Advertisement

Energy-dependent diffusion in a soft periodic Lorentz gas

  • S. Gil-GallegosEmail author
  • R. Klages
  • J. Solanpää
  • E. Räsänen
Regular Article
  • 10 Downloads
Part of the following topical collections:
  1. Microscopic Dynamics, Chaos and Transport in Nonequilibrium Processes

Abstract

The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became relevant as a model for electronic transport in low-dimensional nanosystems such as molecular graphene. However, to more realistically mimic such dynamics, the hard Lorentz gas scatterers should be replaced by soft potentials. Here we study diffusion in a soft Lorentz gas with Fermi potentials under variation of the total energy of the moving particle. Our goal is to understand the diffusion coefficient as a function of the energy. In our numerical simulations we identify three different dynamical regimes: (i) the onset of diffusion at small energies; (ii) a transition where for the first time a particle reaches the top of the potential, characterized by the diffusion coefficient abruptly dropping to zero; and (iii) diffusion at high energies, where the diffusion coefficient increases according to a power law in the energy. All these different regimes are understood analytically in terms of simple random walk approximations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.R. Dorfman, An introduction to chaos in nonequilibrium statistical mechanics (Cambridge University Press, Cambridge, 1999) Google Scholar
  2. 2.
    P. Gaspard, Chaos, scattering, and statistical mechanics (Cambridge University Press, Cambridge, 1998) Google Scholar
  3. 3.
    R. Klages, Microscopic chaos, fractals and transport in nonequilibrium statistical mechanics (World Scientific, Singapore, 2007) Google Scholar
  4. 4.
    R. Klages, J.R. Dorfman, Phys. Rev. Lett. 74, 387 (1995) ADSCrossRefGoogle Scholar
  5. 5.
    R. Klages, J.R. Dorfman, Phys. Rev. E 59, 5361 (1999) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    J. Groeneveld, R. Klages, J. Stat. Phys. 109, 821 (2002) ADSCrossRefGoogle Scholar
  7. 7.
    B.V. Chirikov, Phys. Rep. 52, 263 (1979) ADSCrossRefGoogle Scholar
  8. 8.
    A.B. Rechester, M.N. Rosenbluth, R.B. White, Phys. Rev. A 23, 2664 (1981) ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    J.A. Blackburn, N. Grønbech-Jensen, Phys. Rev. E 53, 3068 (1996) ADSCrossRefGoogle Scholar
  10. 10.
    F. Cagnetta, G. Gonnella, A. Mossa, S. Ruffo, Europhys. Lett. 111, 10002 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    A. Zacherl, T. Geisel, J. Nierwetberg, G. Radons, Phys. Lett. A 114, 317 (1986) ADSCrossRefGoogle Scholar
  12. 12.
    T. Manos, M. Robnik, Phys. Rev. E 89, 022905 (2014) ADSCrossRefGoogle Scholar
  13. 13.
    G. Zaslavsky, Phys. Rep. 371, 461 (2002) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    R. Klages, G. Radons, I.M. Sokolov, Anomalous transport: Foundations and Applications (Wiley-, Berlin, 2008) Google Scholar
  15. 15.
    D. Szasz, Hard-ball systems and the Lorentz gas (Springer, Berlin, 2000) Google Scholar
  16. 16.
    H.A. Lorentz, Acad. Amst. 7, 438 (1905) Google Scholar
  17. 17.
    L.A. Bunimovich, Ya. Sinai, Commun. Math. Phys. 78, 247 (1980) ADSCrossRefGoogle Scholar
  18. 18.
    P. Gaspard, G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990) ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    R. Klages, C. Dellago, J. Stat. Phys. 101, 145 (2000) ADSCrossRefGoogle Scholar
  20. 20.
    T. Harayama, R. Klages, P. Gaspard, Phys. Rev. E 66, 026211 (2002) ADSCrossRefGoogle Scholar
  21. 21.
    R. Klages, N. Korabel, J. Phys. A: Math. Gen. 35, 4823 (2002) ADSCrossRefGoogle Scholar
  22. 22.
    C. Dettmann, Commun. Theor. Phys. 62, 521 (2014) CrossRefGoogle Scholar
  23. 23.
    T. Harayama, P. Gaspard, Phys. Rev. E 64, 036215 (2001) ADSCrossRefGoogle Scholar
