HIGH-FREQUENCY EXCITATION OF QUANTUM-SYSTEMS WITH ADIABATIC NONLINEARITY

The excitation by a high-frequency field of multi-level quantum system s 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 t hat the excitation takes place through a ladder of sharp quasi-resonan ces, 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 spac e. Two classes of examples are considered in detail: for a particle in a positive power-law potential well, the amplitudes exhibit a local c rossover in energy between a regime of exponential decay and an asympt otic power-law tail, which depends on the field parameters. For a nega tive power-law potential well, exponential localization, similar to th e Anderson localization in a finite lattice, is found. The localizatio n length depends on the field parameters as well as on the specific po wer of the potential well. The two classes contain, as special cases, the 'bubble' model and the one-dimensional hydrogen atom; previous res ults are confirmed for these cases, and new results are presented.