Weak dynamical localization in periodically kicked cold atomic gases

Quantum kicked rotor was recently realized in experiments with cold atomic gases and standing optical waves. As predicted, it exhibits dynamical localization in the momentum space. Here we consider the weak localization regime concentrating on the Ehrenfest time scale. The later accounts for the spread-time of a minimal wavepacket and is proportional to the logarithm of the Planck constant. We show that the onset of the dynamical localization is essentially delayed by four Ehrenfest times and give quantitative predictions suitable for an experimental verification.