Diamagnetic behavior of sums of Dirichlet eigenvalues

DOI10.5802/aif.1777zbMath0957.35104OpenAlexW2075533499MaRDI QIDQ1572636

Michael Loss, László Erdős, Vitali Vougalter

Publication date: 19 July 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_3_891_0

zbMATH Keywords

semiclassical bounddiamagnetic inequalitymagnetic laplacian

Mathematics Subject Classification ID

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

Related Items (14)

Estimates for the lowest eigenvalue of magnetic Laplacians ⋮ The Lieb–Thirring inequalities: Recent results and open problems ⋮ Stability and semiclassics in self-generated fields ⋮ Geometric bounds for the magnetic Neumann eigenvalues in the plane ⋮ Sums of magnetic eigenvalues are maximal on rotationally symmetric domains ⋮ A Lieb–Thirring type inequality for magnetic Schrödinger operators with a radial symmetry ⋮ An entropic uncertainty principle for positive operator valued measures ⋮ Balanced distribution-energy inequalities and related entropy bounds ⋮ Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field ⋮ Existence and nonlinear stability of stationary states for the magnetic Schrödinger-Poisson system ⋮ The Berezin inequality on domains of infinite measure ⋮ Lower bounds for the first eigenvalue of the Laplacian with zero magnetic field in planar domains ⋮ Pólya's conjecture in the presence of a constant magnetic field ⋮ Magnetic spectral bounds on starlike plane domains

Cites Work

• On the Schrödinger equation and the eigenvalue problem
• Domination of semigroups and generalization of Kato's inequality
• Schrödinger operators with magnetic fields. I: General interactions
• Sharp Lieb-Thirring inequalities in high dimensions.
• Schrödinger operators with singular potentials
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