Quantum Geometric Limits for Non-Abelian Holonomies
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910267068121088 |
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| author | Impens, François Guéry-Odelin, David |
| author_facet | Impens, François Guéry-Odelin, David |
| contents | Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek--Zee holonomies obey a universal quantum geometric limit~(QGL), in which the holonomy magnitude is bounded by a surface integral of the non-Abelian curvature norm. Recasting holonomic evolution as an effective Stokes--Schrödinger dynamics driven by transported curvature, we identify the QGL as the geometric counterpart of conventional quantum speed limits, with a time-integrated generator norm replaced by a surface-integrated curvature cost. The induced contour--surface variational problem is governed by a non-Abelian Lorentz force, which we address with a brachistochrone ansatz of curvature-weighted geodesics. Applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie-algebra direction, effectively taming non-Abelianity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Geometric Limits for Non-Abelian Holonomies Impens, François Guéry-Odelin, David Quantum Physics Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek--Zee holonomies obey a universal quantum geometric limit~(QGL), in which the holonomy magnitude is bounded by a surface integral of the non-Abelian curvature norm. Recasting holonomic evolution as an effective Stokes--Schrödinger dynamics driven by transported curvature, we identify the QGL as the geometric counterpart of conventional quantum speed limits, with a time-integrated generator norm replaced by a surface-integrated curvature cost. The induced contour--surface variational problem is governed by a non-Abelian Lorentz force, which we address with a brachistochrone ansatz of curvature-weighted geodesics. Applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie-algebra direction, effectively taming non-Abelianity. |
| title | Quantum Geometric Limits for Non-Abelian Holonomies |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.28754 |