Reaction Zones and Quenched Charged-Particle Systems with Long-Range Interactions

We determine the evolving segregated or mixed morphology of charged-particle systems with long-range power-law interactions and overall charge neutrality that have been quenched to a low temperature. Segregated morphology systems are characterized by the size of uniformly charged domains, $L(t)$, the particle separation within the domains, $l_{AA}(t)$, the particle flux-density leaving the domains, $J(t)$, the width of reaction zones between domains, $W(t)$, the particle spacing within the reaction-zones, $l_{AB}(t)$, and the particle lifetime in the reaction-zones, $\tau(t)$. Mixed morphology systems are essentially one large reaction zone, with $L \sim l_{AB} \sim l_{AA}$. By relating these quantities through the scaling behavior of particle fluxes and microscopic annihilation rates within reaction-zones, we determine the characteristic time-exponents of these quantities at late times. The morphology of the system, segregated or mixed, is also determined self-consistently. With this unified approach, we consider systems with diffusion and/or long-range interactions, and with either uncorrelated or correlated high-temperature initial conditions. Finally, we discuss systems with particle-like topological defects and electronic systems in various substrate dimensions --- including quantum-hall devices with skyrmions.