On complex Fermi curves of two-dimensional, periodic Schrödinger operators

• Autorzy: Klauer A.

Identyfikatory

DOI

10.1515/jaa-2014-0006

• Języki publikacji: EN

Abstrakty

EN

The complex Bloch varieties and the associated Fermi curves of two-dimensional periodic Schrödinger operators with quasi-periodic boundary conditions are defined as complex analytic varieties, the Schrödinger potentials being from the Lorentz–Fourier space Fℓ∞,1. Then, an asymptotic analysis of the Fermi curves is performed. The decomposition of a Fermi curve into a compact part, an asymptotically free part, and thin handles, is recovered as expected. Furthermore, it is shown that the set of potentials whose associated Fermi curve has finite geometric genus is a dense subset of Fℓ∞,1. Moreover, the Fourier transforms of the potentials are locally isomorphic to perturbed Fourier transforms induced by the handles. Finally, an asymptotic family of parameters describing the sizes of the handles is introduced. These parameters are good candidates for describing parts of the space of all Fermi curves.

Słowa kluczowe

EN

periodic Schrödinger operator; Bloch variety; Fermi curve; finite type

PL

okresowy operator Schrödingera; rozmaitość Blocha; krzywa Fermiego

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2014
• Tom: Vol. 20, nr 1
• Strony: 55--76
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Klauer A.

• Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany

Bibliografia

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• [3] A. Defant and K. Floret, Tensor Norms and Operator Ideals, Math. Stud. 176, North-Holland, Amsterdam, 1993.
• [4] J. Feldman, H. Kni:irrer and E. Trubowitz, Riemann Surfaces of Infinite Genus, Centre Rech. Math. Univ. Montreal Monogr. Ser. 20, American Mathematical Society, Providence, 2003.
• [5] A. Klauer, On complex Fermi curves of two-dimensional periodic Schrodinger operators, doctoral dissertation thesis, University of Mannheim, 2011, http://madoc.bib.uni-mannheim.de/madoc/volltexte/2011/3171/.
• [6] A. Klauer and M. U. Schmidt, Bloch varieties of higher-dimensional, periodic Schrödinger operators, J. Appl. Anal. 15 (2009), 33-46.
• [7] A. Klauer and M. U. Schmidt, Erratum to: Bloch varieties of higher-dimensional, periodic Schrödinger operators [J. Appl. Anal. 15 (2009), 33-46], J. Appl. Anal. 20 (2013), 305-306.
• [8] M. U. Schmidt, On complex Bloch-spaces of periodic Schrödinger operators, Sfb 288 Preprint no. 200, preprint (1996), http://www-sfb288.math.tu-berlin.de/Publications/preprint-list/151/200.