Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields. I: Nonasymptotic Lieb-Thirring-type estimate.

DOI10.1215/S0012-7094-99-09604-7zbMath1047.81022OpenAlexW2095162538WikidataQ59255807 ScholiaQ59255807MaRDI QIDQ1974876

Jan Philip Solovej, László Erdős

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-09604-7

zbMATH Keywords

Pauli operatorstrong nonhomogeneous magnetic fieldsemiclassical eigenvalue estimates

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (7)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Which magnetic fields support a zero mode? ⋮ Derivation of the magnetic Euler-Heisenberg energy ⋮ Spectral confinement and current for atoms in strong magnetic fields ⋮ Hardy-Lieb-Thirring inequalities for fractional Pauli operators ⋮ Two effective models for the Dirac vacuum in electromagnetic fields ⋮ Confining quantum particles with a purely magnetic field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability of Coulomb systems with magnetic fields. I: The one-electron atom
• Stability of Coulomb systems with magnetic fields. III. Zero energy bound states of the Pauli operator
• Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field, perturbed by a decreasing electric field. I
• Schrödinger operators with magnetic fields. I: General interactions
• Ground-state density of the Pauli operator in the large field limit
• Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions
• Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. II: Leading order asymptotic estimates
• A Lieb-Thirring bound for a magnetic Pauli Hamiltonian
• Magnetic Lieb-Thirring inequalities
• On the Lieb-Thirring estimates for the Pauli operator
• Sur le spectre de l'équation de Dirac (dans $\mathbb{R}^3$ ou $\mathbb{R}^2$) avec champ magnétique
• Spectral Estimates for Magnetic Operators.
• Stability of Matter in Magnetic Fields
• Stability of Coulomb systems in a magnetic field.

This page was built for publication: Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields. I: Nonasymptotic Lieb-Thirring-type estimate.