Berry phase and time-dependent wave operators

The present paper analyses the relation between the theory of the time-dependent wave operator and the Berry phase concept. It is proved that the wave operator approach is consistent with the non-adiabatic (Aharonov-Anandan) Berry phase, given that the wave operator and the parallel transport commute. It is then demonstrated that the non-Abelian Aharonov-Anandan phase can be calculated by working inside a reduced active space in the framework of wave operator theory. Finally an adiabatic transport formula is derived in the wave operator context and the influence of this effective Hamiltonian theory on the Berry phase is analysed. The theoretical results concerning the non-adiabatic Berry phase are confirmed numerically by considering a photodissociation process in the framework of the generalized Floquet theory.