Diffusion Temperature Dependence in Tilted Periodic Potentials Ranging from Underdamped Systems to Overdamped Systems

  • Ivan G. Marchenko National Science Center „Kharkov Institute of Physics and Technology”, Kharkov, Ukraine; V.N. Karazin Kharkov National University, Kharkov, Ukraine https://orcid.org/0000-0003-1341-4950
  • Igor I. Marchenko NTU “Kharkov Polytechnic Institute”, Kharkov, Ukraine https://orcid.org/0000-0002-3071-9169
  • Viktor Tkachenko National Science Center „Kharkov Institute of Physics and Technology”, Kharkov, Ukraine; V.N. Karazin Kharkov National University, Kharkov, Ukraine https://orcid.org/0000-0002-1108-5842
DOI: https://doi.org/10.26565/2312-4334-2018-4-07
Keywords: diffusion, computer simulation, periodic structures, Langevin equation, time-periodic fields

Abstract

Recently, both the experimental data and the data of theoretical research appeared stating that the diffusion coefficient shows nonmonotonic behavior with temperature. The motion of Brownian particles in the space periodic structures is an example of the systems with abnormal temperature dependence of the diffusion.  The aim of the work was to study the change in the temperature dependence of the diffusion coefficient with a change in friction, both in underdamp and overdamped systems. This scientific paper studies the diffusion of particles in tilted spatial-periodic potentials in a wide temperature range. It is shown that in both underdempted and overdamped systems, the diffusion coefficient reaches a maximum value for a certain value of an external force, the value of which depends on the value of the friction coefficient. However, in systems with low and high friction, the temperature dependence of the diffusion coefficient differs. It was established that the systems with a low friction level γ’ show temperature abnormal diffusion (TAD) at which the diffusion coefficient D is increased with a decrease in temperature. At the same time, the diffusion is enhanced at high γ values with the rise in temperature. This scientific paper studies the transition procedure from the exponential dependence of TAD to the ordinary power temperature dependence with an increase in γ’.  It was shown that the energy hump that separates “running” solutions and “localized” solutions is decreased with an increase in the friction coefficient and it vanishes at γ -> 0 . Simultaneously with a decrease in ε, the temperature interval of the TAD also narrows. It was established that the temperature-limited TAD domain appears in the region of intermediate values of the friction coefficient. In a specified force range the diffusion coefficient is first increased with a decrease in temperature and then it begins to decrease again. The diagrams of existence of such domains have been constructed. The results obtained opens up prospects for the creation of new technologies for managing diffusion processes. This is of great importance for the production of nanomaterials with a given structure, the creation of surface nanostructures, etc.

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References

A.N. Gan’shin, V.N. Grigor’ev, V.A. Maidanov, N.F. Omelaenko, A.A. Penzev, E.Ya. Rudavskii and A.S. Rybalko, Low Temperature Physics. 25, 259 (1999), doi: 10.1063/1.593738.

R. Salgado-Garcıa, Phys. Rev. E. 90, 032105 (2014).

J. Spiechowicz, P. Talkner, P. Hänggi and J. Luczka, New J. Phys. 18, 123029 (2016).

J. Spiechowicz, M. Kostur and J. Luczka, Chaos. 27, 023111 (2017).

D. Speer, R. Eichhorn and P. Reimann, Europhys. Lett. 97, 60004 (2012).

E. Heinsalu, T. Örd and R. Tammelo. Phys. Rev. E. 70, 041104 (2004).

J. Spiechowicz, J. Luczka, Phys. Rev. E. 91, 062104 (2015).

E.Heinsalu, R. Tammelo and T. Ord, Phys. Rev. E. 69, 021111 (2004).

D. Dan, A. M. Jayannavar, Phys. Rev. E. 66, 041106 (2002).

L. Angelani, G. Foffi, F. Sciortino and P. Tartaglia, J. Phys. Condens. Matter. 17, L113–L119 (2005).

B. Lindner, M. Kostur and L. Schimansky-Geier, Fluct. and Noise Let. 1, R25-R39 (2001).

C.K. Lee, J. Moix and J. Cao, Journ. Chem. Phys. 142, 164103 (2015).

