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(GQR26) Quantum Geometry Engine for Multi-Centre Quantum Systems.

JAMES SUTTON

Published Jan 2, 2026• 0 citations
Publisher

Abstract

Coherent transport in multi-centre quantum systems—from catalytic clusters and enzyme activesites to moir´e materials, hybrid resonators, and superconducting circuits—is usually analysed insystem-specific parameter spaces or with heavy MD/DFT machinery. Here we introduce a geometry-only framework, the Quantum Geometry Engine (QGE), in which coherent behaviour is encoded bycurvature on a low-dimensional control manifold constructed directly from structural descriptors.An effective potential F(ξ), derived from coherence-relevant observables, defines a Hessian metricgij = ∂i∂jF whose scalar and sectional curvature classify coherent regimes. Coherence corridorsemerge as geodesics, shield plateaus correspond to metric degeneracy (det g ≈ 0), and ladder-likereactivation arises from curvature reappearance and geodesic branching. A Casimir–curvatureextension incorporates boundary-induced vacuum-field effects, placing confined nanostructures andcavity platforms on the same geometric footing as molecular and biological systems. Within thisunified framework, vortex-like rotation of coherent channels, inhibitor-induced collapse in Fe–S andOEC models, isotope and chalcogen anomalies, miniband distortions in moir´e materials, and hybrid-mode splitting in resonators are all revealed as manifestations of a single curvature-based mechanism.QGE thus provides a coordinate-independent, cross-domain description of multi-centre quantumdynamics that operates without molecular dynamics, molecular mechanics, density functional theory,or QM/MM, and is directly implementable as a stand-alone geometry engine for design and analysis. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.

DOI
10.5281/zenodo.18134190

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Einstein’s insight that geometry governs energy and momentum defined the ar-chitecture of physics. Here that principle is extended to coherence itself. TheGated Quantum Resonator (GQR) framework shows that coherent energy trans-fer is governed by a curvature–information lawg2 = κ γϕ, (1)linking coupling strength, geometric curvature, and dephasing rate—an analogueof the energy–curvature–entropy balance in general relativity.We derive this law from a non-Abelian SU(3)coh gauge field that confines co-herence into “coherence-neutral’’ manifolds, the microscopic counterpart of theEinstein–Cartan–Penrose geometric–information framework. Its thermodynamicclosure,δ(g2) = TeffδScoh, (2)mirrors Jacobson’s δQ = T δS, embedding quantum coherence in a unified Einstein–Penrose geometry where curvature, torsion, and information are co-dependent. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
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