TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.039
TI  - Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: The case of an elliptical boundary
PY  - 2024/08/08
UR  - https://scipost.org/SciPostPhys.17.2.039
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 039
A1  - Caldara, Matteo
AU  - Richaud, Andrea
AU  - Massignan, Pietro
AU  - Fetter, Alexander L.
AB  - Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex configurations may be computed on a complicated (curved or bounded) surface, provided that one knows a conformal map that links the latter to a simpler domain (like the full plane, or a circular boundary). We also prove that Hamilton's equations based on the vortex energy agree with the complex dynamical equations for the vortex dynamics, demonstrating that the vortex trajectories are constant-energy curves. We use these ideas to study the dynamics of vortices in a two-dimensional incompressible superfluid with an elliptical boundary, and we derive an analytical expression for the complex potential describing the hydrodynamic flow throughout the fluid. For a vortex inside an elliptical boundary, the orbits are nearly self-similar ellipses.
ER  -

@Article{10.21468/SciPostPhys.17.2.039,
	title={{Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: The case of an elliptical boundary}},
	author={Matteo Caldara and Andrea Richaud and Pietro Massignan and Alexander L. Fetter},
	journal={SciPost Phys.},
	volume={17},
	pages={039},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.039},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.039},
}