M. Guo, H. Gelman and M. Gruebele, PLoS ONE. 9, e113040 (2014).

W.S. Tung, P.J. Griffin, J.S. Meth, et al., ACS Macro Lett. 5, 735-739 (2016).

V.B. Eltsov, A.P. Finne, R. Ha¨nninen, et al., Phys. Rev. Lett. 96, 215302 (2006).

Ch.K. Lee, J. Moix and J. Cao, Chem. Phys. 142, 164103 (2015).

S. Iubini, O. Boada, Y. Omar and F. Piazza, New J. Phys. 17, 113030 (2015).

H. Risken, The Fokker-Planck Equation and Methods of Solution and Applications (Springer, 1989), p. 472.

H. Risken, H.D. Vollmer, Phys. Lett. 69. A, 387-389 (1979).

H. Risken, H.D. Vollmer, Z. Physik B. 33, 297 (1979).

H. Risken, H.D. Vollmer, Z. Physik B. 37, 343-349 (1980).

H. Risken, H.D.Vollmer, Z. Physik B. 34, 313-322 (1979).

H. Risken, H.D.Vollmer, Z. Physik B. 35, 177-184 (1979).

H. Risken, H.D.Vollmer, Z. Physik B. 54 357-370 (1984).

G. Costantini, F. Marchesoni, Europhys. Lett. 48, 491-497 (1999).

M. Borromeo, G. Costantini and F. Marchesoni, Phys. Rev. Lett. 82, 2820–2823 (1999).

K. Lindenberg, J.M. Sancho, A.M. Lacasta and I.M. Sokolov, Phys. Rev. Lett. 98, 020602 (2007).

J. M.Sancho, A.M. Lacasta, K. Lindenberg, I.M. Sokolov and A.H. Romero, Phys. Rev. Lett. 92, 250601 (2004).

M. Khoury, J. P. Gleeson, J. M. Sancho, A. M. Lacasta and K. Lindenberg, Phys. Rev. E. 80, 021123 (2009).

K. Lindenberg, A.M. Lacasta, J.M. Sancho and A.H. Romero, New Jour. of Phys. 7, 29 (2005).

I.G. Marchenko, I.I. Marchenko, Europhys. Let. 100, 5005 (2012).

I.G. Marchenko, I.I. Marchenko and A.V. Zhiglo, Europ. Phys. Jour. B. 87 10 (2014).

I.G. Marchenko, I.I. Marchenko and V.I. Tkachenko, JETP Let. 106, 242–246 (2017).

I.G. Marchenko, I.I. Marchenko and A.V. Zhiglo, Phys. Rev. E. 97, 012121 (2018).

P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J.M. Rubi, and A. Pérez-Madrid, Phys. Rev. E. 65, 031104 (2002).

K. Lindenberg, J.M. Sancho, A.M. Lacasta and I.M. Sokolov, Phys. Rev. Lett. 98, 020602 (2007).

B. Lindner, I.M. Sokolov, Phys. Rev. E. 93, 042106 (2016).

I.G. Marchenko, I.I. Marchenko, JETP Let. 95, 137–142 (2012).

D.G. Alciatore and M.B. Histand, Introduction to Mechatronics and Measurement Systems (McGraw Hill, 2007), p. 553.

Published
2019-01-11
Cited
How to Cite
Marchenko, I. G., Marchenko, I. I., & Tkachenko, V. (2019). Diffusion Temperature Dependence in Tilted Periodic Potentials Ranging from Underdamped Systems to Overdamped Systems. East European Journal of Physics, (4), 58-68. https://doi.org/10.26565/2312-4334-2018-4-07
Issue
No. 4 (2018): East European Journal of Physics
Section
Original Papers

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