Directed chaotic transport in Hamiltonian ratchets

Holger Schanz, Thomas Dittrich, and Roland Ketzmerick
Phys. Rev. E 71, 026228 – Published 16 February 2005

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.

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  • Received 12 August 2004

DOI:https://doi.org/10.1103/PhysRevE.71.026228

©2005 American Physical Society

Authors & Affiliations

Holger Schanz1,*, Thomas Dittrich2, and Roland Ketzmerick3

  • 1Max-Planck-Institut für Strömungsforschung und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstraße 10, D-37073 Göttingen, Germany
  • 2Departamento de Física, Universidad Nacional, Santafé de Bogotá, Colombia
  • 3Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany

  • *Electronic address: holger@chaos.gwdg.de

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Issue

Vol. 71, Iss. 2 — February 2005

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