Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field

Details Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field

2006-05-11

arxiv.org/abs/math/0605298v1

Mathematics

Analysis of PDEs

93pp

Scientific paper

I continue analysis of the Schr\"odinger operator with the strong degenerating magnetic field, started in \cite{IRO6}. Now I consider 4-dimensional case, assuming that magnetic field is generic degenerated and under certain conditions I derive spectral asymptotics with the principal part $\asymp h^{-4}$ and the remainder estimate $O(\mu^{-1/2}h^{-3})$ where $\mu\gg 1$ is the intensity of the field and $h\ll 1$ is the Plank constant; $\mu h\le 1$. These asymptotics can contain correction terms of magnitude $\mu ^{5/4}h^{-3/2}$ corresponding to the short periodic trajectories.

Affiliated with

Also associated with

No associations

Rating

Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field 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 Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-469679