Quantum Zeno effect and adiabatic change

We show that the quantum Zeno effect and the adiabatic change have a close connection even though the former means a halt of the dynamics by frequent measurements and the latter is the dynamics by a slowly changing Hamiltonian. We investigate the motion of a spin under stepping magnetic fields in terms of the (inverse) quantum Zeno effect. The relation between this model and the adiabatic change is studied. Another model is used to integrate the two effects into one formulation which is an extension of the proof of the adiabatic theorem. Despite their good parallelism, the asymptotic behaviors of the transition probability with respect to the total period T have different forms; the former effect shows a T^-1 behavior while the latter scales T^-2.