Index Theorem and Vortex Kinetics in Bose-Einstein Condensates on a Haldane Sphere with a Magnetic Monopole

• URL: http://arxiv.org/abs/2507.03375v1
• Date: Fri, 04 Jul 2025 08:15:50 GMT
• Title: Index Theorem and Vortex Kinetics in Bose-Einstein Condensates on a Haldane Sphere with a Magnetic Monopole
• Authors: Xi-Yu Chen, Lijia Jiang, Tao Yang, Jun-Hui Zheng,
• Abstract summary: We investigate the dynamic effects of geometry-gauge interplay in Bose-Einstein condensates (BECs) on a Haldane sphere with a magnetic monopole.<n>By developing a kinetic theory, we predict scale-invariant vortex dynamics and an emergent duality.<n>This work first presents the dynamical coupling mechanism between spatial geometry and gauge fields, providing deep insights into superfluid systems.
• Score: 4.041127211242457
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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