Eigenvalue Curves for Generalized MIT Bag Models

We study spectral properties of Dirac operators on bounded domains Ω ⊂ R3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ∈ R; the case τ= 0 corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of τ...

Descripción completa

Detalles Bibliográficos
Autores: Arrizabalaga, N., Mas, A., Sanz-Perela, T., Vega, L.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
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:2072/537083
Acceso en línea:http://hdl.handle.net/2072/537083
Access Level:acceso abierto
Palabra clave:Dirac operator, spectral theory, MIT bag model, shape optimization
Descripción
Sumario:We study spectral properties of Dirac operators on bounded domains Ω ⊂ R3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ∈ R; the case τ= 0 corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of τ, and we exploit this monotonicity to study the limits as τ→ ± ∞. We prove that if Ω is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all τ large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as τ↓ - ∞, and we also analyze its first order asymptotics. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Similares en LA Referencia