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
Pages (from-to)2839-2875
Number of pages37
JournalAnnales Henri Poincare
Issue number6
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2023.


  • 35P05
  • 35Q40
  • 81Q10


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