Shell interactions for Dirac operators: On the point spectrum and the confinement

Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The potentials V under consideration are given in terms of surface measures on the bo...

Descripción completa

Detalles Bibliográficos
Autores: Arrizabalaga, N., Mas, A., Vega, L.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/56
Acceso en línea:http://hdl.handle.net/20.500.11824/56
Access Level:acceso abierto
Palabra clave:Dirac operator
Self-adjoint extension
Shell interaction
Singular integral
id ES_bc752a41b536c85958b43ffe9f5dd2d7
oai_identifier_str oai:bird.bcamath.org:20.500.11824/56
network_acronym_str ES
network_name_str España
repository_id_str
spelling Shell interactions for Dirac operators: On the point spectrum and the confinementArrizabalaga, N.Mas, A.Vega, L.Dirac operatorSelf-adjoint extensionShell interactionSingular integralSpectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The potentials V under consideration are given in terms of surface measures on the boundary of bounded regular domains in $\mathbb{R}^3$. A criterion for the existence of point spectrum is given, with applications to electrostatic shell potentials. In the case of the sphere, an uncertainty principle is developed, and its relation to some eigenvectors of the coupling is shown. Furthermore, a criterion for generating confinement is given. As an application, some known results about confinement on the sphere for electrostatic plus Lorentz scalar shell potentials are generalized to regular surfaces.201620162015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/56reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttp://epubs.siam.org/doi/10.1137/14097759Xinfo:eu-repo/grantAgreement/EC/H2020/669689Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/562026-06-19T12:47:47Z
dc.title.none.fl_str_mv Shell interactions for Dirac operators: On the point spectrum and the confinement
title Shell interactions for Dirac operators: On the point spectrum and the confinement
spellingShingle Shell interactions for Dirac operators: On the point spectrum and the confinement
Arrizabalaga, N.
Dirac operator
Self-adjoint extension
Shell interaction
Singular integral
title_short Shell interactions for Dirac operators: On the point spectrum and the confinement
title_full Shell interactions for Dirac operators: On the point spectrum and the confinement
title_fullStr Shell interactions for Dirac operators: On the point spectrum and the confinement
title_full_unstemmed Shell interactions for Dirac operators: On the point spectrum and the confinement
title_sort Shell interactions for Dirac operators: On the point spectrum and the confinement
dc.creator.none.fl_str_mv Arrizabalaga, N.
Mas, A.
Vega, L.
author Arrizabalaga, N.
author_facet Arrizabalaga, N.
Mas, A.
Vega, L.
author_role author
author2 Mas, A.
Vega, L.
author2_role author
author
dc.subject.none.fl_str_mv Dirac operator
Self-adjoint extension
Shell interaction
Singular integral
topic Dirac operator
Self-adjoint extension
Shell interaction
Singular integral
description Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The potentials V under consideration are given in terms of surface measures on the boundary of bounded regular domains in $\mathbb{R}^3$. A criterion for the existence of point spectrum is given, with applications to electrostatic shell potentials. In the case of the sphere, an uncertainty principle is developed, and its relation to some eigenvectors of the coupling is shown. Furthermore, a criterion for generating confinement is given. As an application, some known results about confinement on the sphere for electrostatic plus Lorentz scalar shell potentials are generalized to regular surfaces.
publishDate 2015
dc.date.none.fl_str_mv 2015
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/56
url http://hdl.handle.net/20.500.11824/56
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://epubs.siam.org/doi/10.1137/14097759X
info:eu-repo/grantAgreement/EC/H2020/669689
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418115699310592
score 15,300719

Similares en LA Referencia