On complex Fermi curves of two-dimensional periodic Schrödinger operators

Klauer, Alexander

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URL: http://ub-madoc.bib.uni-mannheim.de/3171
URN: urn:nbn:de:bsz:180-madoc-31713
Document Type: Doctoral dissertation
Year of publication: 2011
Publishing house: Universität Mannheim
Evaluator: Schmidt, Martin
Date of oral examination: 3 June 2011
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematik III (Schmidt, M. 2004-)
Subject: 510 Mathematics
Classification: MSC: 35P20 81U40 ,
Subject headings (SWD): Mathematik , Physik , Schrödinger-Gleichung , Hamiltonoperator , Bandstruktur
Individual keywords (German): Fermikurve, Blochvarietät
Keywords (English): mathematics, physics, Schrödinger equation, Schrödinger operator, Fermi curve, Bloch variety
Abstract: In dimensions~$d\geq 2$, the complex Bloch varieties and the associated Fermi curves of periodic Schrödinger operators with quasi-periodic boundary conditions are defined as complex analytic varieties. The Schrödinger potentials are taken from the Lebesgue space~$L^{d/2}$ in the case~$d>2$, and from the Lorentz--Fourier space~$\mc{F}\ell^{\infty,1}$ in the case~$d
Translation of the title: Über komplexe Fermikurven zweidimensionaler periodischer Schrödingeroperatoren (German)
Translation of the abstract: In~$d\geq 2$ Dimensionen werden die komplexen Blochvarietäten und die zugehörigen Fermikurven periodischer Schrödingeroperatoren mit quasiperiodischen Randbedingungen als komplex analytische Varietäten definiert. Die Schrödinger-Potentiale entstammen im Fall~$d>2$ dem Lebesgueraum~$L^{d/2}$ und im Fall~$d (German)
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