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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 R3\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.

Keywords

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

R2 v1 2026-06-22T07:59:32.091Z