  24. 24.
    L. Mátyás, R. Klages, Physica D 187, 165 (2004) ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    P. Gaspard, R. Klages, Chaos 8, 409 (1998) ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    D. Turaev, V. Rom-Kedar, Nonlinear 11, 575 (1998) ADSCrossRefGoogle Scholar
  27. 27.
    V. Rom-Kedar, D. Turaev, Physica D 130, 187 (1999) ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    A.J. Lichtenberg, M.A. Lieberman, Regular and chaotic dynamics, 2nd edn. (Springer, New York, 1992) Google Scholar
  29. 29.
    A. Kaplan, N. Friedman, M. Andersen, N. Davidson, Physica D 187, 136145 (2004) CrossRefGoogle Scholar
  30. 30.
    A. Knauf, Commun. Math. Phys. 110, 89 (1987) ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    B. Nobbe, J. Stat. Phys. 78, 1591 (1995) ADSCrossRefGoogle Scholar
  32. 32.
    B. Aguer, S. De Bievre, J. Phys. A: Math. Theor. 43, 474001 (2010) ADSCrossRefGoogle Scholar
  33. 33.
    B. Bagchi, R. Zwanzig, M.C. Marchetti, Phys. Rev. A 31, 892 (1985) ADSCrossRefGoogle Scholar
  34. 34.
    T. Geisel, A. Zacherl, G. Radons. Phys. Rev. Lett. 59, 2503 (1987) ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    T. Geisel, A. Zacherl, G. Radons, Z. Phys. B 71, 117 (1988) ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    T. Geisel, J. Wagenhuber, P. Niebauer, G. Obermair, Phys. Rev. Lett. 64, 1581 (1990) ADSCrossRefGoogle Scholar
  37. 37.
    N.C. Panoiu, Chaos 10, 166 (2000) ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    J. Yang, H. Zhao, J. Stat. Mech.: Theor. Exp. 12, L12001 (2010) Google Scholar
  39. 39.
    P.R. Baldwin, Physica D 29, 321 (1988) ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    A. Lorke, J.P. Kotthaus, K. Ploog, Phys. Rev. B 44, 3447 (1991) ADSCrossRefGoogle Scholar
  41. 41.
    D. Weiss, M.L. Roukes, A. Menschig, P. Grambow, K. von Klitzing, G. Weimann, Phys. Rev. Lett. 66, 2790 (1991) ADSCrossRefGoogle Scholar
  42. 42.
    R. Fleischmann, T. Geisel, R. Ketzmerick, Phys. Rev. Lett. 68, 1367 (1992) ADSCrossRefGoogle Scholar
  43. 43.
    M. Fließer, G.J.O. Schmidt, H. Spohn, Phys. Rev. E 53, 5690 (1996) ADSCrossRefGoogle Scholar
  44. 44.
    M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L.N. Pfeiffer, K.W. West, Phys. Rev. B 79, 241406 (2009) ADSCrossRefGoogle Scholar
  45. 45.
    E. Räsänen, C.A. Rozzi, S. Pittalis, G. Vignale, Phys. Rev. Lett. 108, 246803 (2012) ADSCrossRefGoogle Scholar
  46. 46.
    K.K. Gomes, W. Mar, W. Ko, F. Guinea, H.C. Manoharan, Nature 483, 306 (2012) ADSCrossRefGoogle Scholar
  47. 47.
    S. Paavilainen, M. Ropo, J. Nieminen, J. Akola, E. Räsänen, Nano Lett. 16, 3519 (2016) ADSCrossRefGoogle Scholar
  48. 48.
    R. Klages, S. Gil-Gallegos, J. Solanpää, M. Sarvilahti, E. Räsänen, Phys. Rev. Lett. 122, 064102 (2019) ADSCrossRefGoogle Scholar
  49. 49.
    J. Machta, R. Zwanzig, Rev. Lett. 50, 1959 1983 Google Scholar
  50. 50.
    J. Solanpää, P. Luukko, E. Räsänen, Phys. Commun. 199, 133 (2016) ADSCrossRefGoogle Scholar
  51. 51.
    V. Rom-Kedar, G. Zaslavsky, Chaos 9, 697 (1999) ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    S. Gil-Gallegos, Doctoral dissertation, Queen Mary University of London, 2018 Google Scholar
  53. 53.
    M. Harsoula, G. Contopoulos, Phys. Rev. E 97, 022215 (2018) ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    G. Cristadoro, T. Gilbert, M. Lenci, D.P. Sanders, Europhys. Lett. 108, 50002 (2014) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Queen Mary University of London, School of Mathematical SciencesLondonUK
  2. 2.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany
  3. 3.Institute for Theoretical Physics, University of CologneCologneGermany
  4. 4.Computational Physics Laboratory, Tampere UniversityTampereFinland

Personalised recommendations