Show simple item record

dc.contributor.authorArrizabalaga, N.
dc.contributor.authorMas, A.
dc.contributor.authorVega, L. 
dc.date.accessioned2016-06-13T13:09:36Z
dc.date.available2016-06-13T13:09:36Z
dc.date.issued2016-06-01
dc.identifier.issn0010-3616
dc.identifier.urihttp://hdl.handle.net/20.500.11824/57
dc.description.abstractIn this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell potential (which depends on a parameter $\lambda \in \mathbb{R}$) located on the boundary of a smooth domain in $\mathbb{R}^3$. Our main result is an isoperimetric-type inequality for the admissible range of $\lambda$'s for which the coupling $H + V_{\lambda}$ generates pure point spectrum in $(-m,m)$. That the ball is the unique optimizer of this inequality is also shown. Regarding some ingredients of the proof, we make use of the Birman-Schwinger principle adapted to our setting in order to prove some monotonicity property of the admissible $\lambda$'s, and we use this to relate the endpoints of the admissible range of $\lambda$'s to the sharp constant of a quadratic form inequality, from which the isoperimetric-type inequality is derived.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleAn Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/s00220-015-2481-y
dc.relation.publisherversionhttp://link.springer.com/article/10.1007%2Fs00220-015-2481-y
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//SEV-2013-0323en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleCommunications in Mathematical Physicsen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España