SciPost Submission Page
Superfluid vortex dynamics with an elliptical boundary
by Matteo Caldara, Andrea Richaud, Pietro Massignan, Alexander L. Fetter
Submission summary
| Authors (as registered SciPost users): | Matteo Caldara · Pietro Massignan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202311_00039v2 (pdf) |
| Date submitted: | 2024-06-24 09:38 |
| 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.
At the moment, we would decline the transfer to the journal SciPost Physics Core. Instead, we would like our resubmission to be considered for publication in the journal SciPost Physics.
In light of Referees' comments and requests, we have substantially modified our manuscript in order to highlight the original contributions that our work can bring to the field of superfluid vortex dynamics, as well as how it now fulfills the journal acceptance criteria. We summarised the general structure of the new version of our paper at the beginning of the reply to both Referees.
We have replaced the arXiv manuscript with the revised version that seeks to comply with the requests of both Referees. Our detailed point-by-point response to the Referees has been uploaded, too. In our response, we also explicitly reference the acceptance criteria.
In view of the considerable improvements that we have implemented in response to the points raised by the Referees, we are confident that this revised version of our paper can be accepted for publication in SciPost Physics.
Best regards,
The authors
List of changes
A detailed list of changes can be found at the beginning of the reply to both Referees that has been attached as a pdf file.
Current status:
Reports on this Submission
Strengths
1. Well-written, clear and concise manuscript
2. Of interest to a wide audience working in fluid flow in classical and quantum fluids.
3. Novel use of conformal transformations to derive analytical results for modelling complex vortex setups in bounded domains.
Report
The authors have submitted a revised manuscript that includes changes and responses to all of the reviewers’ comments. In doing so, they have adequately addressed the main criticism from both referees regarding the significance and novelty of the work and made significant improvements to the manuscript through revisions and additional research.
The revised introduction clarifies how the present work compares to previously published research. The revised manuscript significantly strides in using conformal transformations to study point vortex dynamics. It shows how the work can be applied to more general cases of point vortex dynamics in bounded domains.
Consequently, I am happy to recommend the publication of this work to SciPost Physics.
Requested changes
The Authors have addressed all changes previously outlined. No more changes are requested.
Recommendation
Publish (meets expectations and criteria for this Journal)