Eigenvalue bounds for radial magnetic bottles on the disk - Archive ouverte HAL Access content directly
Journal Articles Asymptotic Analysis Year : 2012

Eigenvalue bounds for radial magnetic bottles on the disk

Francoise Truc

Abstract

We consider a Schrödinger operator H with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator. Under some assumptions on an additional radial potential V the operator H + V has a discrete negative spectrum and we obtain an upper bound on the number of negative eigenvalues. As a consequence we get an upperbound of the number of eigenvalues of H smaller than any positive value, which involves the minimum of B and the square of the L^2 -norm of A(r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centerde in the origin.
Fichier principal
Vignette du fichier
llthin09hall.pdf (122.72 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00588164 , version 1 (22-04-2011)
hal-00588164 , version 2 (25-05-2011)
hal-00588164 , version 3 (09-09-2011)

Identifiers

Cite

Francoise Truc. Eigenvalue bounds for radial magnetic bottles on the disk. Asymptotic Analysis, 2012, 76, pp.233-248. ⟨10.3233/ASY-2011-1077⟩. ⟨hal-00588164v3⟩
168 View
169 Download

Altmetric

Share

Gmail Facebook X LinkedIn More