Quantum–Relativistic Modeling of Nanoscale Capacitance in Curved Space: Effects of Friction, Magnetic Fields, and Surface Chemistry

This study presents a quantum–relativistic analytical model for evaluating the capacitance behavior of nanoscale systems under the combined influence of magnetic fields, frictional damping, and surface chemical potentials. The model extends the traditional Schrödinger equation by embedding curvature-dependent and dissipative energy terms, resulting in a unified theoretical expression that remains finite and tunable across varying field strengths. The derived relation C = n e² r₀² A² [1/ω + (γ + μ B)/(ħ²k₁)] reveals that nanoscale capacitance is not a static property but a dynamic function of frequency, magnetic moment, and surface adsorption effects. This framework successfully bridges quantum mechanics, relativity, and surface electrochemistry, providing a predictive tool for interpreting charge storage, polarization, and energy conversion processes in nanostructured ferrites, hybrid oxides, and carbon-based composites. The results highlight the significance of curvature-induced fields and spin alignment in enhancing the charge localization and energy density of next-generation quantum capacitors and magneto–ionic materials.