Local spectral density for a periodically driven system of coupled quantum states with strong imperfection in the unperturbed energies

A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong imperfection in the unperturbed energy levels. The system is excited by an external periodic field, the temporal profile of which is close to monochromatic. The shape of the local spectral density is shown to be well described by the contour obtained from a relevant model of a periodically driven two-state system with irreversible losses to an external thermal bath. The shape width and the inverse participation ratio are determined as functions both of the Rabi frequency and of parameters specifying the localization effect for the generic system considered in the absence of an external field.