Skip to main content

Directed Transport in AC-Driven Hamiltonian Systems

  • Chapter
  • First Online:
  • 1000 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 621))

Abstract

We study the mechanism of current rectification in Hamiltonian systems driven by an external periodic force with broken time reversal symmetry. We show that directed transport arises due to breaking the symmetry of fiights near regular islands. In the framework of the continuous time random walk (CTRW) approach we construct a generalized asymmetric fiights model and derive an expression for the current in terms of the characteristics of the relevant islands. The broken-symmetry strategy allows to manipulate the transport properties of both individual particles and statistical ensembles of particles.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Reimann: Phys. Rep. 361, 57 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. H. Risken: The Fokker Planck Equation. (Springer, Berlin, 1984)

    MATH  Google Scholar 

  3. P. Hänggi and R. Bartussek, in: Nonlinear Physics of Complex Systems, Lecture Notes in Physics, 476, ed. by J. Parisi, S. C. Muller, and W. Zimmermann (Springer, Berlin 1996) p.294; P. Jung, J. G. Kissner, and P. Hänggi: Phys. Rev. Lett. 76, 3436 (1996); J. L. Mateos: Phys. Rev. Lett. 84, 258 (2000)

    Chapter  Google Scholar 

  4. S. Flach, O. Yevtushenko, and Y. Zolotaryuk: Phys. Rev. Lett. 84, 2358 (2000)

    Article  ADS  Google Scholar 

  5. T. Dittrich, R. Ketzmerick, M.-F. Otto and H. Schanz: Ann. Phys. (Leipzig) 9, 755 (2000); H. Schanz, M.-F. Otto, R. Ketzmerick, and T. Dittrich: Phys. Rev. Lett 87 07601 (2001)

    Article  MATH  Google Scholar 

  6. R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky: Nonlinear physics: from the pendulum to turbulence and chaos. (Harwood Academic Publ. 1992)

    Google Scholar 

  7. M. F. Shlesinger, G. M. Zaslavsky and J. Klafter: Nature 363, 31 (1993); J. Klafter, M. F. Shlesinger, and G. Zumofen: Physics Today 49, 33 (1996)

    Article  ADS  Google Scholar 

  8. J. Klafter and G. Zumofen: Phys. Rev. E 49, 4873 (1994)

    Article  ADS  Google Scholar 

  9. S. Wiggins: Chaotic transport in dynamical systems. (Springer, Berlin 1992)

    MATH  Google Scholar 

  10. S. Denisov, S. Flach: Phys. Rev. E 64, 056236 (2001)

    Google Scholar 

  11. S. Denisov, J. Klafter, M. Urbakh, and S. Flach, Physica D (in press)

    Google Scholar 

  12. T. Geisel, A. Zacherl, and G. Radons: Phys. Rev. Lett. 59 2503 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  13. S. Denisov, J. Klafter, M. Urbakh, submitted

    Google Scholar 

  14. G. Zumofen, J. Klafter, and A. Blumen: Phys. Rev. E 47, 2183 (1993)

    Article  ADS  Google Scholar 

  15. E. R. Weeks and H. L. Swinney: Phys. Rev. E 57 4915 (1998)

    Article  ADS  Google Scholar 

  16. N. Kac: Statistical Independence in Probability, Analysis, and Number Theory. (Mathematical Association of America, Oberlin, OH, 1959)

    MATH  Google Scholar 

  17. J.R. Robinson et al: Phys. Rev. Lett. 76, 3304 (1996); F. L. Monte et al: Phys. Rev. Lett. 75, 4598 (1995); B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 4044 (1998)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Denisov, S., Klafter, J., Urbakh, M. (2003). Directed Transport in AC-Driven Hamiltonian Systems. In: Rangarajan, G., Ding, M. (eds) Processes with Long-Range Correlations. Lecture Notes in Physics, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44832-2_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-44832-2_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40129-2

  • Online ISBN: 978-3-540-44832-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics