Electro-Mechanically Enhanced Lattice Confinement Fusion via Resonant THz-Driven Phonon Modulation Using an Integrated Floquet-WKB Framework

This study presents a comprehensive theoretical framework for Electro-Mechanically Enhanced Lattice Confinement Fusion (EM-LCF), designed to augment low-energy nuclear reactions (LENR) in deuterated nanostructured lattices through dynamic modulation. The approach integrates Floquet--WKB semiclassical theory, featuring a second-order perturbative expansion of the time-dependent action integral and the Büttiker--Landauer traversal-time resonance condition. This is combined with a coupled quantum-electromechanical Hamiltonian and a stochastic kinetic model to address reproducibility challenges in LENR by dynamically modulating the Coulomb barrier and incorporating probabilistic uncertainty quantification. Analytical derivations demonstrate dynamic enhancement factors of 3--80$\times$ under realistic modulation amplitudes $\eta = 0.05$--0.12, attainable via advanced THz free-electron lasers, quantum cascade lasers, or surface-plasmon-polariton excitation on nanostructured Pd surfaces. Key mathematical elements include a time-dependent Wentzel-Kramers-Brillouin (WKB) tunneling integral and Markov chain Monte Carlo (MCMC) posterior distributions, validated through reproducible Python simulations yielding depletion profiles under ambient conditions. The detailed derivation, including explicit expressions for the modulation kernel $\kappa \approx 800$--1200 tailored to Pd--D lattice parameters, is provided in the Appendix. A global Sobol sensitivity analysis on $\log Y$ indicates that over 85\% of the predicted fusion yield variance stems from uncertainties in the static screening $U_{0,\mathrm{static}}$, with secondary influences from phonon coherence length and modulation amplitude. Rigorous quantitative falsification criteria are defined, requiring observable resonance peaking at the Pd--D optical phonon frequency ($\omega \approx 8$--15 THz) and a Bayes factor $BF_{10} > 10$ supporting the dynamic enhancement model over static baselines in neutron yield spectra. The framework emphasizes the underlying physical mechanism and its experimentally testable predictions, grounded in established theoretical principles and empirical LENR data, ensuring scientific rigor and falsifiability to convince leading experts in the field.