GQR IV: A Quantum Shield Law for Coherence and Tunnelling

GQR IV: A Quantum Shield Law for Coherence and Tunnelling Abstract We present the Gated Quantum Resonator (GQR), a Hamiltonian framework in which reactive coordinates act as coupled vibronic–electronic resonators perturbed by a finite alphabet of gates (A–J). Its central construct is the Quantum Shield law g 2 = κγϕ, which delineates incoherent decay from recoherent dynamics. Time- dependent Schrödinger simulations confirm that below-Shield trajectories decay monotonically, whereas above-Shield trajectories exhibit oscillatory recoherence and Stückelberg interference. We show how the same Shield condition aligns long- range protein electron-transfer data (Gray–Winkler) with isotope-resolved proton tunnelling in enzymes (Scrutton/Masgrau), where mass-dependent overlaps and environmental deformations jointly explain electron-transfer slopes and softened isotope responses. The framework complements Lindblad–GKLS open-system dynamics by furnishing a microscopic threshold for decoherence, and it yields testable predictions for ultrafast spectroscopy, coherent-quantum TEM, and flux-tunnelling materials. GQR thus places the transition from decoherence to recoherence as a measurable boundary condition linking theory, computation, and experiment across condensed-phase and biological quantum systems.