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

TL;DR

This paper develops a self-consistent hydrodynamic model for diffusion-annihilation systems with long-range interactions, providing analytical solutions and comparing them with existing theories and simulations.

Contribution

It introduces a novel coarse-grained hydrodynamic framework that accounts for fluctuations and long-range interactions in diffusion-annihilation systems.

Findings

Derived analytically solvable equations for the system.

Obtained asymptotic behaviors for different time regimes.

Validated results against existing theories and simulations.

Abstract

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.