Landau-Zener transitions in a level-crossing system with periodic modulations of the diagonal energy

We clarify some aspects of population dynamics of a level-crossing system, in which a periodic modulation of the relative energy is superimposed on the energy change with a constant velocity. For moderate values of the off-diagonal coupling, the temporal evolution of the system is well described by a transfer-matrix formalism. It is shown that the existence probability on one level shows a series of steplike changes both in the high-frequecy limit and the low-frequency limit of the periodic modulation, reflecting the quasiquantization of the oscillating held in the former case, while reflecting the multiple real crossings in the latter case. (C) 2000 The American Physical Society.