Semiclassical dynamics of a bound system in a high-frequency field

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Abstract
The quantal behaviour of a particle in a one-dimensional triangular potential well, driven by a monochromatic electric field, is studied. A classical high-frequency expansion together with semiclassical uniform methods are used to obtain an explicit form of the Floquet evolution operator in the unperturbed basis. A local exact solution is found for the eigenvalue equation of this operator under certain conditions. The local solution provides a tool for the quantitative investigation of the eigenstates. It predicts the appearance of quasi-resonances, or photonic states, and gives their location, shape and width as a function of parameters. It also predicts a local crossover from a decaying region to a more extended region as a function of n, with a point of crossover nc between them. The results concerning the local structures are used to justify and extend a previously suggested method for the investigation of the asymptotic properties of the eigenstates. These are found to decay with a power depending on the field parameters (first proposed by Benvenuto et al., 1991). The specific system studied here is suggested as a prototype model for a class of driven one-dimensional bound systems. Whose main characteristic is an increasing density of states as a function of energy.