Skip to main content
SpringerLink
Log in

Anomalous transport and diffusion of coupled Brownian particles with periodic driving forces

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Transport and diffusion of coupled Brownian particles in a spatially periodic potential are investigated under a constant biased force and two periodic driving forces. The impact of the periodic driving forces on the transport characteristics of coupled particles is discussed by Brownian dynamic simulation methods. The force–velocity relation which has been described for the coupled particles displays complex and rich behaviors, including absolute, nonlinear and differential negative mobilities. When the particle number or the coupled strength between particles increases, the anomalous transport and multiple current reversals will gradually disappear. In addition, we analyze anomalous diffusions (subdiffusion, superdiffusion and hyperdiffusion) corresponding to these anomalous mobilities. Meanwhile, we discuss physical mechanisms behind these findings via the mean square displacement, the probability distribution of the velocity and mobility coefficient of the coupled particles. Our results may contribute to further understanding of peculiar transport phenomena in the microworld.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability Statement

This manuscript has associated data in a data repository.[Authors comment: In this paper, the transport characteristics of multiple particles are simulated and some anomalous diffusion and transport are found, which will help us to study the phenomena in the micro-world, but additional experimental studies need to be further developed. (https://doi.org/10.1103/PhysRevLett.124.075001), (https://doi.org/10.1103/PhysRevLett.117.174501). We have made substantial contributions to the conception or design of the work; or the acquisition analysis, or interpretation of data for the work; and we have approved the final version to be published; and we agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.]

References

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

    Article  ADS  MathSciNet  Google Scholar 

  2. P. Reimann, P. Hänggi, Appl. Phys. A 75, 169 (2002)

    Article  ADS  Google Scholar 

  3. J.H. Li, S.G. Chen, Phys. Rev. Lett. 93, 014102 (2004)

    Article  ADS  Google Scholar 

  4. D. Wu, S. Zhu, Phys. Rev. E 73, 051107 (2006)

    Article  ADS  Google Scholar 

  5. P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  6. R. Gommers, P. Douglas, S. Bergamini, M. Goonasekera, P.H. Jones, F. Renzoni, Phys. Rev. Lett. 94, 143001 (2005)

    Article  ADS  Google Scholar 

  7. L. Wu, S. Zhu, X. Luo, D. Wu, Phys. Rev. E 81, 061118 (2010)

    Article  ADS  Google Scholar 

  8. R.D. Astumian, P. Hänggi, Phys. Today 55, 33 (2002)

    Article  Google Scholar 

  9. P. Hänggi, F. Marchesoni, F. Nori, Ann. Phys 14, 51 (2005)

    Article  MathSciNet  Google Scholar 

  10. R.D. Astumian, M. Bier, Phys. Rev. Lett. 72, 1766 (1994)

    Article  ADS  Google Scholar 

  11. J. Krim, D.H. Solina, R. Chiarello, Phys. Rev. Lett. 66, 181 (1991)

    Article  ADS  Google Scholar 

  12. H.G.E. Hentschel, F. Family, Y. Braiman, Phys. Rev. Lett. 83, 104 (1999)

    Article  ADS  Google Scholar 

  13. I. Derényi, C. Lee, A.L. Barábasi, Phys. Rev. Lett. 80, 1473 (1998)

    Article  ADS  Google Scholar 

  14. Y. Luo, C. Zeng, Chaos 30, 053115 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  15. A.G. Cherstvy, R. Metzler, Phys. Rev. E 90, 012134 (2014)

    Article  ADS  Google Scholar 

  16. W. Wang, A.G. Cherstvy, X. Liu, R. Metzler, Phys. Rev. E 102, 012146 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  17. A.G. Cherstvy, H. Safdari, R. Metzler, J. Phys. D: Appl. Phys. in press (2021). https://doi.org/10.1088/1361-6463/abdff0

  18. J. Spiechowicz, P. Hänggi, J. Łuczka, New J. Phys. 21, 083029 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  19. N. Khatri, P.S. Burada, J. Chem. Phys. 151, 094103 (2019)

