Localization of diffusive excitation in multi-level systems

The excitation of multi-level systems by a periodic field is considered in the regime of quasiclassical diffusion which takes place in the region of classical dynamical chaos. It is shown that quantum effects lead to a limitation of diffusion and to the localization of quasienergy eigenfunctions (QEE). The expression for the QEE localization length in terms of the classical diffusion rate ( l = D/2) is obtained and the analogy between this phenomenon and the Anderson localization in solid-state problems is analyzed. The localization length for photon transitions in the energy spectrum is found.