Magnetic barriers of compact support and eigenvalues in spectral gaps
We consider Schr"odinger 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 o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/48/abstr.html |
| Summary: | We consider Schr"odinger 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. |
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| ISSN: | 1072-6691 |