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Eigenvalue estimates for a three-dimensional magnetic Schr��dinger operator

Authors :
Helffer, Bernard
Kordyukov, Yuri A.
Publication Year :
2012
Publisher :
arXiv, 2012.

Abstract

We consider a magnetic Schr��dinger operator $H^h=(-ih\nabla-\vec{A})^2$ with the Dirichlet boundary conditions in an open set $��\subset {\mathbb R}^3$, where $h>0$ is a small parameter. We suppose that the minimal value $b_0$ of the module $|\vec{B}|$ of the vector magnetic field $\vec{B}$ is strictly positive, and there exists a unique minimum point of $|\vec{B}|$, which is non-degenerate. The main result of the paper is upper estimates for the low-lying eigenvalues of the operator $H^h$ in the semiclassical limit. We also prove the existence of an arbitrary large number of spectral gaps in the semiclassical limit in the corresponding periodic setting.<br />20 pages

Details

Database :
OpenAIRE
Accession number :
edsair.doi...........445edd07f5c525751bb6da47cc09bfe9
Full Text :
https://doi.org/10.48550/arxiv.1203.4021