On the stability of the Abrikosov lattice in the Lowest Landau Level
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910403278143488 |
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| author | Germain, Pierre Schwinte, Valentin Thomann, Laurent |
| author_facet | Germain, Pierre Schwinte, Valentin Thomann, Laurent |
| contents | We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of stationary solutions. Then we investigate the linear stability of the lattice solution and prove it is stable for the (hexagonal) Abrikosov lattice, but unstable for rectangular lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stability of the Abrikosov lattice in the Lowest Landau Level Germain, Pierre Schwinte, Valentin Thomann, Laurent Analysis of PDEs We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of stationary solutions. Then we investigate the linear stability of the lattice solution and prove it is stable for the (hexagonal) Abrikosov lattice, but unstable for rectangular lattices. |
| title | On the stability of the Abrikosov lattice in the Lowest Landau Level |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.06085 |