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, $L\left(t\right),$ the particle separation within the domains, $l_{\mathrm{AA}}\mathrm{}\left(t\right),$ the particle flux density leaving the domains, $J\left(t\right),$ the width of reaction zones between domains, $W\left(t\right),$ the particle spacing within the reaction zones, $l_{\mathrm{AB}}\mathrm{}\left(t\right),$ and the particle lifetime in the reaction zones, $\tau \mathrm{}\left(t\right).$ Mixed morphology systems are essentially one large reaction zone, with $L\sim l_{\mathrm{AB}}\sim l_{\mathrm{AA}}.$ 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 particlelike topological defects and electronic systems in various substrate dimensions—including quantum Hall devices with Skyrmions.