Diana Barseghyan, Pavel Exner, Hynek Kovarik, Timo Weidl
Semiclassical bounds in magnetic bottles
(242K, pdf)

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.