Transporting cold atoms in optical lattices with ratchets: Symmetries   and Mechanisms
  The objective of this work is to provide a general introduction into the symmetry analysis of the rachet effect using a simple, non-interacting one-particle dynamics. Despite its simplicity, this model contains all the basic aspects of classical and quantum ratchet dynamics, and may be used also as a starting point of incorporating atom-atom interactions. 
S. Denisov, S. Flach, and P. H\"anggi