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arXiv · 2304.06289

Resonances at the Threshold for Pauli Operators in Dimension Two

Jonathan Breuer·Hynek Kovařík
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Abstract

It is well-known that, due to the interaction between the spin and the magnetic field, the two-dimensional Pauli operator has an eigenvalue $0$ at the threshold of its essential spectrum. We show that when perturbed by an effectively positive perturbation, $V$, coupled with a small parameter $\varepsilon$, these eigenvalues become resonances. Moreover, we derive explicit expressions for the leading terms of their imaginary parts in the limit $\varepsilon\searrow 0$. These show, in particular, that the dependence of the imaginary part of the resonances on $\varepsilon$ is determined by the flux of the magnetic field. The cases of non-degenerate and degenerate zero eigenvalue are treated separately. We also discuss applications of our main results to particles with anomalous magnetic moments.

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Jonathan Breuer, Hynek Kovařík. 2023-04-13. Resonances at the Threshold for Pauli Operators in Dimension Two. https://arxiv.org/abs/2304.06289

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