Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures
Abstract
:1. Motivation Behind Bogomolny Approach
2. Elementary Introduction to Bogomolny Theory
3. A Short Description of the Bogomolny Equations for a Usual Gauged G-L Model
4. The Gauged G-L Model in a Curved Space and the Concept of Strong Necessary Conditions in the Equations of Motion
- Make a certain part of the dual equations linearly dependent—the remaining equations are just the Bogomolny equations;
- Obtain a condition for the potential of the given field-theoretical model. The Bogomolny decomposition (the Bogomolny equations) exists only for this model, whose potential satisfies such a condition.
5. Derivation of the Bogomolny Equations for the Gauged G-L Model in a Flat Space
6. Deriving the Bogomolny Equations of the G-L Model in a Curved Space
7. Perturbative Approach in the Description of the Josephson Junction
Perturbative G-L Approach
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Stȩpień, Ł.T.; Pomorski, K. Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures. Quantum Rep. 2025, 7, 4. https://doi.org/10.3390/quantum7010004
Stȩpień ŁT, Pomorski K. Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures. Quantum Reports. 2025; 7(1):4. https://doi.org/10.3390/quantum7010004
Chicago/Turabian StyleStȩpień, Łukasz T., and Krzysztof Pomorski. 2025. "Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures" Quantum Reports 7, no. 1: 4. https://doi.org/10.3390/quantum7010004
APA StyleStȩpień, Ł. T., & Pomorski, K. (2025). Towards Ginzburg–Landau Bogomolny Approach and a Perturbative Description of Superconducting Structures. Quantum Reports, 7(1), 4. https://doi.org/10.3390/quantum7010004