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Rocking Ratchets at High Frequencies

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Stochastic Processes in Physics, Chemistry, and Biology

Part of the book series: Lecture Notes in Physics ((LNP,volume 557))

Abstract

A pedagogical introduction to basic physical and mathematical concepts of stochastic modeling is given for the specific example of a rocking ratchet system. Perturbative methods are illustrated by deriving the leading order behavior of the particle current for asymptotically fast rocking forces.

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References

  1. Smoluchowski, M. v. (1912) Experimentell nachweisbaxe, der üblichen Thermodynamik widersprechende Molekularphänomene. Phys. Zeitschr. 13, 1069

    Google Scholar 

  2. Feynman R. P., Leighton R. B., and Sands M. (1963) The Feynman Lectures on Physics, Vol. 1, Chapter 46, Addison Wesley, Reading MA

    Google Scholar 

  3. Hänggi P. and Bartussek R. (1996) Brownian rectifiers: how to convert Brownian motion into directed transport. In: Eds. Parisi J. et al. Lecture Notes in Physics, Springer-Series Vol. 476, Springer, Berlin, 294

    Google Scholar 

  4. Astumian R. D. (1997) Thermodynamics and kinetics of a Brownian motor. Science 276, 917

    Article  Google Scholar 

  5. Jülicher F., Ajdari A., and Prost J. (1997) Modeling molecular motors. Rev. Mod. Phys. 69, 1269

    Article  ADS  Google Scholar 

  6. Magnasco M. O. (1993) Forced thermal ratchets. Phys. Rev. Lett. 71, 1477

    Article  ADS  Google Scholar 

  7. Bartussek R., Hänggi P., and Kissner J. G. (1994) Periodically rocked thermal ratchets. Europhys. Lett. 28, 459

    Article  ADS  Google Scholar 

  8. Ajdari A., Mukamel D., Peliti L., and Prost J. (1994) Rectified motion induced by ac forces in periodic structures. J. Phys. I France 4, 1551

    Article  Google Scholar 

  9. Schreier M., Reimann P., Hänggi P., and Pollak E. (1998) Giant enhancement of diffusion and particle separation in rocked periodic potentials. Europhys. Lett. 44, 416

    Article  ADS  Google Scholar 

  10. Plata J. (1998) Rocked thermal ratchets: the hight frequency limit. Phys. Rev. E 57, 5154

    Article  ADS  Google Scholar 

  11. Milstein G. N. and Tretyakov M. V. (1999) Mean velocity of noise-induced transport in the limit of weak periodic forcing. J. Phys. A 32, 5795

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Zapata I., Bartussek R., Sols F., and Hanggi P. (1996) Voltage rectification by a SQUID ratchet. Phys. Rev. Lett. 77, 2292

    Article  ADS  Google Scholar 

  13. Weiss S., Koelle D., Müller J., Barthel K., and Gross R. (2000) Ratchet effect in dc SQUIDs. Europhys. Lett., submitted

    Google Scholar 

  14. Reimann P., Grifoni M. and Hänggi P. (1997) Quantum ratchets. Phys. Rev. Lett. 79, 10

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Linke H., Humphrey T. E., Löfgren A., Sushkov A. O., Newbury R., Taylor R. P., and Omling P. (1999) Experimental tunneling ratchets. Science 286, 2314

    Article  Google Scholar 

  16. Grabert H., Hänggi P., and Talkner P. (1980) Microdynamics and nonlinear stochastic processes of gross variables. J. Stat. Phys. 22, 537

    Article  ADS  Google Scholar 

  17. Van den Broeck, C. (1983) On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process. J. Stat. Phys. 31, 467

    Article  MATH  ADS  Google Scholar 

  18. Risken H. (1984) The Fokker-Planck Equation. Springer, Berlin

    MATH  Google Scholar 

  19. Doering C.R., Horsthemke W., and Riordan J. (1994) Nonequilibrium fluctuation-induced transport. Phys. Rev. Lett. 72, 2984

    Article  ADS  Google Scholar 

  20. Luczka J., Czernik T., and Hänggi P. (1997) Symmetric white noise can induce directed current in ratchets. Phys. Rev. E 56, 3968

    Article  ADS  Google Scholar 

  21. Reimann P., Bartussek R., Häussler R., and Hanggi P. (1996) Brownian motors driven by temperature oscillations. Phys. Lett. A 215, 26

    Article  ADS  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Reimann, P. (2000). Rocking Ratchets at High Frequencies. In: Freund, J.A., Pöschel, T. (eds) Stochastic Processes in Physics, Chemistry, and Biology. Lecture Notes in Physics, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45396-2_5

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  • DOI: https://doi.org/10.1007/3-540-45396-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41074-4

  • Online ISBN: 978-3-540-45396-3

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