Semiclassical bounds in magnetic bottles

Abstract

The aim of the paper is to derive spectral estimates into several classes of magnetic systems. They include three-dimensional regions with Dirichlet boundary as well as a particle in ${\mathbb{R}}^3$ confined by a local change of the magnetic field. We establish two-dimensional Berezin-Li-Yau and Lieb-Thirring-type bounds in the presence of magnetic fields and, using them, get three-dimensional estimates for the eigenvalue moments of the corresponding magnetic Laplacians.

35 pages, no figures

References in corpus (1)

• Sharp spectral estimates in domains of infinite volume

Cited by in corpus (2)

• Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field
• Eigenvalue bound for Schroedinger operators with unbounded magnetic field