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  • Open Access

Dynamics of quantized vortices under quasi-periodic boundary conditions

Fabio Magistrelli1,* and Marco Antonelli2,†

  • *Contact author: fabio.magistrelli@uni-jena.de
  • †Contact author: antonelli@lpccaen.in2p3.fr
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Phys. Rev. A 113, 013307 – Published 5 January, 2026

DOI: https://doi.org/10.1103/6jbn-t4zl

Abstract

The Gross-Pitaevskii equation is widely used for vortex dynamics, but finite domains with hard walls or confining potentials distort bulk behavior through vortex-image effects or induced flows. Periodic boundaries reduce wall artifacts yet cannot realize finite net vorticity because of topological obstruction, so bulk simulations with nonzero circulation are typically unavailable. Hence, we impose quasi-periodic boundary conditions that keep the superfluid's density periodic while enforcing phase windings consistent with a net prescribed total vorticity. This setting conserves the net number of vortices and enables long-time tracking of vortex trajectories in settings that finite containers cannot capture. This allows us to study vortex depinning and nucleation leading to the creation of Kármán vortex streets and perfectly periodic vortex arrays. The framework also provides a toy model for studying vortex dynamics in the bulk of neutron stars, free of possible limitations induced by confining potentials.

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Phys. Rev. A 113, 013307– Published 5 January, 2026
  • Received 29 September 2025
  • Accepted 19 December 2025
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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.

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