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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chen, Xi-Yu, Jiang, Lijia, Yang, Tao, Zheng, Jun-Hui
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916825732743168
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
id 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