On the asymptotic number of edge states for magnetic Schrödinger operators

Details On the asymptotic number of edge states for magnetic Schrödinger operators On the asymptotic number of edge states for magnetic Schrödinger operators

2006-03-17

arxiv.org/abs/math-ph/0603046v1

Physics

Mathematical Physics

Scientific paper

We consider a Schr\"odinger operator $(h\mathbf D -\mathbf A)^2$ with a positive magnetic field $B=\curl\mathbf A$ in a domain $\Omega\subset\R^2$. The imposing of Neumann boundary conditions leads to spectrum below $h\inf B$. This is a boundary effect and it is related to the existence of edge states of the system. We show that the number of these eigenvalues, in the semi-classical limit $h\to 0$, is governed by a Weyl-type law and that it involves a symbol on $\partial\Omega$. In the particular case of a constant magnetic field, the curvature plays a major role.

Affiliated with

Also associated with

No associations

Rating

On the asymptotic number of edge states for magnetic Schrödinger operators 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 On the asymptotic number of edge states for magnetic Schrödinger operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the asymptotic number of edge states for magnetic Schrödinger operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-489814