Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula

We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time-evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of ${\rm SU}(2)$ operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the ${\rm SU}(2)$ operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level-crossings.