A study of quantum dynamics in the classically chaotic regime

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Abstract
The authors examine the effect of the Coulomb singularity on the classical and semiclassical dynamics of the one-dimensional model for atomic hydrogen, sometimes called the surface-state-electron model, in a periodic electric field and determine a necessary condition, in terms of the field strength, frequency and the initial quantum number, for the violation of the uncertainty principle. They show that when this violation occurs the quantal transition probabilities are significantly less than the equivalent classical probabilities. This criterion is tested numerically and shown to provide a good estimate of the boundary to one of the regions in which classical dynamics fails. The authors also show that when the uncertainty principle is not violated the fluctuations of the quantal about the classical probability spectra can be related to structure in classical phase space. These fluctuations are due to different classical and quantal transport through cantori.