    Article  ADS  Google Scholar 

  20. B.-Q. Ai, L. Liu, Phys. Rev. E 76, 042103 (2007)

    Article  ADS  Google Scholar 

  21. D. Wu, S. Zhu, Phys. Rev. E 90, 012131 (2014)

    Article  ADS  Google Scholar 

  22. Y. Jiao, F. Yang, C. Zeng, Eur. Phys. J. Plus 135, 1–11 (2020)

    Article  Google Scholar 

  23. L. Du, D. Mei, Phys. Rev. E 85, 011148 (2012)

    Article  ADS  Google Scholar 

  24. D. Wu, S. Zhu. Phys. Rev. E 85, 061101 (2012)

    Article  ADS  Google Scholar 

  25. J. Brugués, J. Casademunt, Phys. Rev. Lett. 102, 118104 (2009)

    Article  ADS  Google Scholar 

  26. S. Savel’ev, F. Marchesoni, F. Nori, Phys. Rev. Lett. 91, 010601 (2003)

  27. C. Yao, M. Zhan, Phys. Rev. E 81, 061129 (2010)

    Article  ADS  Google Scholar 

  28. C. Allison, C. Hughes, Sci. Prog. 75, 403–442 (1991)

    Google Scholar 

  29. E. Ben-Jacob, A. Tenenbaum, O. Shochet, O. Avidan, Physica A 202, 1–47 (1994)

    Article  ADS  Google Scholar 

  30. H. Chaté, F. Ginelli, G. Grégoire, F. Raynaud, Phys. Rev. E 77, 046113 (2008)

    Article  ADS  Google Scholar 

  31. A. Czirók, A. Barabási, T. Vicsek, Phys. Rev. Lett. 82, 209–212 (1999)

    Article  ADS  Google Scholar 

  32. R. Eichhorn, P. Reimann, P. Hänggi, Phys. Rev. Lett. 88, 190601 (2002)

    Article  ADS  Google Scholar 

  33. R. Eichhorn, P. Reimann, P. Hänggi, Phys. Rev. E 66, 066132 (2002)

    Article  ADS  Google Scholar 

  34. R. Eichhorn, P. Reimann, P. Hänggi, Physica A 325, 101 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  35. L. Machura, M. Kostur, P. Talker, J. Łuczka, P. Hänggi, Phys. Rev. Lett. 98, 040601 (2007)

    Article  ADS  Google Scholar 

  36. D. Speer, R. Eichhorn, P. Reimann, Europhys. Lett. 79, 1005 (2007)

    Article  Google Scholar 

  37. D. Speer, R. Eichhorn, P. Reimann, Phys. Rev. E 76, 051110 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  38. J. Spiechowicz, J. Łuczka, P. Hänggi, Sci. Rep. 6, 30948 (2016)

    Article  ADS  Google Scholar 

  39. M. Kostur, L. Machura, P. Talkner, P. Hänggi, J. Łuczka, Phys. Rev. B 77, 104509 (2008)

    Article  ADS  Google Scholar 

  40. F. Deng, Y. Luo, Y. Fang, F. Yang, C. Zeng, Chaos. Solitons and Fractals 147, 110959 (2021)

    Article  Google Scholar 

  41. Y. Luo, C. Zeng, B. Ai, Phys. Rev. E 102, 042114 (2020)

    Article  ADS  Google Scholar 

  42. L. Kong, R. Wan, H. Fang, Chin. Phys. Lett. 33, 020501 (2016)

    Article  Google Scholar 

  43. D. Wu, S. Zhu, X. Luo, Physica A 391, 1032–1037 (2012)

    Article  ADS  Google Scholar 

  44. R. Metzler, J.H. Jeon, A.G. Cherstvy, E. Barkai, Phys. Chem. Chem. Phys. 16, 24128–24164 (2014)

    Article  Google Scholar 

  45. R. Eichhorn, P. Reimann, B. Cleuren, C. Van den Broeck, Chaos 15, 026113 (2005)

    Article  ADS  Google Scholar 

  46. J. Spiechowicz, J. Łuczka, Sci. Rep. 7, 16451 (2017)

    Article  ADS  Google Scholar 

  47. J. Spiechowicz, J. Łuczka, Chaos 29, 013105 (2019)

    Article  ADS  Google Scholar 

  48. A. Ros, R. Eichhorn, J. Regtmeier, T.T. Duong, P. Reimann, D. Anselmetti, Nature 436, 928 (2005)

    Article  ADS  Google Scholar 

  49. J. Nagel, D. Speer, T. Gaber, A. Sterck, R. Eichhorn, P. Reimann, K. Ilin, M. Siegel, D. Koelle, R. Kleiner, Phys. Rev. Lett. 100, 217001 (2008)

    Article  ADS  Google Scholar 

  50. A. Słapik, J. Łuczka, P. Hänggi, J. Spiechowicz, Phys. Rev. Lett. 122, 070602 (2019)

    Article  ADS  Google Scholar 

  51. A. Słapik, J. Łuczka, P. Hänggi, J. Spiechowicz, Phys. Rev. Appl. 12, 054002 (2019)

    Article  ADS  Google Scholar 

  52. Y. He, B.-Q. Ai, C. Dai, C. Song, R. Wang. W. Sun, F. Liu, Y. Yeng, Phys. Rev. Lett. 124, 075001 (2020)

  53. A. Sarracino, F. Cecconi, A. Puglisi, A. Vulpiani, Phys. Rev. Lett. 117, 174501 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants No. 12075090), the Yunnan Fundamental Research Projects (Grant No. 2019FI002 and 202101AS070018), the Key-Area Research and Development Program of Guangdong Province (Grant No. 2019B030330001), the Yunnan Province Ten Thousand Talents Plan Young and Elite Talents Project and Yunnan Province Computational Physics and Applied Science and Technology Innovation Team, and Science and Technology Program of Guangzhou (Grant No. 2019050001).

Author information

Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, China

    Ying Wang & Chunhua Zeng

  2. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou, 510006, China

    Bao-Quan Ai

Authors
  1. Ying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunhua Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bao-Quan Ai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Chunhua Zeng or Bao-Quan Ai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Zeng, C. & Ai, BQ. Anomalous transport and diffusion of coupled Brownian particles with periodic driving forces. Eur. Phys. J. Plus 136, 1071 (2021). https://doi.org/10.1140/epjp/s13360-021-02047-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-02047-x

Search

Navigation