Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator

Bernard Helffer; Yuri A. Kordyukov

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arXiv · 1312.5488

Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator

Bernard Helffer·Yuri A. Kordyukov

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Abstract

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly positive, and the corresponding minimum is unique and non-degenerate. The purpose is to get the control on the spectrum in an interval $(hb_0, h(b_0 +\gamma_0)]$ for some $\gamma_0>0$ independent of the semiclassical parameter $h$. The previous papers by Helffer-Mohamed and by Helffer-Kordyukov were only treating the ground-state energy or a finite (independent of $h$) number of eigenvalues. Note also that N. Raymond and S. Vu Ngoc have recently developed a different approach of the same problem.

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BibTeX RIS

Bernard Helffer, Yuri A. Kordyukov. 2013-12-19. Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator. https://arxiv.org/abs/1312.5488

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