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Dynamical properties of an asymmetric bistable system with quantum fluctuations in the strong-friction limit

  • Research Article
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Central European Journal of Physics

Abstract

The dynamical properties of an overdamped Brownian particle moving in an asymmetric bistable system with quantum fluctuations are investigated. Within the strong-friction limit (the quantum Smoluchowski regime), the analytic expression for the relaxation time of the system is derived by means of the projection-operator method, in which the effects of the memory kernels are taken into account. Based on the relaxation time, we consider both the overdamped quantum case and its classical counterpart.In these contexts, the effects of the quantum fluctuations and the asymmetry of the potential are discussed. It is found that: (i) The quantum effects in an asymmetric bistable system on time scales of the relaxation process are more prominent for lower temperatures and smaller asymmetries of the potential. (ii) The quantum effects speed up the rate of fluctuation decay of the state-space variable for lower temperatures. (iii) The asymmetry of the potential first slows down the rate of fluctuation decay of the state-space variable and then increases it.

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References

  1. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1996)

    MATH  Google Scholar 

  2. S. Bouzat, H.S. Wio, Phys. Rev. E 59, 5142 (1999)

    Article  ADS  Google Scholar 

  3. H.S. Wio, S. Bouzat, Braz. J. Phys. 29, 136 (1999)

    Article  Google Scholar 

  4. A. Nikitin, N.G. Stocks, A.R. Bulsara, Phys. Rev. E 68, 016103 (2003)

    Article  ADS  Google Scholar 

  5. A. Nikitin, N.G. Stocks, A.R. Bulsara, Phys. Lett. A 334, 12 (2005)

    Article  MATH  ADS  Google Scholar 

  6. A. Nikitin, N.G. Stocks, A.R. Bulsara, Phys. Rev. E 76, 041138 (2007)

    Article  ADS  Google Scholar 

  7. Y. Jin, W. Xu, M. Xu, Chaos Soliton. Fract. 26, 1183 (2005)

    Article  MATH  ADS  Google Scholar 

  8. L.-J. Ning, W. Xu, M.-L. Yao, Chin. Phys. 17, 486 (2008)

    Article  Google Scholar 

  9. G. Lindblad, Commun. Math. Phys. 48, 119 (1976)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications (Springer, Berlin, 1982)

    Google Scholar 

  11. H. Spohn, Rev. Mod. Phys. 52, 569 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  12. J. Ankerhold, P. Pechukas, H. Grabert, Phys. Rev. Lett 87, 086802 (2001)

    Article  ADS  Google Scholar 

  13. J. Ankerhold, H. Grabert, Phys. Rev. Lett 101, 119903 (2008)

    Article  ADS  Google Scholar 

  14. J. Ankerhold, H. Grabert, Phys. Rev. Lett 101, 169902 (2008)

    Article  ADS  Google Scholar 

  15. R. Dillenschneider, E. Lutz, Phys. Rev. E 80, 042101 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  16. J. Ankerhold, Phys. Rev. E 64, 060102(R) (2001)

    Article  ADS  Google Scholar 

  17. B.-q. Ai, H. Zheng, H.-z. Xie, L.-g. Liu, Cent. Eur. J. Phys. 4, 270 (2006)

    Article  Google Scholar 

  18. U. Weiss, Quantum Dissipative Systems, 2nd edition (World Scientific, Singapore, 1999)

    Book  MATH  Google Scholar 

  19. L. Machura, M. Kostur, P. Hänggi, P. Talkner, J. Luczka, Phys. Rev. E 70, 031107 (2004)

    Article  ADS  Google Scholar 

  20. J. Łuczka, R. Rudnicki, P. Hänggi, Physica A 351, 60 (2005)

    Article  ADS  Google Scholar 

  21. M. Łukasz, J. Łuczka, P. Talkner, P. Hänggi, Acta Phys. Pol. B 38, 1855 (2007)

    ADS  Google Scholar 

  22. C. Zeng, A. Gong, Y. Luo, Int. J. Mod. Phys. B (in press)

  23. L. Machura, M. Kostur, P. Talkner, J. Luczka, P. Hänggi, Phys. Rev. E 73, 031105 (2006)

    Article  ADS  Google Scholar 

  24. J. Casademunt, R. Mannellaetal, Phys. Rev. A 35, 5183 (1987)

    Article  ADS  Google Scholar 

  25. D.C. Mei, C.W. Xie, L. Zhang, Phys. Rev. E 68, 051102 (2003)

    Article  ADS  Google Scholar 

  26. D.C. Mei, C.W. Xie, Y.L. Xiang, Physica A 343, 167 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  27. F. Long, L.-C. Du, D.-C. Mei, Phys. Scripta 79, 045007 (2009)

    Article  ADS  Google Scholar 

  28. C. Zeng, Chin. J. Phys. 48, 57 (2010)

    Google Scholar 

  29. C. Zeng, X. Zhou, S. Tao, Cent. Eur. J. Phys. 7, 534 (2009)

    Article  Google Scholar 

  30. S.A. Maier, J. Ankerhold, Phys. Rev. E 81, 021107 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  31. J.M. Noriega et al., Phys. Rev. A 38, 5670 (1988)

    Article  Google Scholar 

  32. J.M. Noriega et al., Phys. Rev. A 44, 2094 (1991)

    Article  ADS  Google Scholar 

  33. A. Hernandez-Machado, M. San Miguel, J.M. Sancho, Phys. Rev. A 29, 3388 (1984)

    Article  ADS  Google Scholar 

  34. R.L. Stratonovich, In: R.L. Stratonovich (Ed.), Topics in the Theory of Random Noise (Gordon and Breach, New York, 1967) 223

    Google Scholar 

  35. H. Fujisaka, S. Grossmann, Z. Phys. B Con. Mat. 43, 69 (1981)

    Article  ADS  Google Scholar 

  36. C.W. Xie, D.C. Mei, Phys. Lett. A 323, 421 (2004)

    Article  MATH  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Chunhua Zeng & Ailing Gong

  2. Department of Physics, Yunnan University, Kunming, 650091, China

    Chongwei Xie

Authors
  1. Chunhua Zeng
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  2. Ailing Gong
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  3. Chongwei Xie
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Correspondence to Chunhua Zeng.

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Zeng, C., Gong, A. & Xie, C. Dynamical properties of an asymmetric bistable system with quantum fluctuations in the strong-friction limit. centr.eur.j.phys. 9, 198–204 (2011). https://doi.org/10.2478/s11534-010-0041-9

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  • DOI: https://doi.org/10.2478/s11534-010-0041-9

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