Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (5)

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Posted 2025-10-20 05:37:44
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5. Conclusion

Based on Topological Vortex Theory, this paper systematically studied the characteristic features of vortices and antivortices in rotational and translational motion, and thoroughly explored their intrinsic relationships with topological structures such as loops and knots. The research shows that differences in the rotational direction of vortices and antivortices can induce rich topological phase transition behaviors, while their translational characteristics can reveal propagation patterns through knot theory. Loops and knots, as important topological invariants, provide key theoretical tools for analyzing the dynamical behaviors of vortex-antivortex pairs. These results not only deepen the theoretical understanding of topological defect dynamics but also lay a theoretical foundation for applied research in related fields such as optical vortices and quantum condensed matter physics.

References

  1. Congy, T., Azam, P., Kaiser, R., & Pavloff, N. (2024). Topological Constraints on the Dynamics of Vortex Formation in a Two-Dimensional Quantum Fluid. Physical Review Letters, *132*, 033804. https://doi.org/10.1103/physrevlett.132.033804.
  2. Zhong, J., & Zhan, Q. (2023). Optical toroidal vortices under topological perspective. Physics, *52*(10), 673-681. (Note: This is a citation for the Chinese journal (Wuli)). An English version of the article is available at: https://www.thepaper.cn/newsDetail_forward_25544446.
  3. Bai, W. (2021). Research on Knot Dynamics in Bose-Einstein Condensates (Doctoral dissertation, Northwest University). https://wf.pub/thesis/article:D02560789.
  4. Zhu, R., Zheng, S., Li, X., Wang, T., Tan, C., Yu, T., Liu, Z., Wang, X., Li, J., Wang, J., & Gao, P. (2024). Atomic-Scale Tracking Topological Phase Transition Dynamics of Polar Vortex-Antivortex Pairs. Advanced Materials, 2312072. https://doi.org/10.1002/adma.202312072.
  5. Jing Wang, Rongzhen Gao, Shiyu Tang, Shouzhe Dong, etc. (2025). General principle of ferroelectric topological domain formation. Science Advances, *11*(7). https://www.science.org/doi/10.1126/sciadv.adu6223.

Academic Statement

Certain analyses and discussions in this paper have referenced and drawn upon recent cutting-edge research published in journals such as Physical Review Letters, Science Advances, and Advanced Materials, including but not limited to topological constraints on vortex-antivortex pairs in quantum fluids, the generation and characterization of optical vortex rings, and knot dynamics in Bose-Einstein condensates. The authors hereby express gratitude to the researchers and teams behind these works. This paper is intended for international academic exchange. Reproduction without permission is prohibited.

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