A connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians in the context of shape optimization problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917278114643968 |
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| author | Duran, Joaquim Mas, Albert Sanz-Perela, Tomás |
| author_facet | Duran, Joaquim Mas, Albert Sanz-Perela, Tomás |
| contents | This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in $\mathbb{R}^2$. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type inequalities for $\overline\partial$-Robin Laplacians. Thanks to this, we prove them in the case of simply connected domains for quantum dot boundary conditions asymptotically close to zigzag boundary conditions. Finally, we also study the case of negative mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians in the context of shape optimization problems Duran, Joaquim Mas, Albert Sanz-Perela, Tomás Analysis of PDEs Mathematical Physics Primary: 35P05, 35Q40, Secondary: 47A10, 81Q10 This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in $\mathbb{R}^2$. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type inequalities for $\overline\partial$-Robin Laplacians. Thanks to this, we prove them in the case of simply connected domains for quantum dot boundary conditions asymptotically close to zigzag boundary conditions. Finally, we also study the case of negative mass. |
| title | A connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians in the context of shape optimization problems |
| topic | Analysis of PDEs Mathematical Physics Primary: 35P05, 35Q40, Secondary: 47A10, 81Q10 |
| url | https://arxiv.org/abs/2507.18698 |