title: Classical and quantum Hamiltonian ratchets.
abstract: We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and we derive a classical sum rule which allows one to predict the chaotic transport velocity from properties of regular phase-space components. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one to resolve the classical phase-space structure. We derive a quantum sum rule analogous to the classical one, based on the relation between quantum transport and band structure.
authors.affiliation: Max-Planck-Institut für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstrasse 10, 37073 Göttingen, Germany.
authors.forename: H
authors.initials: H
authors.lastname: Schanz
authors.forename: M F
authors.initials: MF
authors.lastname: Otto
authors.forename: R
authors.initials: R
authors.lastname: Ketzmerick
authors.forename: T
authors.initials: T
authors.lastname: Dittrich