The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation

This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an...

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Detalles Bibliográficos
Autores: Mas, A., Pizzichillo, F.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/714
Acceso en línea:http://hdl.handle.net/20.500.11824/714
Access Level:acceso abierto
Palabra clave:Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentials
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spelling The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximationMas, A.Pizzichillo, F.Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentialsThis note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich, Exner and Seba [Dirac operators with a spherically symmetric $\delta$-shell interaction, J. Math. Phys. 30.12 (1989), 2875-2882] and by Arrizabalaga, Mas and Vega [Shell interactions for Dirac operators, J. Math. Pures et Appl. 102.4 (2014), 617-639] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.201720172017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/714reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2013-0323info:eu-repo/grantAgreement/MINECO//MTM2014-53145-Pinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/7142026-06-19T12:47:47Z
dc.title.none.fl_str_mv The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
title The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
spellingShingle The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
Mas, A.
Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentials
title_short The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
title_full The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
title_fullStr The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
title_full_unstemmed The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
title_sort The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
dc.creator.none.fl_str_mv Mas, A.
Pizzichillo, F.
author Mas, A.
author_facet Mas, A.
Pizzichillo, F.
author_role author
author2 Pizzichillo, F.
author2_role author
dc.subject.none.fl_str_mv Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentials
topic Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentials
description This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich, Exner and Seba [Dirac operators with a spherically symmetric $\delta$-shell interaction, J. Math. Phys. 30.12 (1989), 2875-2882] and by Arrizabalaga, Mas and Vega [Shell interactions for Dirac operators, J. Math. Pures et Appl. 102.4 (2014), 617-639] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017
2017
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dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/714
url http://hdl.handle.net/20.500.11824/714
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
info:eu-repo/grantAgreement/MINECO//MTM2014-53145-P
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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