Quantum Poincare' recurrences in microwave ionization of Rydberg atoms
  We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field. The quantum survival probability follows the classical one up to the Heisenberg time and then decays inversely proportional to time, due to tunneling and localization effects. We provide parameter values which should allow one to observe such decay in laboratory experiments. Relations to the $1/f$ noise are also discussed. 
Giuliano Benenti, Giulio Casati