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  • Letter
  • Open Access

Analytic phase solution and point vortex model for dipolar quantum vortices

Ryan Doran*

Thomas Bland†

  • Joint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom and MARS: Mathematics for AI in Real-world Systems, School of Mathematical Sciences, Lancaster University, Lancaster LA1 4YF, United Kingdom

  • Mathematical Physics, LTH, Lund University, Post Office Box 118, S-22100 Lund, Sweden

  • *Contact author: r.doran@lancaster.ac.uk
  • †Contact author: thomas.bland@fysik.lu.se
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Phys. Rev. Research 8, L042014 – Published 30 October, 2026

DOI: https://doi.org/10.1103/299h-xjc4

Abstract

We derive an analytic expression for the phase of a quantum vortex in a dipolar Bose-Einstein condensate, capturing anisotropic effects from long-range dipole-dipole interactions. This solution provides a foundation for a dipolar point vortex model (DPVM), incorporating both phase-driven flow and dipolar forces. The DPVM reproduces key features of vortex pair dynamics seen in full simulations, including anisotropic velocities, deformed orbits, and directional motion, offering a minimal and accurate model for dipolar vortex dynamics. Our results open the door to analytic studies of vortices in dipolar quantum matter and establish a platform for exploring vortex dynamics and turbulence in these systems.

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Phys. Rev. Research 8, L042014– Published 30 October, 2026
  • Received 4 July 2025
  • Revised 27 October 2025
  • Accepted 9 October 2026
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