Geodesic
Magnetic barriers of compact support and eigenvalues in spectral gaps
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider Schrödinger operators $H = -\Delta + V$ in $L_2(\mathbb{R}^2)$ with a spectral gap, perturbed by a strong magnetic field $\mathcal{B}$ of compact support. We assume here that the support of $\mathcal{B}$ is connected and has a connected complement; the total magnetic flux may be zero or non-zero. For a fixed point $E$ in the gap, we show that (for a sequence of couplings tending to $\infty$) the signed spectral flow across $E$ for the magnetic perturbation is equal to the flow of eigenvalues produced by a high potential barrier on the support of the magnetic field. This allows us to use various estimates that are available for the high barrier case.
Classification : 35J10, 81Q10, 35P20
Keywords: Schrödinger operator, magnetic field, eigenvalues, spectral gaps, strong coupling 
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     author = {Hempel, Reiner and Besch, Alexander},
     title = {Magnetic barriers of compact support and eigenvalues in spectral gaps},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a45/}
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Hempel, Reiner; Besch, Alexander. Magnetic barriers of compact support and eigenvalues in spectral gaps. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a45/