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Relaxation high-temperature ratchets

Author

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  • Shapochkina, I.V.
  • Rozenbaum, V.M.
  • Sheu, S.-Y.
  • Yang, D.-Y.
  • Lin, S.H.
  • Trakhtenberg, L.I.

Abstract

We consider the overdamped motion of a Brownian particle in an asymmetric spatially periodic potential which fluctuates periodically in time, under assumption of finite duration of the relaxation response of the system on deterministic dichotomous fluctuations. It is assumed that the period of these fluctuations is much larger than the characteristic diffusion time and the potential barrier height is small as compared to the thermal energy (an adiabatic high-temperature flashing ratchet). We derive an analytical expression for the average particle velocity, which is concretized for a saw-tooth potential profile. It is revealed the different, linear and quadratic, asymptotic behavior of the average velocity as a function of the relaxation time for extremely and not extremely asymmetric potential profiles, respectively. The result is interpreted in terms of the self-similar representation.

Suggested Citation

  • Shapochkina, I.V. & Rozenbaum, V.M. & Sheu, S.-Y. & Yang, D.-Y. & Lin, S.H. & Trakhtenberg, L.I., 2019. "Relaxation high-temperature ratchets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 71-78.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:71-78
    DOI: 10.1016/j.physa.2018.09.039
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    References listed on IDEAS

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    1. B. Spagnolo & A. Dubkov, 2006. "Diffusion in flashing periodic potentials," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 299-303, March.
    2. Rozenbaum, V.M. & Yang, D.-Y. & Lin, S.H. & Tsong, T.Y., 2006. "Energy losses in a flashing ratchet with different potential well shapes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 211-216.
    3. Jean-Charles Delvenne & Renaud Lambiotte & Luis E. C. Rocha, 2015. "Diffusion on networked systems is a question of time or structure," Nature Communications, Nature, vol. 6(1), pages 1-10, November.
    4. Sumithra, K. & Sintes, T., 2001. "Efficiency optimization in forced ratchets due to thermal fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(1), pages 1-12.
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