Sarma-Bogomol'nyi equations in superconductivity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909881127141376 |
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| author | Kyler, Mia Kolomeisky, Eugene B. |
| author_facet | Kyler, Mia Kolomeisky, Eugene B. |
| contents | Topological defects occurring in nonlinear classical field theories are described by a system of second-order differential equations. A breakthrough was made in 1976 by E. B. Bogomoln'yi who demonstrated that in several field theories these equations can be reduced to first-order provided the coupling constants take on particular values. One of the examples involved a string in the Abelian Higgs model which is equivalent to the Abrikosov flux line of the Ginzburg-Landau theory of superconductivity. In a similar vein, in the 1966 textbook Superconductivity of Metals and Alloys P. G. de Gennes explained how to reduce the second-order Ginzburg-Landau equations to first-order at a particular value of the Ginzburg-Landau parameter by a method due to G. Sarma. We analyze the two ways of arriving at the first-order Sarma-Bogomol'nyi equations and conclude that while they both rely on the same operator identity, Sarma's method is free of the assumption that there is a topological defect. The implication is that Bogomol'nyi equations found in other field theories may be a source of a wider range of solutions beyond topological defects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sarma-Bogomol'nyi equations in superconductivity Kyler, Mia Kolomeisky, Eugene B. Superconductivity High Energy Physics - Theory Mathematical Physics Topological defects occurring in nonlinear classical field theories are described by a system of second-order differential equations. A breakthrough was made in 1976 by E. B. Bogomoln'yi who demonstrated that in several field theories these equations can be reduced to first-order provided the coupling constants take on particular values. One of the examples involved a string in the Abelian Higgs model which is equivalent to the Abrikosov flux line of the Ginzburg-Landau theory of superconductivity. In a similar vein, in the 1966 textbook Superconductivity of Metals and Alloys P. G. de Gennes explained how to reduce the second-order Ginzburg-Landau equations to first-order at a particular value of the Ginzburg-Landau parameter by a method due to G. Sarma. We analyze the two ways of arriving at the first-order Sarma-Bogomol'nyi equations and conclude that while they both rely on the same operator identity, Sarma's method is free of the assumption that there is a topological defect. The implication is that Bogomol'nyi equations found in other field theories may be a source of a wider range of solutions beyond topological defects. |
| title | Sarma-Bogomol'nyi equations in superconductivity |
| topic | Superconductivity High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2410.05179 |