Quasi-holonomy in non-adiabatic quantum evolution

Abstract:We develop a framework for quasi-holonomy in non-adiabatic quantum time evolution of subspaces along loops in a complex Grassmannian. By factoring the Schrödinger evolution into dynamical and connection-induced contributions in a moving basis, we obtain an effective geometric generator that depends explicitly on the dynamical propagator. This quasi-connection does not define a genuine connection on the original Grassmann bundle, since its gauge transformation law acquires a history-dependent, nonlocal term. Other ways of factoring the Schrödinger evolution are briefly discussed. All these approaches suffer from the same type of history-dependence, thereby defining transport of subspaces in which geometric and dynamical effects are generally intertwined, just as in the case of the quasi-holonomy. Our work sheds light on the issue of separating quantum evolution of subspaces into holonomic and dynamical parts from an essentially gauge-theoretic perspective.

arXiv:2607.05218 [quant-ph]

(or arXiv:2607.05218v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.05218 Focus to learn more arXiv-issued DOI via DataCite

J. Phys. A: Math. Theor. 59, 355308 (2026)

https://doi.org/10.1088/1751-8121/ae9e6e Focus to learn more DOI(s) linking to related resources

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