Sharp spectral asymptotics for four-dimensional Schr\"odinger operator with a strong degenerating magnetic field

arXivmath/0605298MaRDI QIDQ6477175

Victor Ivrii

Publication date: 11 May 2006

Abstract: 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 $O(m{u}^{-1/2}{h}^{-3})$ where $mugg1$ is the intensity of the field and $hll1$ is the Plank constant; $muhle1$. These asymptotics can contain correction terms of magnitude $m{u}^{5/4}{h}^{-3/2}$ corresponding to the short periodic trajectories.

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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