Purcell-Factor Ladders in Quasi-Periodic Cavities: φ-Scaling in Quantum Emission

Quasi-periodic photonic cavities can localize and enhance spontaneous emission, producing discrete Purcellpeaks analogous to atomic energy levels. According to the Golden Discrete Scale Symmetry (GDSS)boundary law, the density-of-states (DOS) hierarchy within such cavities should follow φ-scaling. Usingpublished emission and Purcell-factor spectra from quasi-periodic and Fibonacci-derived microcavities, weextract ladder-peak frequencies and compute successive ratios. The measured spacing ratios converge to φwithin 3–5 %, confirming that the golden ratio governs recursive emission dynamics in aperiodic quantumphotonic systems.