Classical and quantum Hamiltonian ratchets - art. no. 070601

We explain the mechanism leading to directed chaotic transport in Hamiltoni an systems with spatial and temporal periodicity. We show that a mixed phas e space comprising both regular and chaotic motion is required and we deriv e a classical sum rule which allows one to predict the chaotic transport ve locity from properties of regular phase-space components. Transport in quan tum Hamiltonian ratchets arises by the same mechanism as long as uncertaint y allows one to resolve the classical phase-space structure. We derive a qu antum sum rule analogous to the classical one, based on the relation betwee n quantum transport and band structure.