It is well-known that the interaction between the spin and a magnetic field typically gives rise to zero energy eigenfunctions of two-dimensional Pauli and Dirac operators, the so called Aharonov-Casher states. In this talk we will consider an additional multiplicative perturbation with a small coupling parameter. We will show that if the perturbation is positive in certain weak sense, then the Aharonov-Casher states turn into resonances. We will also provide the leading terms of their lifetimes in the weak coupling expansion. The talk is based on a joint work with Jonathan Breuer (Hebrew University, Jerusalem).
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