Structured Energy Return in Quantum Systems

Decoherence is a fundamental challenge in quantum mechanics, resulting in phase coherence loss and a transition from quantum to classical behavior. The Structured Energy Return (SER) model proposes a feedback-based mechanism that actively reshapes coherence loss. Here, we extend our previous findings by systematically exploring the parameter space involving coupling and feedback strengths. The results highlight robust scale-invariance and clarify optimal operating conditions, significantly enhancing the practical applicability of the SER model. The SER Model shows that it can: Can redistribute coherence loss over time instead of merely slowing it, Sometimes re-purifies the system to a near-pure state (especially in 2×2 simulations), In higher dimensions (e.g., 4×4), can drive the system toward a partially mixed but stable state— maintaining significant coherence, In physically realistic quantum-optical systems (e.g., Jaynes–Cummings model), sustains Rabi oscillations and partially preserves qubit coherence.This unified document outlines the development of SER, from the earliestsingle-particle wavefunction formulation to the Lindblad-based densitymatrix approach, culminating in positivity-enforced simulations across multiple system sizes and the latest Jaynes–Cummings results.