A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise its eigenvalues in terms of the Birman–Schwinger principle and we bound i...

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Detalles Bibliográficos
Autores: Cassano, B., Pizzichillo, F., Vega, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1088
Acceso en línea:http://hdl.handle.net/20.500.11824/1088
Access Level:acceso abierto
Palabra clave:Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
spectral properties
ground state
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spelling A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operatorCassano, B.Pizzichillo, F.Vega, L.Dirac operatorCoulomb potentialHardy inequalityself-adjoint operatorspectral propertiesground stateWe prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise its eigenvalues in terms of the Birman–Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if V verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that V is the Coulomb potential.202020202019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1088reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://doi.org/10.1007/s13163-019-00311-4info:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/10882026-06-19T12:47:47Z
dc.title.none.fl_str_mv A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
title A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
spellingShingle A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
Cassano, B.
Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
spectral properties
ground state
title_short A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
title_full A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
title_fullStr A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
title_full_unstemmed A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
title_sort A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
dc.creator.none.fl_str_mv Cassano, B.
Pizzichillo, F.
Vega, L.
author Cassano, B.
author_facet Cassano, B.
Pizzichillo, F.
Vega, L.
author_role author
author2 Pizzichillo, F.
Vega, L.
author2_role author
author
dc.subject.none.fl_str_mv Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
spectral properties
ground state
topic Dirac operator
Coulomb potential
Hardy inequality
self-adjoint operator
spectral properties
ground state
description We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise its eigenvalues in terms of the Birman–Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if V verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that V is the Coulomb potential.
publishDate 2019
dc.date.none.fl_str_mv 2019
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1088
url http://hdl.handle.net/20.500.11824/1088
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1007/s13163-019-00311-4
info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
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
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