Quantum Klein-Gordon model of Quantum Many-BodyHysteresis in Topological Insulators for Hydrogen Switching inMg-Ni Alloys and CO2 Reduction Catalysis

This work integrates the Simple Binary Memory (SBM-ODE) model with topological insulator (TI) dynamics and quantum many-body hysteresis, extending to quantum Klein-Gordon (KG) frameworks for hydrogen switching in Mg-Ni alloys and CO2 reduction. We canonically quantize Duffing oscillator chains to derive quantum KG equations, incorporating synchronization for efficient absorption/desorption. Using Chiba’s Renormalization Group Method (RGM), we prove SU(2)-symmetry breaking preservation via Schur’s lemma, derive scale-dependent flows for N-dependent hysteresis, and evaluate Hartree- Fock-Bogoliubov (HFB) self-consistency. Numerical simulations with QuTiP show oscillatory ⟨σz⟩ (amplitude ∼0.1, period 5) with damping in quantum KG under Mg-Ni lattice, confirming winding number shifts (w: 1 → 0 at μ = ±2t). Model Predictive Control (MPC) optimizes multi-electron transfers, yielding 15-25% improvements. This bridges spintronics, quantum materials, and sustainable energy, aligning with 2025 trends in topological many-body systems[15][33][1].