Anomalous Growth of the Diffusion in Space-Periodic Systems with a Low Energy Dissipation

  • Ivan Marchenko V.N. Karazin Kharkiv National University, Kharkiv, Ukraine; National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
  • Igor Marchenko NTU "Kharkov Polytechnic Institute”, Kharkiv, Ukraine
Keywords: diffusion, computer simulation, crystals, Langevin equation


Computer simulation methods were used to investigate the particle diffusion in the periodic spatial potential under constant force exposure. The paper shows that, unlike a superdamped case, in the systems with weak energy dissipation a new critical force value arises due to the appearance of a fork-like bifurcation point. About this point an exponential growth of the diffusion coefficient with temperature decreasing is observed. It is noted that the time of transition to the steady-state distribution tends to infinity while the temperature tends to zero.


Download data is not yet available.


Hänggi P., Marchesoni F. Artificial Brownian motors: Controlling transport on the nanoscale // Rev. Mod. Phys.- 2009.- Vol. 81.- P. 337-442.

Risken H. The Fokker-Planck equation and methods of solution and applications. - Springer, 1989.- 485p.

Machura L., Kostur M., Talkner P., et. al. Brownian motors: Current fluctuations and rectification efficiency // Phys. Rev.- 2004.- Vol. E70.- P. 061105 (8 pp.).

Reimann P., Van den Broeck C., Linke H., Hänggi P., Rubi J.M., Perez-Madrid A. Diffusion in tilted periodic potentials: Enhancement, universality, and scaling // Phys. Rev.- 2002.- Vol. E 65.- P. 031104 (16 pp.).

Coffey W.T. Kalmykov Yu.P., Waldron J.T. The Langevin equation. - Singapore: World Scientific publishing, 2004.- 678 p.

Sancho J.M., Lacasta A.M. The rich phenomenology of Brownian particles in nonlinear potential landscapes // Eur. Phys. J. Special Topics. - 2010.- Vol.187.- P. 49–62.

Lacasta A.M., Sancho J.M., Romero A.H., Sokolov I.M., Lindenberg K. From subdiffusion to superdiffusion of particles on solid surfaces // Phys. Rev. - 2004. - Vol. E70. - P. 051104 (10 pp.).

Marchenko I.G., Marchenko I.I. Anomalous Temperature Dependence of Diffusion in Crystals in Time-Periodic External Fields // JETP Letters.- 2012.- Vol. 95, №3. - P. 137–142.

Verlet L. Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules // Phys. Rev. - 1967.- Vol. 159.- P. 98 – 103.

Кузнецов Д.Ф. Стохастические дифференциальные уравнения: теория и практика численного решения.- Санкт-Петербург: Политехнический университет, 2007.- 769 с.

Lindenberg K., Lacasta A.M., Sancho J.M., Romero A.H. Transport and diffusion on crystalline surfaces under external forces // New Journal of Physics. - 2005.- Vol. 7.- P. 29 (19 pp.).

Reimann P., Van den Broeck C., Linke H., Hänggi P., Rubi J.M., Pérez-Madrid A. Giant Acceleration of Free Diffusion by Use of Tilted Periodic Potentials // Phys. Rev. Lett.- 2001.- Vol. 87.- P. 010602 (4 pp.).

Strogatz S. H. Nonlinear Dynamics And Chaos. - Massachusetts: Perseus Books Publishing L.L.S., 1994.- 498 p.

0 article
How to Cite
Marchenko, I., & Marchenko, I. (2012). Anomalous Growth of the Diffusion in Space-Periodic Systems with a Low Energy Dissipation. East European Journal of Physics, (1025(4), 62-68. Retrieved from