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  • Open Access

Separation of quantum time evolution into holonomic and dynamical parts

Adam Fredriksson1,2,* and Erik Sjöqvist1,†

  • 1Department of Physics and Astronomy, Uppsala University, Box 524, SE-751 20 Uppsala, Sweden
  • 2Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany

  • *Contact author: Adam.Fredriksson@uni-siegen.de
  • †Contact author: erik.sjoqvist@physics.uu.se
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Phys. Rev. A 113, 062202 – Published 1 June, 2026

DOI: https://doi.org/10.1103/n9tc-4ppk

Abstract

The issue of separating Schrödinger-type quantum time evolution into a product of holonomic and dynamical parts in the nonadiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible, and we prove that separability is a gauge-invariant property of quantum time evolution. The general analysis is implemented in a three-level system with Λ-type coupling structures. The typical case where the holonomic and dynamical parts do not separate is illustrated by means of two noncommuting Λ-type Hamiltonians.

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Phys. Rev. A 113, 062202– Published 1 June, 2026
  • Received 3 June 2025
  • Revised 12 February 2026
  • Accepted 13 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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