SELF-CONSISTENT MODEL OF AN ANNIHILATION-DIFFUSION REACTION WITH LONG-RANGE INTERACTIONS

We introduce coarse-grained hydrodynamic equations of motion for a dif fusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - c harge density - we derive an analytically solvable approximation for t he nonconserved order parameter - total particle density. Asymptotic s olutions are obtained for the case of random Gaussian initial conditio ns and for system dimensionality d greater than or equal to 2. Large-t , intermediate-t, and small-t asymptotics were calculated and compared with existing scaling theories, exact results, and simulation data.