Quantum Geometric Limits for Non-Abelian Holonomies

• URL: http://arxiv.org/abs/2605.28754v1
• Date: Wed, 27 May 2026 17:13:07 GMT
• Title: Quantum Geometric Limits for Non-Abelian Holonomies
• Abstract summary: Wilczek--Zee holonomies obey a universal quantum geometric limit(QGL)<n>We recast holonomic evolution as an effective Stokes-Schrdinger dynamics driven by transported curvature.<n>applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie- algebra direction.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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