Rotational and Translational Characteristics of Topological...

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

Blogs Literature

Posted 2025-10-20 05:27:07

1K

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.

Please log in to like, share and comment!

如何经营夫妻关系

99%的夫妻关系变差，都跟性格不和、身份差距、乃至生活习惯、兴趣爱好都没什么关系，真正的根源在于以下三点。不信，你就对照一下：...

By 2025-10-27 06:45:26 1 953

巴黎世家官網購物指南｜經典包款與機車包全解析

說到高端時尚品牌，巴黎世家（Balenciaga）絕對是近年來在年輕消費者間最具討論度的名字之一。從服飾、鞋款到配件，巴黎世家都展現出前衛且獨特的設計風格。其中，最受歡迎的單品莫過於...

By 2025-09-19 02:35:32 0 1K

MK經典包款推薦：水桶包與長夾一次擁有

在眾多精品配件品牌中，mk 包包（Michael Kors）一向以其實用性與時尚感深受女性青睞。無論是日常上班、假日休閒或出遊旅行，MK 總能提供適合不同場合的包款選擇。這篇文章將帶你一探...

By 2025-08-02 02:29:38 0 2K

All the high-quality department store products you need from China, I have them.

I have all kinds of industrial products in China in stock and am committed to serving thousands...

By 2025-06-27 08:27:44 0 3K

An Overview of the Development of Topological Vortex Theory (TVT)

1. Introduction: On the Topological Vortex Theory (TVT) and Topological vortices Topological...

By 2025-10-13 04:22:11 0 1K