Semiclassical bounds in magnetic bottles
Mathematical Physics
2019-12-10 v1 math.MP
Spectral Theory
Quantum Physics
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 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.
Cite
@article{arxiv.1501.02950,
title = {Semiclassical bounds in magnetic bottles},
author = {Diana Barseghyan and Pavel Exner and Hynek Kovarik and Timo Weidl},
journal= {arXiv preprint arXiv:1501.02950},
year = {2019}
}
Comments
35 pages, no figures