Propagators weakly associated to a family of Hamiltonians and the   adiabatic theorem for the Landau Hamiltonian with a time-dependent   Aharonov-Bohm flux
  We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian. 
J. Asch, I. Hradecky, P. Stovicek