Index Theorem and Vortex Kinetics in Bose-Einstein Condensates on a Haldane Sphere with a Magnetic Monopole
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916825732743168 |
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| author | Chen, Xi-Yu Jiang, Lijia Yang, Tao Zheng, Jun-Hui |
| author_facet | Chen, Xi-Yu Jiang, Lijia Yang, Tao Zheng, Jun-Hui |
| contents | The geometry-gauge interplay constitutes a fundamental issue in quantum physics, with profound implications spanning from quantum gravity to topological matter. Here, we investigate the dynamic effects of geometry-gauge interplay in Bose-Einstein condensates (BECs) on a Haldane sphere with a magnetic monopole. We reveal an index theorem that establishes a correspondence between BEC vortices and the topology of the gauge field, enabling the construction of vortex-monopole composites. Furthermore, we derive the universal logarithmic interaction between composites, which governs the structure of the ground-state vortex lattice. By developing a kinetic theory, we predict scale-invariant vortex dynamics and an emergent duality. Both are confirmed through numerical simulations. This work first presents the dynamical coupling mechanism between spatial geometry and gauge fields, providing deep insights into superfluid systems with topological gauge structures in curved space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_03375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Index Theorem and Vortex Kinetics in Bose-Einstein Condensates on a Haldane Sphere with a Magnetic Monopole Chen, Xi-Yu Jiang, Lijia Yang, Tao Zheng, Jun-Hui Quantum Gases Pattern Formation and Solitons Quantum Physics The geometry-gauge interplay constitutes a fundamental issue in quantum physics, with profound implications spanning from quantum gravity to topological matter. Here, we investigate the dynamic effects of geometry-gauge interplay in Bose-Einstein condensates (BECs) on a Haldane sphere with a magnetic monopole. We reveal an index theorem that establishes a correspondence between BEC vortices and the topology of the gauge field, enabling the construction of vortex-monopole composites. Furthermore, we derive the universal logarithmic interaction between composites, which governs the structure of the ground-state vortex lattice. By developing a kinetic theory, we predict scale-invariant vortex dynamics and an emergent duality. Both are confirmed through numerical simulations. This work first presents the dynamical coupling mechanism between spatial geometry and gauge fields, providing deep insights into superfluid systems with topological gauge structures in curved space. |
| title | Index Theorem and Vortex Kinetics in Bose-Einstein Condensates on a Haldane Sphere with a Magnetic Monopole |
| topic | Quantum Gases Pattern Formation and Solitons Quantum Physics |
| url | https://arxiv.org/abs/2507.03375 |