TEMPERATURE - ABNORMAL DIFFUSIVITY IN TILTED SPATIALLY PERIODIC POTENTIALS
Keywords:
diffusion, computer simulation, periodic structures, Langevin equation, time-periodic fields
Abstract
The paper describes diffusion of particles in a tilted spatially periodic potential under the action of external forces in the case of a low friction. It is shown that in underdamped systems, a region of temperature-abnormal diffusivity (TAD) exists, in which the diffusion coefficient increases with decreasing temperature. The TAD width and its position depend on the friction coefficient and the system parameters. The analytical expression for diffusion coefficients in TAD area is derived. These results are important for experimental investigations of TAD and its application.Downloads
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References
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28. Hänggi P., Talkner P., Borkovec M. Reaction-rate theory: fifty years after Kramers // Rev. Mod. Phys. – 1990. – Vol. 62. – P. 251–341.
2. Hänggi P., Marchesoni F. Artificial Brownian motors: Controlling transport on the nanoscale // Rev. Mod. Phys. – 2009. – Vol. 81. – P.337-442.
3. Risken H. The Fokker-Planck Equation and Methods of Solution and Applications. – Springer, 1989. – 472 p.
4. Lee S.-H., Grier D.G. Giant Colloidal Diffusivity on Corrugated Optical Vortices // Phys. Rev. Let. –2006. – Vol. 96. - P. 190601.
5. Tierno P., Reimann P., Johansen T.H., Sagu´es F. Giant transversal particle diffusion in a longitudinal magnetic ratchet // Phys. Rev. Let. – 2010. – Vol. 105. - P. 230602.
6. Eshuis P., van der Weele K., Lohse D., van der Meer D. Experimental Realization of a Rotational Ratchet in a Granular Gas // Phys. Rev. Let. – 2010. – Vol. 104. – P. 248001.
7. Pagliara S., Schwall C., Keyser U.F. Optimizing Diffusive Transport Through a Synthetic Membrane Channel // Advanc. Mat. – 2013. - Vol. 25. – P. 844.
8. Risken H., Vollmer H.D. Low friction nonlinear mobility for the diffusive motion in periodic potentials // Phys. Lett. - 1979. – Vol. 69A. – No.6. – P.387- 389.
9. Risken H., Vollmer H.D. Brownian Motion in Periodic Potentials; Nonlinear Response to an External Force // Z. Physik. - 1979. – Vol. B 33. – P.297.
10. Risken H., Vollmer H.D. Bistability Effects of the Brownian Motion in Periodic Potentials // Z. Physik.- 1980. – Vol. B 37. – P. 343-349.
11. Risken H., Vollmer H.D. Distribution Functions for the Brownian Motion of Particles in a Periodic Potential Driven by an External Force // Z. Physik. – 1979. – Vol. B34. – P. 313-322.
12. Risken H., Vollmer H.D. Nonlinear Response to an External Force // Z. Physik. – 1979. – Vol. B 35. – P. 177-184.
13. Jung P., Risken H., Eigenvalues for the Extremely Underdamped Brownian Motion in an Inclined Periodic Potential // Z. Physik. – 1984. – Vol. B 54. – P. 357-370.
14. Costantini G., Marchesoni F. Threshold diffusion in a tilted washboard potential // Europhys. Lett. – 1999. – Vol. 48. – P. 491-497.
15. Borromeo M., Costantini G., Marchesoni F. Critical Hysteresis in a Tilted Washboard Potential // Phys. Rev. Lett. – 1999. – Vol. 82. – P. 2820–2823.
16. Lindenberg K., Sancho J.M., Lacasta A.M., Sokolov I.M. Dispersionless Transport in a Washboard Potential // Phys. Rev. Lett. – 2007. – Vol. 98. – P. 020602.
17. Sancho J. M.,1 Lacasta A.M., Lindenberg K., Sokolov I.M., Romero A. H. Diffusion on a Solid Surface: Anomalous is Normal // Phys. Rev. Lett. – 2004. – Vol. 92. – P. 250601.
18. Khoury M., Gleeson J. P., Sancho J. M., Lacasta A. M., Lindenberg K. Diffusion coefficient in periodic and random potentials // Phys. Rev. – 2009. – Vol. E 80. – P. 021123.
19. Lindenberg K, Lacasta A.M., Sancho J.M., Romero A.H. Transport and diffusion on crystalline surfaces under external forces // New Jour. of Phys. – 2005. – Vol. 7. – P. 29.
20. Marchenko I.G., Marchenko I.I. Diffusion in the systems with low dissipation: Exponential growth with temperature drop // Europhisics Letters. – 2012. – Vol. 100. – P. 5005.
21. Marchenko I.G., Marchenko I.I., Zhiglo A.V. Temperature-abnormal diffusivity in underdamped space-periodic systems driven by external time-periodic force, http://arxiv.org/abs/1701.01424.- 2017.
22. Marchenko I.G., Marchenko I.I., Zhiglo A.V. Particle transport in space-periodic potentials in underdamped systems // Europ. Phys. Jour. – 2014. – Vol. B87. – P. 10.
23. Lindner B., Sokolov I.M. Giant diffusion of underdamped particles in a biased periodic potential // Phys. Rev. – 2016. – Vol. E93. – P. 042106.
24. Reimann, P., Van den Broeck C., Linke H., Hänggi P., Rubí J. M., Pérez-Madrid A. Diffusion in tilted periodic potentials: Enhancement, universality, and scaling // Phys. Rev. – 2002. – Vol. E65. – P. 031104.
25. Kuznetsov D.F. Stohasticheskie differencial'nye uravnenija: teorija i praktika chislennogo reshenija [Stochastic differential equations: theory and practice of numerical solution]. – SPb: Sankt-Peterburg, Iz-vo Politeh. un-ta, 2007. – 800p. (in Russian)
26. Lindner B., Nicola E.M. Critical Asymmetry for Giant Diffusion of Active Brownian Particles // Phys. Rev. Let. – 2008. – Vol. 101. – P. 190603.
27. van den Broeck C. Taylor dispersion revisited // Physica. – 1990. – Vol. A168. – P. 677-696.
28. Hänggi P., Talkner P., Borkovec M. Reaction-rate theory: fifty years after Kramers // Rev. Mod. Phys. – 1990. – Vol. 62. – P. 251–341.
Published
2017-05-13
Cited
How to Cite
Marchenko, I. G., Marchenko, I. I., & Tkachenko, V. I. (2017). TEMPERATURE - ABNORMAL DIFFUSIVITY IN TILTED SPATIALLY PERIODIC POTENTIALS. East European Journal of Physics, 4(1), 47-55. https://doi.org/10.26565/2312-4334-2017-1-03
Section
Original Papers
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