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.

Vă rugăm să vă autentificați pentru a vă dori, partaja și comenta!

電子菸菸彈推薦｜YOOZ 煙彈、一次性小煙、IQOS 與 Relx 6000口全面解析

在現代年輕族群與菸友之間，電子菸菸彈與一次性小煙已逐漸取代傳統紙菸，成為市場上的新寵。隨著品牌選擇愈加多樣，像是 YOOZ 煙彈、YOOZ 電子菸、IQOS 電子煙與 Relx...

By 2025-08-29 02:42:31 0 2K

คู่มือเลือกบุหรี่ไฟฟ้า RELX และหัวพอดรุ่นใหม่ที่เหมาะกับคุณ

ตลาดบุหรี่ไฟฟ้าในประเทศไทยเติบโตอย่างต่อเนื่อง และหนึ่งในแบรนด์ที่ได้รับความนิยมสูงสุดคือ...

By 2025-11-17 01:45:51 0 769

Evolving Dynamics and Future Opportunities in the Smart Home Device Market Trends

The global demand for smart technologies continues to reshape the way people live,...

By 2025-10-30 06:35:51 0 1K

The Growing Demand for Ethernet Cable in a Connected World

The Ethernet Cable Market has been experiencing rapid growth in recent years, driven by...

By 2025-09-24 09:20:06 0 1K

gan

gous脸书

By 2025-09-12 14:46:48 0 2K