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Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary
by Matteo Caldara, Andrea Richaud, Pietro Massignan, Alexander L. Fetter
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Matteo Caldara · Pietro Massignan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202311_00039v3 (pdf) |
| Date accepted: | 2024-07-23 |
| Date submitted: | 2024-07-18 13:02 |
| Submitted by: | Caldara, Matteo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Thank you for sending us the reports of the two Referees. We have addressed all the points raised by the second Referee, implementing their requests in the revised version of our paper. We have updated our arXiv manuscript and we have uploaded our response to the Referees.
In view of these latest improvements, we are confident that our work can be ready for publication in SciPost Physics.
Best regards,
The authors
List of changes
A detailed list of changes has been attached as a pdf file in the response to the second Referee.
Published as SciPost Phys. 17, 039 (2024)