A connection between quantum dot Dirac operators and ∂ˉ-Robin Laplacians in the context of shape optimization problems
This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in R2. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type inequalities for ∂ˉ-Robin Laplacians. Thanks to this, we prove them in the case of...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/489253 |
| Acceso en línea: | https://hdl.handle.net/2072/489253 |
| Access Level: | acceso abierto |
| Palabra clave: | Dirac operator Spectral theory Shape optimization 51 |
| Sumario: | This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in R2. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type inequalities for ∂ˉ-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. |
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