Scattering and wave asymptotics of the multi-pole Aharonov–Bohm Hamiltonian

Abstract: The famous Aharonov–Bohm effect demonstrates the non-trivial quantum mechanical effect of (singular) magnetic potentials. Although the single pole case has been studied widely using rotational and scaling invariance, the technique fails to work for the Aharonov–Bohm Hamiltonian with multiple poles. In this talk, we will discuss a new framework to study the resolvent, resonances, and wave asymptotics of the Aharonov–Bohm Hamiltonian with multiple poles. This results in an interesting behavior where scattering and wave asymptotics depend on the magnetic fluxes, interpolating the odd and even dimensional Euclidean scattering. This talk includes joint works with Tanya Christiansen and Kiril Datchev.