Hydrodynamics of Quantum Vortices on a Closed Surface
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913226528129024 |
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| author | Xiong, Yanqi Yu, Xiaoquan |
| author_facet | Xiong, Yanqi Yu, Xiaoquan |
| contents | We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane, the covariant vortex fluid equation on a curved surface contains an additional term proportional to Gaussian curvature multiplying the circulation quantum. This term describes the coupling between topological defects and curvature in the macroscopic level. For a sphere, the simplest nontrivial stationary vortex flow is obtained analytically and this flow is analogous to the celebrated zonal Rossby-Haurwitz wave in classical fluids on a nonrotating sphere. For this flow the difference between the coarse-grained vortex velocity field and the fluid velocity field generated by vortices is solely driven by curvature and vanishes in the corresponding vortex flow on a plane when the radius of the sphere goes to infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_05373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hydrodynamics of Quantum Vortices on a Closed Surface Xiong, Yanqi Yu, Xiaoquan Quantum Gases Other Condensed Matter Superconductivity Fluid Dynamics We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane, the covariant vortex fluid equation on a curved surface contains an additional term proportional to Gaussian curvature multiplying the circulation quantum. This term describes the coupling between topological defects and curvature in the macroscopic level. For a sphere, the simplest nontrivial stationary vortex flow is obtained analytically and this flow is analogous to the celebrated zonal Rossby-Haurwitz wave in classical fluids on a nonrotating sphere. For this flow the difference between the coarse-grained vortex velocity field and the fluid velocity field generated by vortices is solely driven by curvature and vanishes in the corresponding vortex flow on a plane when the radius of the sphere goes to infinity. |
| title | Hydrodynamics of Quantum Vortices on a Closed Surface |
| topic | Quantum Gases Other Condensed Matter Superconductivity Fluid Dynamics |
| url | https://arxiv.org/abs/2305.05373 |