Dynamics of a generic quantum system under a periodic perturbation

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Abstract
We characterize the evolution operator of a quantum system with generic spectral properties (in agreement with random-matrix theory), with a time-dependent Hamiltonian. The results are applied to the independent-electron model for the dissipation of energy: an example of a physical application would be the absorption of low-frequency electromagnetic radiation by small metallic particles. We discuss the statistical properties of the various regimes of the model, which depend on whether the perturbation is large enough to mix levels, and on whether the frequency is low enough for the quantum adiabatic theorem to apply. We also show that the eigenstates of the evolution operator are Anderson localized in the adiabatic basis, and present results concerning the localization length. This localization causes a saturation of the energy absorption if the Hamiltonian is periodic in time. The addition of a small amount of noise to the Hamiltonian destroys this nonclassical saturation effect.