Spectral asymptotics for $\delta$-interactions on sharp cones
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral pr...
| Autores: | , , |
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| 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:20.500.11824/731 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/731 |
| Access Level: | acceso abierto |
| Palabra clave: | Schrödinger operator $\delta$-interaction conical surface eigenvalue asymptotic analysis |
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Spectral asymptotics for $\delta$-interactions on sharp conesOurmières-Bonafos, T.Pankrashkin, K.Pizzichillo, F.Schrödinger operator$\delta$-interactionconical surfaceeigenvalueasymptotic analysisWe investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral properties for sharp cones, that is when the cone aperture goes to zero, and we describe the asymptotic behavior of the eigenvalues and of the eigenvalue counting function. A part of the results are given in terms of numerical constants appearing as solutions of transcendental equations involving modified Bessel functions.201720172017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/731reponame: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:20.500.11824/7312026-06-19T12:47:47Z |
| dc.title.none.fl_str_mv |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| title |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| spellingShingle |
Spectral asymptotics for $\delta$-interactions on sharp cones Ourmières-Bonafos, T. Schrödinger operator $\delta$-interaction conical surface eigenvalue asymptotic analysis |
| title_short |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| title_full |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| title_fullStr |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| title_full_unstemmed |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| title_sort |
Spectral asymptotics for $\delta$-interactions on sharp cones |
| dc.creator.none.fl_str_mv |
Ourmières-Bonafos, T. Pankrashkin, K. Pizzichillo, F. |
| author |
Ourmières-Bonafos, T. |
| author_facet |
Ourmières-Bonafos, T. Pankrashkin, K. Pizzichillo, F. |
| author_role |
author |
| author2 |
Pankrashkin, K. Pizzichillo, F. |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Schrödinger operator $\delta$-interaction conical surface eigenvalue asymptotic analysis |
| topic |
Schrödinger operator $\delta$-interaction conical surface eigenvalue asymptotic analysis |
| description |
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral properties for sharp cones, that is when the cone aperture goes to zero, and we describe the asymptotic behavior of the eigenvalues and of the eigenvalue counting function. A part of the results are given in terms of numerical constants appearing as solutions of transcendental equations involving modified Bessel functions. |
| publishDate |
2017 |
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2017 2017 2017 |
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info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion |
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article |
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acceptedVersion |
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http://hdl.handle.net/20.500.11824/731 |
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http://hdl.handle.net/20.500.11824/731 |
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Inglés |
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Inglés |
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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 |
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Reconocimiento-NoComercial-CompartirIgual 3.0 España http://creativecommons.org/licenses/by-nc-sa/3.0/es/ info:eu-repo/semantics/openAccess |
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Reconocimiento-NoComercial-CompartirIgual 3.0 España http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
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openAccess |
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application/pdf |
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reponame:BIRD. BCAM's Institutional Repository Data instname:Basque Center for Applied Mathematics (BCAM) |
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Basque Center for Applied Mathematics (BCAM) |
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BIRD. BCAM's Institutional Repository Data |
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BIRD. BCAM's Institutional Repository Data |
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