited reactions,Phys. Rev. A 38:3035 (1988).
B. Chopard and M. Droz, Cellular automata model for the diffusion equation,J. Stat. Phys. 64:859 (1991); Microscopic study of the properties of the reaction front in an A+B→C reaction-diffusion process,Europhy. Lett. 15:459 (1991).
Z. Jiang and C. Ebner, Simulations of irreversible diffusion-limited reactions,Phys. Rev. A 41:5333 (1990).
K. Lindenberg, P. Argyrakis, and R. Kopelman, Diffusion-limited binary reactions: The hierarchy of nonclassical regimes for correlated initial conditions,J. Phys. Chem., to appear; The hierarchies of non-classical regimes for diffusion-limited binary reactions: A review, inFluctuations and Order: The New Synthesis, M. M. Millonas, ed. (Springer-Verlag, New York, in press); P. Argyrakis, R. Kopelman, and K. Lindenberg, Diffusion-limited binary reactions: The hierarchy of nonclassical regimes,M.R.S. Symp. Proc. 20:365 (1993).
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Koza, Z. The A+B→0 diffusion-limited reaction with correlated initial condition. J Stat Phys 76, 857–866 (1994). https://doi.org/10.1007/BF02188689
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DOI: https://doi.org/10.1007/BF02188689