Resonances at the Threshold for Pauli Operators in Dimension Two

Jonathan Breuer*, Hynek Kovařík

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 ε , these eigenvalues become resonances. Moreover, we derive explicit expressions for the leading terms of their imaginary parts in the limit ε↘ 0 . These show, in particular, that the dependence of the imaginary part of the resonances on ε 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.

Original languageAmerican English
JournalAnnales Henri Poincare
StateAccepted/In press - 2023

Bibliographical note

Funding Information:
This work was supported in part by the Vigevani Research Project Prize (JB and HK) and the Israel Science Foundation (JB, Grant No. 1378/20). JB acknowledges the hospitality of the Sezione di Matematica at the Università degli studi di Brescia, and HK acknowledges the hospitality of the Einstein Institute of Mathematics at the Hebrew University of Jerusalem, where parts of this work were done. We thank Arne Jensen for drawing our attention to the papers Cattaneo et al. [] and Jensen and Nenciu []. We wish to thank the anonymous referees for their careful reading of the paper and their useful comments.

Publisher Copyright:
© 2023, Springer Nature Switzerland AG.


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