Geometric invariants of the quantum Hall effect

DOI10.1007/BF01218259zbMath0682.46044OpenAlexW2164631646MaRDI QIDQ1824168

Jingbo Xia

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf01218259

zbMATH Keywords

quantum Hall effecttopological indexThom isomorphisms\(C^*\) crossed productsConnes cyclic cohomology theoryone-particle in a two-dimensional sample of infinite size with a random potential

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) Applications of selfadjoint operator algebras to physics (46L60) General mathematical topics and methods in quantum theory (81Q99) Miscellaneous applications of functional analysis (46N99)

Related Items

Magnetic Schrödinger operator from the point of view of noncommutative geometry, The noncommutative geometry of the Landau Hamiltonian: differential aspects, Quantum Hall Effect and Noncommutative Geometry, A pairing between super Lie-Rinehart and periodic cyclic homology., Continuous fields of \(C^*\)-algebras coming from group cocycles and actions, Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases, A discrete model of the integer quantum Hall effect, Low energy bands do not contribute to quantum Hall effect, Magnetic Bloch theory and noncommutative geometry, Quantum differentiability on quantum tori, REVISITING THE CHARGE TRANSPORT IN QUANTUM HALL SYSTEMS, The noncommutative geometry of the Landau Hamiltonian: metric aspects, The Floquet theory and the state density of quasi-periodic Schrödinger operators, Applications of noncommutative geometry in function theory and mathematical physics, Toeplitz algebras and Rieffel deformations, Charge deficiency, charge transport and comparison of dimensions

Cites Work

• Adiabatic theorems and applications to the quantum Hall effect
• The quantum Hall effect for electrons in a random potential
• The spectrum of operators elliptic along the orbits of \({\mathbb{R}}^ n\) actions
• Cyclic cohomology for one-parameter smooth crossed products
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• The density of states for almost periodic Schrödinger operators and the frequency module: A counter example
• \(C^*\)-algebras of almost periodic pseudo-differential operators
• THE SPECTRAL THEORY AND THE INDEX OF ELLIPTIC OPERATORS WITH ALMOST PERIODIC COEFFICIENTS
• Shape theory for $C^*$-algebras.
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