Resonances of Dirac Operators
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
This thesis consists of a summary of four papers dealing with resonances of Dirac operators on Euclidean 3-space. In Paper I we show that the Complex Absorbing Potential (CAP) method is valid in the semiclassical limit for resonances sufficiently close to the real line if the potential is smooth and compactly supported. In Paper II we continue the investigations initiated in Paper I but here we study clouds of resonances close to the real line and show that in some sense the CAP method remains valid also for multiple resonances. In Paper III we study perturbations of Dirac operators with smooth decaying scalar potentials and show that these possess many resonances near certain points related to the maximum and the minimum of the potential. In Paper IV we show a trace formula of Poisson type for Dirac operators having compactly supported potentials which is related to resonances. The techniques mainly stem from complex function theory and scattering theory.
Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2014.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 84
Semiclassical analysis, Dirac operator, resonances, Poisson trace formula, scattering theory, complex absorbing potential, pseudodifferential operator
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-223841ISBN: 978-91-506-2400-7OAI: oai:DiVA.org:uu-223841DiVA: diva2:714342
2014-06-09, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, plan 0, Hus 1, Uppsala, 10:15 (English)
Staubach, Wolfgang, Associate Professor
List of papers