Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916350678532096 |
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| author | Caldara, Matteo Richaud, Andrea Massignan, Pietro Fetter, Alexander L. |
| author_facet | Caldara, Matteo Richaud, Andrea Massignan, Pietro Fetter, Alexander L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13545 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary Caldara, Matteo Richaud, Andrea Massignan, Pietro Fetter, Alexander L. Quantum Gases 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. |
| title | Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2311.13545 |