- AutorIn
- Christian Seifert
- Titel
- Measure-perturbed one-dimensional Schrödinger operators
- Untertitel
- A continuum model for quasicrystals
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa-102766
- Datum der Einreichung
- 28.06.2012
- Datum der Verteidigung
- 27.11.2012
- Abstract (EN)
- In this Dissertation thesis the spectral theory of Schrödinger operators modeling quasicrystals in dimension one ist investigated. We allow for a large class of measures as potentials covering also point interactions. The main results can be stated as follows: If the potential can be very well approximated by periodic potentials, then the correspondig Schrödinger operator does not have any eigenvalues. If the potential is aperiodic and satisfies a certain finite local complexity condition, the absolutely continuous spectrum is absent. We also prove Cantor spectra of zero Lebesgue measure for a large class of (a randomized version of) the operator.
- Freie Schlagwörter (DE)
- Schrödinger Operator, Spektraltheorie, Quasikristalle
- Freie Schlagwörter (EN)
- Schrödinger operator, spectral theory, quasicrystals
- Klassifikation (DDC)
- 515
- Normschlagwörter (GND)
- Hamilton-Operator, Spektraltheorie
- GutachterIn
- Prof. Dr. Peter Stollmann
- Prof. Dr. Daniel Lenz
- BetreuerIn
- Prof. Dr. Peter Stollmann
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:bsz:ch1-qucosa-102766
- Veröffentlichungsdatum Qucosa
- 23.01.2013
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch