On the Meissner state for type-II inhomogeneous superconductors
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917822255333376 |
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| author | Díaz-Vera, Matías Román, Carlos |
| author_facet | Díaz-Vera, Matías Román, Carlos |
| contents | We consider extreme type-II superconductors modeled by the Ginzburg--Landau energy with a pinning term $a_\varepsilon(x)$, which we assume to be a bounded measurable function such that $b\leq a_\varepsilon(x)\leq 1$ for some constant $b>0$. A crucial feature of this type of superconductors is the occurrence of vortices, which appear above the so-called first critical field $H_{c_1}$. In this paper we estimate this value and characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the energy below $H_{c_1}$. In addition, we show that beyond this value, for applied fields whose strength is slightly below the so-called superheating field $H_{sh}$, there exists a unique Meissner-type solution that locally minimizes the energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Meissner state for type-II inhomogeneous superconductors Díaz-Vera, Matías Román, Carlos Analysis of PDEs Mathematical Physics We consider extreme type-II superconductors modeled by the Ginzburg--Landau energy with a pinning term $a_\varepsilon(x)$, which we assume to be a bounded measurable function such that $b\leq a_\varepsilon(x)\leq 1$ for some constant $b>0$. A crucial feature of this type of superconductors is the occurrence of vortices, which appear above the so-called first critical field $H_{c_1}$. In this paper we estimate this value and characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the energy below $H_{c_1}$. In addition, we show that beyond this value, for applied fields whose strength is slightly below the so-called superheating field $H_{sh}$, there exists a unique Meissner-type solution that locally minimizes the energy. |
| title | On the Meissner state for type-II inhomogeneous superconductors |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2410.22438 |