The Topological Bloch-Floquet Transform and Some Applications

DOI10.1007/978-3-0348-0414-1_5zbMath1270.81087arXiv0911.5270OpenAlexW1829947092MaRDI QIDQ2841832

Gianluca Panati, Giuseppe De Nittis

Publication date: 30 July 2013

Published in: Spectral Analysis of Quantum Hamiltonians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.5270

zbMATH Keywords

spectral decompositionHilbert bundletopological quantum numbersBloch-Floquet transform

Mathematics Subject Classification ID

(C^*)-modules (46L08) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Topology of vector bundles and fiber bundles (57R22) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Decomposition theory for (C^*)-algebras (46L45)

Related Items (2)

Direct integrals of strongly continuous operator semigroups ⋮ Good Wannier bases in Hilbert modules associated to topological insulators

Cites Work

• Generalized TKNN-equations
• Triviality of Bloch and Bloch-Dirac bundles
• Hofstadter butterfly as quantum phase diagram
• Noncommutative Bloch theory
• The noncommutative geometry of the quantum Hall effect
• Champs continus d'espaces hilbertiens et de $C^*$-algèbres
• Floquet theory for partial differential equations
• \(C^*\)-algebras by example
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