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...

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Detalles Bibliográficos
Autores: Duran, Joaquim, Mas, Albert, Sanz-Perela, Tomás
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
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Descripción
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.