The noncommutative geometry of the Landau Hamiltonian: metric aspects
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Publication:2024536
DOI10.3842/SIGMA.2020.146MaRDI QIDQ2024536
Maximiliano Sandoval, Giuseppe De Nittis
Publication date: 4 May 2021
Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.06785
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) 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
Bulk–edge correspondence for unbounded Dirac–Landau operators ⋮ Dixmier trace and the DOS of magnetic operators ⋮ The noncommutative geometry of the Landau Hamiltonian: differential aspects ⋮ Duffin-Kemmer-Petiau oscillator with spin non-commutativity
Cites Work
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- Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
- Pseudo-Riemannian spectral triples and the harmonic oscillator
- 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
- Singular traces. Theory and applications
- Moyal planes are spectral triples
- A Dixmier trace formula for the density of states
- The spectral localizer for even index pairings
- Quantum Hall effect and noncommutative geometry
- The quantum Hall effect for electrons in a random potential
- Functional analysis, Sobolev spaces and partial differential equations
- On the Landau levels on the hyperbolic plane
- Notes on non-commutative integration
- Schrödinger operators with magnetic fields. I: General interactions
- Charge deficiency, charge transport and comparison of dimensions
- Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases
- Perturbation theory for linear operators.
- On the twisted convolution product and the Weyl transformation of tempered distributions
- Geometric invariants of the quantum Hall effect
- The local index formula in noncommutative geometry
- A discrete model of the integer quantum Hall effect
- Random operators and crossed products
- Quantum differentiability on noncommutative Euclidean spaces
- Quantum differentiability on quantum tori
- The geometry of (non-abelian) Landau levels
- Existence and regularity properties of the integrated density of states of random Schrödinger operators
- Finite volume calculation of \(K\)-theory invariants
- Spectral geometry of the Moyal plane with harmonic propagation
- Dynamical delocalization in random Landau Hamiltonians
- Produits croises d'une \(C^ *\)-algèbre par un groupe d'automorphismes
- Twisted group algebras I, II
- A non-commutative extension of abstract integration
- A non-commutative framework for topological insulators
- Index theory for locally compact noncommutative geometries
- A Computational Non-commutative Geometry Program for Disordered Topological Insulators
- QUANTIZATION OF THE HALL CONDUCTANCE AND DELOCALIZATION IN ERGODIC LANDAU HAMILTONIANS
- Algebras of distributions suitable for phase-space quantum mechanics. I
- Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
- Harmonic Analysis in Phase Space. (AM-122)
- The noncommutative geometry of the quantum Hall effect
- QUASI-CLASSICAL VERSUS NON-CLASSICAL SPECTRAL ASYMPTOTICS FOR MAGNETIC SCHRÖDINGER OPERATORS WITH DECREASING ELECTRIC POTENTIALS
- SELF-ADJOINT OPERATORS AFFILIATED TO C*-ALGEBRAS
- Noncommutative integration calculus
- Index formulas and charge deficiencies on the Landau levels
- Linear Response Theory
- Spectral Flow Argument Localizing an Odd Index Pairing
- COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES
- Motion in a Constant Magnetic Field
