Index formulas and charge deficiencies on the Landau levels

Abstract

The notion of charge deficiency from Avron, Seiler, Simon (Charge deficiency, charge transport and comparison of dimensions, Comm. Math. Phys. 159) is studied from the view of $KK$-theory and is applied to the Landau levels in $\C^n$. We calculate the charge deficiencies of the higher Landau levels in $\C^n$ by means of an Atiyah-Singer type index theorem.

18 pages

References in corpus (4)

• Charge Deficiency, Charge Transport and Comparison of Dimensions
• D-Branes, RR-Fields and Duality on Noncommutative Manifolds
• Geometric K-Homology of Flat D-Branes
• Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential

Cited by in corpus (6)

• Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
• The Geometry of (non-Abelian) Landau levels
• Index pairings for ${\mathbb{R}}^n$-actions and Rieffel deformations
• The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
• Berezin-Toeplitz quantization asssociated with higher Landau levels of the Bochner Laplacian
• Resonances and Spectral Shift Function Singularities for Magnetic Quantum Hamiltonians