  We study the dynamics of a classical particle moving in a punctured plane
under the influence of a strong homogeneous magnetic field, an electrical
background, and driven by a time-dependent singular flux tube through the hole.
  We exhibit a striking classical (de)localization effect: in the far past the
trajectories are spirals around a bound center; the particle moves inward
towards the flux tube loosing kinetic energy. After hitting the puncture it
becomes ``conducting'': the motion is a cycloid around a center whose drift is
outgoing, orthogonal to the electric field, diffusive, and without energy loss.
