Zobrazit minimální záznam

dc.contributor.authorExner , Pavel
dc.contributor.authorBarseghyan , Diana
dc.date.accessioned2017-02-09T08:16:11Z
dc.date.available2017-02-09T08:16:11Z
dc.date.issued2013
dc.identifier.citationActa Polytechnica. 2013, vol. 53, no. 3.
dc.identifier.issn1210-2709 (print)
dc.identifier.issn1805-2363 (online)
dc.identifier.urihttp://hdl.handle.net/10467/67057
dc.description.abstractIn this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when the allowed phase space is infinite but the operator still has a discrete spectrum. First we analyze two-dimensional operators with the potential |xy|p - ?(x2 + y2)p/(p+2)where p?1 and ??0. We show that there is a critical value of ? such that the spectrum for ??crit it is unbounded from below. In the subcriticalcase we prove upper and lower bounds for the eigenvalue sums. The second part of work is devoted toestimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions havinginfinite cusps which are geometrically nontrivial being either curved or twisted; we are going to showhow these geometric properties enter the eigenvalue bounds.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherČeské vysoké učení technické v Prazecs
dc.publisherCzech Technical University in Pragueen
dc.relation.ispartofseriesActa Polytechnica
dc.relation.urihttps://ojs.cvut.cz/ojs/index.php/ap/article/view/1801
dc.rightsCreative Commons Attribution 4.0 International Licenseen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectSchrödinger operatoren
dc.subjectdiscrete spectrumen
dc.subjectLieb-Thirring inequalityen
dc.subjectcusp-shaped regionsen
dc.subjectgeometrically induced spectrumen
dc.titleSpectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior
dc.typearticleen
dc.date.updated2017-02-09T08:16:11Z
dc.rights.accessopenAccess
dc.type.statusPeer-reviewed
dc.type.versionpublishedVersion


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Zobrazit minimální záznam

Creative Commons Attribution 4.0 International License
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