Analytic Phase Solution and Point Vortex Model for Dipolar Quantum Vortices

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 new platform for exploring vortex dynamics and turbulence in these systems.