Emergent Robustness in Hierarchical Quantum Dot Ensembles: A Unified Model of Self-Healing Materials

Self-healing in materials at room temperature remains a critical challenge. While colloidal quantum dots exhibit recovery of excitonic states at cryogenic temperatures, thermal decoherence at 300 K destroys the effect. We propose a hierarchical model of quantum dot ensembles organized into weakly coupled clusters. We show that for a cluster size M=10 with a voting threshold of K=7, an emergent boost in restoration efficiency occurs: from 45% for a single dot to over 99% for the cluster at T=300 K. The model predicts a universal activation energy Ea = 0.35 eV, linking quantum transitions to classical defect diffusion. We validate the model against three independent experimental systems (MXene-graphene-Au, perovskite-polyurethane, and carbon quantum dots), achieving agreement within 6-8%. The model forecasts a 3.4× increase in exciton lifetime for M=10 clusters, providing a directly testable prediction.