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 SU(2) operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the 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.