Pearson's random walk and some statistical properties of a quasiperiodic observable in a simple quantum model

The dynamics of the atomic inversion of a quantum model of field-atom interaction is studied from a statistical point of view. We determine its mean motion and its partial recurrence frequencies. We employed by the mathematical analysis used by Lagrange, Wintner, and Weyl in their pioneering studies of the perturbed planetary motion and its connection with the studies of Pearson's random walks