Symmetry of pulsating ratchets

  • V. M. Rozenbaum
  • I. V. Shapochkina
  • Y. Teranishi
  • L. I. Trakhtenberg


Using an exact expression for the average velocity of inertialess motion of pulsating ratchets, a simple proof is given for the recently discovered hidden space-time symmetry of Cubero–Renzoni (D.Cubero, F. Renzoni, 2016). The conditions are revealed for the absence of the ratchet effect in systems with potential energies described by products of periodic functions of coordinate and time possessing the symmetry of the main types. In particular, it is shown that the ratchet effect is absent for the time dependence of the universal symmetry type (which combines three standard symmetries), and this restriction is removed when inertia is taken into account, unless the coordinate dependence of the potential energy is related to symmetric or antisymmetric functions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. D. Astumian and M. Bier, Phys. Rev. Lett. 72, 1766 (1994).ADSCrossRefGoogle Scholar
  2. 2.
    F. Jülicher, A. Ajdari, and J. Prost, Rev. Mod. Phys. 69, 1269 (1997).ADSCrossRefGoogle Scholar
  3. 3.
    Y. Okada and N. Hirokawa, Science 283, 1152 (1999).ADSCrossRefGoogle Scholar
  4. 4.
    J. Rousselet, L. Salome, A. Ajdari, and J. Prost, Nature (London) 370, 446 (1994).ADSCrossRefGoogle Scholar
  5. 5.
    C. C. de Souza Silva, J. Van de Vondel, M. Morelle, and V. V. Moshchalkov, Nature (London) 440, 651 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    R. Gommers, S. Bergamini, and F. Renzoni, Phys. Rev. Lett. 95, 073003 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    O. Kedem, B. Lau, and E.A. Weiss, Nano Lett. 17, 5848 (2017).ADSCrossRefGoogle Scholar
  8. 8.
    P. Reimann, Phys. Rev. Lett. 86, 4992 (2001).ADSCrossRefGoogle Scholar
  9. 9.
    P. Reimann, Phys. Rep. 361, 57 (2002).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    S. Denisov, S. Flach, and P. Hänggi, Phys. Rep. 538, 77 (2014).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    D. Cubero and F. Renzoni, Phys. Rev. Lett. 116, 010602 (2016).ADSCrossRefGoogle Scholar
  12. 12.
    V. M. Rozenbaum, JETP 110, 653 (2010).ADSCrossRefGoogle Scholar
  13. 13.
    V. M. Rozenbaum and I. V. Shapochkina, JETP Lett. 92, 120 (2010).ADSCrossRefGoogle Scholar
  14. 14.
    V. M. Rozenbaum, T. Ye. Korochkova, A. A. Chernova, and M. L. Dekhtyar, Phys. Rev. E 83, 051120 (2011).ADSCrossRefGoogle Scholar
  15. 15.
    V. M. Rozenbaum, Y. A. Makhnovskii, I. V. Shapochkina, S.-Y. Sheu, D.-Y. Yang, and S. H. Lin, Phys. Rev. E 85, 041116 (2012).ADSCrossRefGoogle Scholar
  16. 16.
    V. M. Rozenbaum, Yu. A. Makhnovskii, I. V. Shapochkina, S.-Y. Sheu, D.-Y. Yang, and S. H. Lin, Phys. Rev. E 89, 052131 (2014).ADSCrossRefGoogle Scholar
  17. 17.
    H. Riskin, The Fokker-Plank Equation. Methods of Solution and Applications, Springer-Verlag, Berlin (1989).CrossRefGoogle Scholar
  18. 18.
    D. Cubero, Personal communication, December 31, 2017.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • V. M. Rozenbaum
    • 1
    • 2
    • 3
  • I. V. Shapochkina
    • 1
    • 2
    • 4
  • Y. Teranishi
    • 1
  • L. I. Trakhtenberg
    • 5
    • 6
  1. 1.Institute of PhysicsNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Institute of Atomic and Molecular SciencesAcademia SinicaTaipeiTaiwan
  3. 3.Chuiko Institute of Surface ChemistryNational Academy of Sciences of UkraineKievUkraine
  4. 4.Department of PhysicsBelarusian State UniversityMinskBelarus
  5. 5.Semenov Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia
  6. 6.State Scientific Center of Russian FederationKarpov Institute of Physical ChemistryMoscowRussia

Personalised recommendations