SEMICLASSICAL DYNAMICS OF A BOUND SYSTEM IN A HIGH-FREQUENCY FIELD

The quantal behaviour of a particle in a one-dimensional triangular po tential 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 Roquet evolution operator in the unperturbed basis. A local exact solution is found for the eigenvalue equation of this operator under certain conditions. Th e local solution provides a tool for the quantitative investigation of the eigenstates. It predicts the appearance of quasi-resonances, or p hotonic states, and gives their location, shape and width as a functio n of parameters. It also predicts a local crossover from a decaying re gion to a more extended region as a function of n, with a point of cro ssover n, between them. The results concerning the local structures ar e used to justify and extend a previously suggested method for the inv estigation of the asymptotic properties of the eigenstates. These are found to decay with a power depending on the field parameters (first p roposed by Benvenuto et al). The specific system studied here is sugge sted 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.