Noncommutative Bloch theory

DOI10.1063/1.1369122zbMath1016.81061arXivmath-ph/9901011OpenAlexW2950712978MaRDI QIDQ2774908

Michael J. Gruber

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0006021

zbMATH Keywords

spectral properties\(C^*\)-algebrasCantor spectraelliptic operators on Hilbert \(C^*\)-modulesquantum pendulum

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (C^*)-modules (46L08) Many-body theory; quantum Hall effect (81V70) Noncommutative geometry in quantum theory (81R60) Operator algebra methods applied to problems in quantum theory (81R15) Noncommutative geometry (à la Connes) (58B34)

Related Items (15)

On the \(K\)-theoretic classification of topological phases of matter ⋮ Magnetic Schrödinger operator from the point of view of noncommutative geometry ⋮ Spectral properties of Schrödinger operators on decorated graphs ⋮ Positive measure spectrum for Schrödinger operators with periodic magnetic fields ⋮ Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown ⋮ On the hyperbolic Bloch transform ⋮ Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields ⋮ EXISTENCE OF SPECTRAL GAPS, COVERING MANIFOLDS AND RESIDUALLY FINITE GROUPS ⋮ Magnetic Bloch theory and noncommutative geometry ⋮ Good Wannier bases in Hilbert modules associated to topological insulators ⋮ Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry ⋮ APPLICATIONS OF MAGNETIC ΨDO TECHNIQUES TO SAPT ⋮ An overview of periodic elliptic operators ⋮ The Topological Bloch-Floquet Transform and Some Applications ⋮ Two-cocycle twists and Atiyah–Patodi–Singer index theory

Cites Work

• Quantum Hall effect on the hyperbolic plane
• Quantum Hall effect on the hyperbolic plane in the presence of disorder
• The structure of the irrational rotation \(C^*\)-algebra
• Discrete magnetic Laplacian
• Gauge-periodic point perturbations on the Lobachevsky plane
• Bloch theory and quantization of magnetic systems
• THE INDEX OF ELLIPTIC OPERATORS OVERC*-ALGEBRAS
• Density of the self-adjoint elements with finite spectrum in an irrational rotation $C^*$-algebra.
• Group C*-Algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold
• On the spectrum of periodic elliptic operators
• TWISTED INDEX THEORY ON GOOD ORBIFOLDS, I: NONCOMMUTATIVE BLOCH THEORY
• Twisted index theory on good orbifolds. II: Fractional quantum numbers

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