Matches in SemOpenAlex for { <https://semopenalex.org/work/W2769372382> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2769372382 abstract "This thesis explores the spectral properties of Schrodinger-type operators on variousdomains such as R^2, rectangles, and metric graphs. In particular, we consider special types of operators called point scatterers that act as the Laplacian away from a discrete set of points. Such a model provides a simple tool to study how the presence of point-wise potentials perturbs the spectral properties of the Laplacian.In Chapter 1, we introduce the general procedure to properly define the point scattererson a general domain. The theory of self-adjoint extension and Krein’s formula play importantroles in the process.In Chapter 2, we formulate point scatterers in R^2 using the renormalization processmentioned in the previous chapter. We start with the one-point scatterer which is thesimplest case and then generalize the result to finitely many point scatterers and infinitelymany point scatterers. Then we consider a special case in which the scatterers are placedperiodically as a combination of infinitely many point scatterers and the Floquet-Blochtheory of solid-state physics for crystal structures. As an application inspired by carbonnano-structures such as graphene, we prove that honeycomb lattice point scatterers generateconic singularities on the dispersion relation.In Chapter 3, we consider a point scatterer on a rectangular domain to investigate howthe eigenfunctions on the rectangle are affected by the point-wise perturbation. We provethat a point scatterer eventually acts as a barrier confining the eigenfunction as the domaingets thinner.In Chapter 4, we introduce how the point scatterers can be incorporated with the notion ofquantum graphs. In addition, the resonances of quantum graphs are investigated. We providethe quantum graph version of a Fermi golden rule, which provides an explicit expression forthe infinitesimal change of states in terms of the scattering resonances." @default.
- W2769372382 created "2017-12-04" @default.
- W2769372382 creator A5082407014 @default.
- W2769372382 date "2016-01-01" @default.
- W2769372382 modified "2023-09-27" @default.
- W2769372382 title "Spectral Analysis on Point Interactions" @default.
- W2769372382 cites W1176699082 @default.
- W2769372382 cites W1483899504 @default.
- W2769372382 cites W1496092454 @default.
- W2769372382 cites W1595143359 @default.
- W2769372382 cites W1598909796 @default.
- W2769372382 cites W1657375769 @default.
- W2769372382 cites W1971551140 @default.
- W2769372382 cites W2003060384 @default.
- W2769372382 cites W2003742140 @default.
- W2769372382 cites W2009138636 @default.
- W2769372382 cites W2013553110 @default.
- W2769372382 cites W2014698679 @default.
- W2769372382 cites W2026237155 @default.
- W2769372382 cites W2036225447 @default.
- W2769372382 cites W2036846056 @default.
- W2769372382 cites W2038434789 @default.
- W2769372382 cites W2056722718 @default.
- W2769372382 cites W2082282370 @default.
- W2769372382 cites W2083487180 @default.
- W2769372382 cites W2112930989 @default.
- W2769372382 cites W2115336412 @default.
- W2769372382 cites W2118720823 @default.
- W2769372382 cites W2141729039 @default.
- W2769372382 cites W2169681623 @default.
- W2769372382 cites W2962908824 @default.
- W2769372382 cites W2963645054 @default.
- W2769372382 cites W3098893027 @default.
- W2769372382 cites W3100545372 @default.
- W2769372382 cites W3105229201 @default.
- W2769372382 hasPublicationYear "2016" @default.
- W2769372382 type Work @default.
- W2769372382 sameAs 2769372382 @default.
- W2769372382 citedByCount "0" @default.
- W2769372382 crossrefType "journal-article" @default.
- W2769372382 hasAuthorship W2769372382A5082407014 @default.
- W2769372382 hasConcept C121332964 @default.
- W2769372382 hasConcept C128803854 @default.
- W2769372382 hasConcept C134306372 @default.
- W2769372382 hasConcept C158693339 @default.
- W2769372382 hasConcept C165700671 @default.
- W2769372382 hasConcept C2524010 @default.
- W2769372382 hasConcept C2781302577 @default.
- W2769372382 hasConcept C33923547 @default.
- W2769372382 hasConcept C62520636 @default.
- W2769372382 hasConceptScore W2769372382C121332964 @default.
- W2769372382 hasConceptScore W2769372382C128803854 @default.
- W2769372382 hasConceptScore W2769372382C134306372 @default.
- W2769372382 hasConceptScore W2769372382C158693339 @default.
- W2769372382 hasConceptScore W2769372382C165700671 @default.
- W2769372382 hasConceptScore W2769372382C2524010 @default.
- W2769372382 hasConceptScore W2769372382C2781302577 @default.
- W2769372382 hasConceptScore W2769372382C33923547 @default.
- W2769372382 hasConceptScore W2769372382C62520636 @default.
- W2769372382 hasLocation W27693723821 @default.
- W2769372382 hasOpenAccess W2769372382 @default.
- W2769372382 hasPrimaryLocation W27693723821 @default.
- W2769372382 hasRelatedWork W1523975396 @default.
- W2769372382 hasRelatedWork W174794859 @default.
- W2769372382 hasRelatedWork W1863430029 @default.
- W2769372382 hasRelatedWork W1964095209 @default.
- W2769372382 hasRelatedWork W1991737393 @default.
- W2769372382 hasRelatedWork W2012491465 @default.
- W2769372382 hasRelatedWork W2044056698 @default.
- W2769372382 hasRelatedWork W2070893372 @default.
- W2769372382 hasRelatedWork W2075766457 @default.
- W2769372382 hasRelatedWork W2102315609 @default.
- W2769372382 hasRelatedWork W2162513915 @default.
- W2769372382 hasRelatedWork W21723188 @default.
- W2769372382 hasRelatedWork W2224794282 @default.
- W2769372382 hasRelatedWork W2883059764 @default.
- W2769372382 hasRelatedWork W2960834159 @default.
- W2769372382 hasRelatedWork W3037063271 @default.
- W2769372382 hasRelatedWork W3043403663 @default.
- W2769372382 hasRelatedWork W3100713020 @default.
- W2769372382 hasRelatedWork W3103142786 @default.
- W2769372382 hasRelatedWork W3110709816 @default.
- W2769372382 isParatext "false" @default.
- W2769372382 isRetracted "false" @default.
- W2769372382 magId "2769372382" @default.
- W2769372382 workType "article" @default.