Self-Consistent Model of Annihilation-Diffusion Reaction with Long-Range Interactions

Details Self-Consistent Model of Annihilation-Diffusion Reaction with Long-Range Interactions Self-Consistent Model of Annihilation-Diffusion Reaction with Long-Range Interactions

1996-05-21

arxiv.org/abs/cond-mat/9605135v3

Physics

Condensed Matter

22 pages, RevTEX, 1 PostScript figure

Scientific paper

10.1103/PhysRevE.55.395

We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an analytically solvable approximation for the nonconserved order parameter - total particle density. Asymptotic solutions are obtained for the case of random Gaussian initial conditions and for system dimensionality $d \geq 2$. Large-t, intermediate-t and small-t asymptotics were calculated and compared with existing scaling theories, exact results and simulation data.

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