Sur le spectre de l'équation de Dirac (dans $\mathbb{R}^3$ ou $\mathbb{R}^2$) avec champ magnétique

DOI10.24033/asens.1591zbMath0703.35127OpenAlexW2509374940MaRDI QIDQ3482227

Bernard Helffer, X. P. Wang, J. F. Nourrigat

Publication date: 1989

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1989_4_22_4_515_0

zbMATH Keywords

magnetic fieldDirac operatoressential spectrum

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) PDEs in connection with quantum mechanics (35Q40)

Related Items (16)

Counting Function of Magnetic Eigenvalues for Non-definite Sign Perturbations ⋮ Unnamed Item ⋮ Compactness of the solution operator to \(\overline\partial\) in weighted \(L^{2}\)-spaces ⋮ A note on the spectrum of magnetic Dirac operators ⋮ Maximal inequalities and Riesz transform estimates on \(L^p\) spaces for magnetic Schrödinger operators. II ⋮ Confinement-deconfinement transitions for two-dimensional Dirac particles ⋮ On the spectrum of magnetic Dirac operators with Coulomb-type perturbations ⋮ Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields. I: Nonasymptotic Lieb-Thirring-type estimate. ⋮ SPECTRAL THEORY OF NO-PAIR HAMILTONIANS ⋮ EIGENFUNCTIONS AT THE THRESHOLD ENERGIES OF MAGNETIC DIRAC OPERATORS ⋮ Maximal inequalities and Riesz transform estimates on \(L^p\) spaces for magnetic Schrödinger operators I ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Exponential decay of eigenfunctions of Hamiltonians with short range potential ⋮ Scaling of the ground-state energy of relativistic ions in high locally bounded magnetic fields ⋮ Two-parameter asymptotics in magnetic Weyl calculus

Cites Work

• Un exemple de champ magnetique dans \(R^{\nu}\)
• The essential spectrum of two-dimensional Schrödinger operators with perturbed constant magnetic fields
• Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. (Maximal hypoellipticity for polynomial operators of vector fields)
• Stability of Coulomb systems with magnetic fields. I: The one-electron atom
• Stability of Coulomb systems with magnetic fields. II. The many-electron atom and the one-electron molecule
• Stability of Coulomb systems with magnetic fields. III. Zero energy bound states of the Pauli operator
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• 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)
• On the point spectrum of Dirac operators
• Schrödinger operators with magnetic fields. I: General interactions
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