C. E. Creffield and F. Sols (Phys. Rev. Lett. 103, 200601 (2009)) recently reported finite, directed time-averaged ratchet current, for a noninteracting quantum particle in a periodic potential even when time-reversal symmetry holds. As we explain in
this Comment, this result is incorrect, that is, time-reversal symmetry implies a vanishing current.
Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system
as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help understanding the dynamics of quantum entanglement generation in chaotic quantum systems.
