Eigenvalue curves for generalized MIT bag models

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

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Detalles Bibliográficos
Autores: Arrizabalaga, Naiara, Mas Blesa, Albert|||0000-0002-8322-1663, Sanz Perela, Tomás|||0000-0002-1210-1111, Vega González, Luis
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/381227
Acceso en línea:https://hdl.handle.net/2117/381227
https://dx.doi.org/10.1007/s00220-022-04526-3
Access Level:acceso abierto
Palabra clave:Mathematical physics
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:We study spectral properties of Dirac operators on bounded domains O¿R3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter t¿R; the case t=0 corresponds to the MIT bag model. We show that the eigenvalues are parametrized as increasing functions of t, and we exploit this monotonicity to study the limits as t¿±8. We prove that if O is not a ball then the first positive eigenvalue is greater than the one of a ball with the same volume for all t large enough. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as t¿-8, and we also analyze its first order asymptotics.