Dynamical symmetries of time-periodic Hamiltonians

Group theoretical methods were employed to study the DS-related properties (quantum numbers, nonaccidental degenracies) of quantum systems possesing high-order dynamical symmetries. As explicit examples finite-order rotation symmetry in point and plane groups and a circularly polarized laser field was taken. It was found that nonaccidental degeneracies induced by spatial and time-reversal symmetries might not be lifted inside the laser field. The results showed that the time-evolution operator needs to be computed only upto 1/N of the optical cycle, whereN is the order of the dynamical symmetries.