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

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.

Please log in to like, share and comment!

Topological Vortex Space-Time Ontology (TVSTO)

3.3 Symmetry Transition Theory: Proposes higher-order symmetry groups G_n to describe the vortex...

By 2025-10-10 07:33:21 0 999

Regional Insights into the Teeth Whitening Market: Growth Hotspots in North America, Europe, and Asia-Pacific

The global teeth whitening market size was USD 7.02 Billion in 2022 and is expected to register a...

By 2025-08-26 11:00:11 0 2K

Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (2)

2. Rotational Characteristics of Topological Vortices and Antivortices 2.1 Rotational Direction...

By 2025-10-20 05:13:27 0 795

gan

gous脸书

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

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...

By 2025-10-15 01:51:27 0 969