Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2438-2465 |
| Seitenumfang | 28 |
| Fachzeitschrift | Journal of mathematical physics |
| Jahrgang | 42 |
| Ausgabenummer | 6 |
| Publikationsstatus | Veröffentlicht - 1 Juni 2001 |
| Extern publiziert | Ja |
Abstract
For differential operators which are invariant under the action of an Abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new noncommutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hubert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies, e.g., to differential operators invariant under a projective group action, such as Schrödinger, Dirac, and Pauli operators with periodic magnetic field, as well as to discrete models, such as the almost Matthieu equation and the quantum pendulum.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Mathematik (insg.)
- Mathematische Physik
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in: Journal of mathematical physics, Jahrgang 42, Nr. 6, 01.06.2001, S. 2438-2465.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Noncommutative Bloch theory
AU - Gruber, Michael J.
PY - 2001/6/1
Y1 - 2001/6/1
N2 - For differential operators which are invariant under the action of an Abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new noncommutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hubert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies, e.g., to differential operators invariant under a projective group action, such as Schrödinger, Dirac, and Pauli operators with periodic magnetic field, as well as to discrete models, such as the almost Matthieu equation and the quantum pendulum.
AB - For differential operators which are invariant under the action of an Abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new noncommutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hubert C*-modules. It relates properties of C*-algebras to spectral properties of module operators such as band structure, weak genericity of cantor spectra, and absence of discrete spectrum. It applies, e.g., to differential operators invariant under a projective group action, such as Schrödinger, Dirac, and Pauli operators with periodic magnetic field, as well as to discrete models, such as the almost Matthieu equation and the quantum pendulum.
UR - http://www.scopus.com/inward/record.url?scp=0035534454&partnerID=8YFLogxK
U2 - 10.1063/1.1369122
DO - 10.1063/1.1369122
M3 - Article
AN - SCOPUS:0035534454
VL - 42
SP - 2438
EP - 2465
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 6
ER -