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arXiv · 2507.09162

A modified Fermi Golden Rule at threshold for 3D magnetic Schr\"odinger operators

Pavel Exner·Arne Jensen·Hynek Kovarik
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Abstract

In this paper we consider three-dimensional Schr\"odinger operators with a simple threshold eigenvalue. We show, under certain assumptions, that when a small magnetic field is introduced, this eigenvalue turns into a resonance in the time-dependent sense. We find the leading term in the asymptotic expansion of the imaginary part of the resonance and discuss the principal differences with respect to resonances induced by weak electric fields obtained previously in the literature.

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Pavel Exner, Arne Jensen, Hynek Kovarik. 2025-07-12. A modified Fermi Golden Rule at threshold for 3D magnetic Schr\"odinger operators. https://arxiv.org/abs/2507.09162

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