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Quasi-holonomy in non-adiabatic quantum evolution

  • Erik Sjöqvist
  • Adam Fredriksson
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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.

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Cite

BibTeXRIS
BibTeX
@misc{sjoqvist2026quasiholonomy,
  title = {{Quasi-holonomy in non-adiabatic quantum evolution}},
  author = {Erik Sjöqvist and Adam Fredriksson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.05218},
  eprint = {2607.05218},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.05218},
}
RIS
TY  - UNPB
TI  - Quasi-holonomy in non-adiabatic quantum evolution
AU  - Erik Sjöqvist
AU  - Adam Fredriksson
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.05218
UR  - https://arxiv.org/abs/2607.05218
AB  - 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.
ER  -