Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

The famous Aharonov–Bohm effect shows that for an infinitely long solenoid with a magnetic field only inside it, even though there is no magnetic field outside, a charged particle can experience a phase difference when traveling along different trajectories on either side of the solenoid due to the existence of the magnetic vector potential. The Aharonov–Bohm effect demonstrates the non-trivial quantum mechanical effect of vector potentials. Although the single solenoid case has been studied widely using rotational and scaling invariance, the technique fails to work for the Aharonov–Bohm Hamiltonian with multiple solenoids. In this talk, I will discuss a new framework to study the resolvent, resonances, and wave decay of the Aharonov–Bohm Hamiltonian with multiple poles. This results in an interesting behavior where scattering and wave decay depend on the fluxes.

TBA