Classical Particle and Time-Periodic Aharonov-Bohm Flux
We study the motion of a charged massive classical particle moving in a plane and under the influence of a homogeneous magnetic field and a time-periodic singular flux tube. In particular we are interested in the stability of the system. We show that there is a interesting resonant effect between the strength of the magnetic field and the frequency of the flux. The trajectories of the particle are either bounded or (in the case of resonance) get arbitrarily close to and far from the tube.