LOCATING THE SPECTRUM FOR MAGNETIC SCHRöDINGER AND DIRAC OPERATORS

DOI10.1081/PDE-120004894zbMath1009.35058OpenAlexW2088325835MaRDI QIDQ3149953

Philippe Briet, Horia D. Cornean

Publication date: 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120004894

zbMATH Keywords

perturbed spectrumspectral properties of magnetic Schrödinger and Dirac operators perturbed by long range magnetic fieldsunperturbed spectrum

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (16)

Bulk–edge correspondence for unbounded Dirac–Landau operators ⋮ Diamagnetic expansions for perfect quantum gases ⋮ The Faraday effect revisited: thermodynamic limit ⋮ Spectral edge regularity of magnetic Hamiltonians ⋮ Localization for one-dimensional Anderson-Dirac models ⋮ On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators ⋮ A rigorous proof of the Landau-Peierls formula and much more ⋮ Localization for gapped Dirac Hamiltonians with random perturbations: application to graphene antidot lattices ⋮ On perturbations of Dirac operators with variable magnetic field of constant direction ⋮ The essential spectrum of Schrödinger, Jacobi, and CMV operators ⋮ On the atomic orbital magnetism: a rigorous derivation of the Larmor and Van Vleck contributions ⋮ Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field ⋮ The model magnetic Laplacian on wedges ⋮ On the Regularity of the Hausdorff Distance Between Spectra of Perturbed Magnetic Hamiltonians ⋮ Adiabatically switched-on electrical bias and the Landauer–Büttiker formula ⋮ On the continuity of spectra for families of magnetic pseudodifferential operators

Cites Work

• Spectral stability under tunneling
• Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique. (Characterization of the essential spectrum of the Schrödinger operator with a magnetic field)
• Schrödinger operators with magnetic fields. I: General interactions
• On eigenfunction decay for two dimensional magnetic Schrödinger operators
• On the essential spectrum of two-dimensional periodic magnetic Schrödinger operators
• Stability of gaps for periodic potentials under variation of a magnetic field
• Opérateurs différentiels magnétiques : stabilité des trous dans le spectre, invariance du spectre essentiel et applications
• On asymptotic perturbation theory for quantum mechanics: Almost invariant subspaces and gauge invariant magnetic perturbation theory
• Bender–Wu formula for the Zeeman effect
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