Revivals of wave packets: General theory and application to Rydberg clusters

A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum ${\mathit{E}}_{\mathit{n}}$ exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum ${\mathit{E}}_{\mathit{n}}$. The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. © 1996 The American Physical Society.