Related Experiment Video
Updated: Aug 19, 2026

Controlling Flow Speeds of Microtubule-Based 3D Active Fluids Using Temperature
Published on: November 26, 2019
Directed chaotic transport in Hamiltonian ratchets
Holger Schanz1, Thomas Dittrich, Roland Ketzmerick
1Max-Planck-Institut für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstrasse 10, D-37073 Göttingen, Germany. holger@chaos.gwdg.de
Abstract:
We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport like a mixed classical phase space. A sum rule is derived which connects the contributions of different phase-space components to transport. We show that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems. For quantized Hamiltonian ratchets we study transport in terms of the evolution of wave packets and derive a semiclassical expression for the distribution of level velocities which encode the quantum transport in the Floquet band spectra. We discuss the role of dynamical tunneling between transporting islands and the chaotic sea and the breakdown of transport in quantum ratchets with broken spatial periodicity.
Related Concept Videos
Energy to Drive Translocation
Generally, polypeptides are unfolded by two distinct...
Relating Angular And Linear Quantities - II
Classical Mechanics
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Rab Cascades
Conservation of Angular Momentum: Application