We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.
Cite
@article{arxiv.0705.0370,
title = {Sub-ballistic behavior in quantum systems with L\'evy noise},
author = {A. Romanelli and R. Siri and V. Micenmacher},
journal= {arXiv preprint arXiv:0705.0370},
year = {2009}
}