The Campbell-Baker-Hausdorff expansion for classical and quantum kicked dynamics

A technique based on the Campbell-Baker-Hausdorff (CBH) formula is introduced to calculate the effective Hamiltonian for kicked dynamics, classical and quantum. An integrable example is exactly solved by this method. A non-integrable kicked spin dynamics is treated approximately up to seventh order in a perturbation parameter. The CBH expansion is evaluated in a transparent way with the help of a REDUCE program, thereby illustrating that the CBH expansion is asymptotic.