Hempel, RainerBesch, Alexander2020-11-232020-11-232003-04-24Hempel, R., & Besch, A. (2003). Magnetic barriers of compact support and eigenvalues in spectral gaps. <i>Electronic Journal of Differential Equations, 2003</i>(48), pp. 1-25.1072-6691https://hdl.handle.net/10877/12988We 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.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalSchrodinger operatormagnetic fieldeigenvaluesspectral gapsstrong couplingArticle