Magnetic barriers of compact support and eigenvalues in spectral gaps
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We consider Schrödinger operators H = -Δ + V in L2(ℝ2) with a spectral gap, perturbed by a strong magnetic field B of compact support. We assume here that the support of B is connected and has a connected complement; the total magnetic flux may be zero or non-zero. For a fixed point in the gap, we show that (for a sequence of couplings tending to ∞) 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.
CitationHempel, R., & Besch, A. (2003). Magnetic barriers of compact support and eigenvalues in spectral gaps. Electronic Journal of Differential Equations, 2003(48), pp. 1-25.
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