Quantum adiabatic theorem and universal holonomy

We give a simplified proof of the quantum adiabatic theorem for a system of possibly degenerate Hamiltonians by taking Berry's phase into account. We also relate the adiabatic transformation to the parallel transport induced by the holonomy in the universal bundle over a Grassman manifold. The special case of a nondegenerate Hamiltonian is precisely the cyclic quantum evolution studied by Aharanov and Anandan © 1988 Kluwer Academic Publishers.link_to_subscribed_fulltex