Abstract
The excitation by a high-frequency field of multi-level quantum systems with a slowly varying density of states is investigated. This class of systems includes hydrogen-like atoms, surface electrons in metals, charge bubbles in liquid helium and other bound systems. It is found that the excitation takes place through a ladder of sharp quasi-resonances, whose shape is universal, namely independent of the driving-field parameters and of the details of the system. The amplitudes of these peaks satisfy a system-dependent tight-binding equation in energy space. Two classes of examples are considered in detail: for a particle in a positive power-law potential well, the amplitudes exhibit a local crossover in energy between a regime of exponential decay and an asymptotic power-law tail, which depends on the field parameters. For a negative power-law potential well, exponential localization, similar to the Anderson localization in a finite lattice, is found. The localization length depends on the field parameters as well as on the specific power of the potential well. The two classes contain, as special cases, the `bubble' model and the one-dimensional hydrogen atom; previous results are confirmed for these cases, and new results are presented.
Published Version
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