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The solution to Maxwell-Bloch systems using an integral-equation-basedframework has proven effective at capturing collective features of laser-drivenand radiation-coupled quantum dots, such as light localization andmodifications of Rabi oscillations. Importantly, it enables observation of thedynamics of each quantum dot in large ensembles in a rigorous,error-controlled, and self-consistent way without resorting to spatialaveraging. Indeed, this approach has demonstrated convergence in ensemblescontaining up to $10^4$ interacting quantum dots. Scaling beyond $10^4$ quantumdots tests the limit of computational horsepower, however, due to the$\mathcal{O}(N_t N_s^2)$ scaling (where $N_t$ and $N_s$ denote the number oftemporal and spatial degrees of freedom). In this work, we present an algorithmthat reduces the cost of analysis to $\mathcal{O}(N_t N_s \log^2 N_s)$. Whilethe foundations of this approach rely on well-knownparticle-particle/particle-mesh and adaptive integral methods, we addrefinements specific to transient systems and systems with multiple spatial andtemporal derivatives. Accordingly, we offer numerical results that validate theaccuracy, effectiveness and utility of this approach in analyzing the dynamicsof large ensembles of quantum dots.

Acceleration techniques for semiclassical Maxwell-Bloch systems: An application to discrete quantum dot ensembles