MCS-MP Seminar: Marie Fialová

Speaker: Marie Fialová (ISTA)

Title: Virtual bound states of the Pauli operator with an Aharonov–Bohm potential

Abstract: I will introduce the maximal realization of the Pauli operator with the singular Aharonov--Bohm magnetic field. This is a non-negative operator with purely essential spectrum. We find that, contrary to the case of regular magnetic fields, both components of the operator are critical. In other words, an arbitrarily small electric perturbation creates two bound states. These are known as virtual bound states in physics. We employ the Birman--Schwinger analysis to derive the asymptotics of such eigenstates.

This talk is based on joint work with David Krejčiřík.