Peierls' substitution for low lying spectral energy windows
| Autor: | Radu Purice, Horia D. Cornean, Bernard Helffer |
|---|---|
| Přispěvatelé: | Department of Mathematical Sciences [Aalborg], Aalborg University [Denmark] (AAU), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Wannier functions
Spectral gaps FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Mathematics - Spectral Theory [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Quantum mechanics 0103 physical sciences FOS: Mathematics 0101 mathematics [MATH]Mathematics [math] Spectral Theory (math.SP) Eigenvalues and eigenvectors Mathematical Physics Physics Wannier function Magnetic pseudo-differential operators spectral gaps Wannier functions Chern class Magnetic pseudo-differential operators Operator (physics) 010102 general mathematics Spectrum (functional analysis) Spectral density Statistical and Nonlinear Physics Mathematical Physics (math-ph) Mathematics::Spectral Theory Magnetic field Brillouin zone Geometry and Topology |
| Zdroj: | Cornean, H, Helffer, B & Purice, R 2019, ' Peierls' substitution for low lying spectral energy windows ', Journal of Spectral Theory, vol. 9, no. 4, pp. 1179-1222 . https://doi.org/10.4171/JST/274 Journal of Spectral Theory Journal of Spectral Theory, European Mathematical Society, In press |
| ISSN: | 1664-039X 1664-0403 |
| DOI: | 10.4171/JST/274 |
| Popis: | We consider a $2d$ magnetic Schr\"odinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of the spectrum, under the hypothesis that the lowest Bloch eigenvalue of the unperturbed operator remained simple on the whole Brillouin zone, even though its range may overlap with the range of the second eigenvalue. We also assumed that the first Bloch spectral projection was smooth and had a zero Chern number. In this paper we extend our previous results to the only two remaining possibilities: either the first Bloch eigenvalue remains isolated while its corresponding spectral projection has a non-zero Chern number, or the first two Bloch eigenvalues cross each other. Comment: 27 pages |
| Databáze: | OpenAIRE |
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