Rotational and Translational Characteristics of Topological...

加入

登录

注册

搜索

主题切换

夜间模式

Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (4)

网站博客 Literature

已发布 2025-10-20 05:27:07

807

4. Topological Significance of Loops and Knots

4.1 Topological Invariants in Loop Structures

As an important topological model for describing vortex-antivortex pairs in three-dimensional space, the stability of loop structures can be characterized by a series of topological invariants. Taking the optical vortex ring as an example, its knot number determines the topological undeformability of the structure. Changes in the knot number can reflect the interaction between vortex-antivortex pairs: co-rotating vortex pairs tend to form stable loop structures with higher knot numbers, while counter-rotating pairs may lead to structural annihilation due to a decrease in the knot number. Therefore, topological invariants provide an important theoretical tool for analyzing the stability of vortex-antivortex pairs.

4.2 Topological Phase Transition Behavior in Knot Theory

Knot theory provides an effective framework for understanding the topological phase transitions of vortex-antivortex pairs. For example, in optical vortices, changes in the kinking number can cause significant transitions in the phase structure. Such phase transitions are closely related to the rotational and translational behaviors of vortex-antivortex pairs: co-rotating vortex pairs help form topological structures with stable kinking numbers, while counter-rotating pairs may trigger topological phase transitions due to abrupt changes in the kinking number. This mechanism provides a theoretical basis for topological control in optical device design and quantum information transmission.

请登录以点赞、分享和评论！

1代煙彈與 2代阿爾法升級版完整解析

在電子菸市場中，悅刻（RELX）...

通过 2025-09-05 02:52:57 0 2千

The quantum is not a cat that is both dead and alive (4)

4. Integrating Kant's "Thing-in-Itself": A Philosophical Revolution Resolving the Observer...

通过 2025-10-15 01:51:27 0 969

On the Topological Nature of Noether's Theorem (5)

References Kibble, T. W. B. (1976). Topology of Cosmic Domains and Strings. Journal of Physics...

通过 2025-11-27 03:24:30 0 732

Evolving Financial Landscape Drives Global Accounting Services Market Expansion

The global Accounting Services Market Share is experiencing significant growth as organizations...

通过 2025-10-30 08:27:24 0 788

Competitive Landscape in the Paints and Coatings Market: Innovations, Key Players, and Strategic Moves

The global paints and coatings market size was USD 178.42 Billion in 2022 and is expected to...

通过 2025-08-26 11:24:25 0 2千