Combining quantum and classical perturbation theories

A method is proposed for combining quantum and classical perturbation theories into a single formalism. The method is applied to a model consisting of a periodically kicked particle in one dimension. The small-denominator problem and the transition, as ħ→0, from quantum to classical dynamics are discussed. It is found that the quantum to classical transition is characterized by two times, one scaling as ${\mathrm{ħ}}^{\mathrm{-}2/3}$ and one scaling as ${\mathrm{ħ}}^{\mathrm{-}1}$.