This analysis shows how a small magnetic field introduces resonance at a threshold eigenvalue, contrasting previous findings with electric fields.
In this paper we consider three-dimensional Schrödinger 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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Exner et al. (2025) studied this question.
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