Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions

TL;DR

This paper introduces a comprehensive scaling model for charged particle annihilation with long-range interactions, identifying three regimes based on dimensionality and force decay, aligning well with simulations and theory.

Contribution

It presents a new general scaling model for annihilation kinetics involving long-range forces, expanding understanding of different dynamical regimes.

Findings

Identifies three distinct kinetic regimes based on parameters.

Derives a phase diagram consistent with simulations.

Provides theoretical insights into long-range annihilation processes.

Abstract

We propose the general scaling model for the diffusio n-annihilation reaction $A_{+} + A_{-} \longrightarrow \emptyset$ with long-range power-law i nteractions. The presented scaling arguments lead to the finding of three different regimes, dep ending on the space dimensionality d and the long-range force power e xponent n. The obtained kinetic phase diagram agrees well with existing simulation data and approximate theoretical results.