Eigenvalue bounds for radial magnetic bottles on the disk

Details Eigenvalue bounds for radial magnetic bottles on the disk Eigenvalue bounds for radial magnetic bottles on the disk

2011-04-22

arxiv.org/abs/1104.4459v3

Physics

Mathematical Physics

Scientific paper

We consider a Schr\"odinger 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.

Affiliated with

Also associated with

No associations

Rating

Eigenvalue bounds for radial magnetic bottles on the disk does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Eigenvalue bounds for radial magnetic bottles on the disk, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenvalue bounds for radial magnetic bottles on the disk will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-330895