Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states

  • T. Reichenbach
  • T. Franosch
  • E. Frey


We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system’s phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall’s delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.


05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 05.60.-k Transport processes 64.60.-i General studies of phase transitions 72.25.-b Spin polarized transport 


  1. 1.
    B. Schmittmann, R.K.P. Zia, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, Vol. 17 (Academic Press, London, 1995).Google Scholar
  2. 2.
    J. Krug, Phys. Rev. Lett. 67, 1882 (1991).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    I.T. Georgiev, B. Schmittmann, R.K.P. Zia, Phys. Rev. Lett. 94, 115701 (2005).CrossRefADSGoogle Scholar
  4. 4.
    C.T. MacDonald, J.H. Gibbs, A.C. Pipkin, Biopolymers 6, 1 (1968).CrossRefGoogle Scholar
  5. 5.
    N. Hirokawa, Science 279, 519 (1998).CrossRefADSGoogle Scholar
  6. 6.
    J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Press, Sunderland, Massachusetts, 2001).Google Scholar
  7. 7.
    R. Lipowsky, S. Klumpp, T.M. Nieuwenhuizen, Phys. Rev. Lett. 87, 108101 (2001).CrossRefADSGoogle Scholar
  8. 8.
    K. Kruse, K. Sekimoto, Phys. Rev. E 66, 031904 (2002).CrossRefADSGoogle Scholar
  9. 9.
    S. Klumpp, R. Lipowsky, J. Stat. Phys. 113, 233 (2003).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    G.A. Klein, K. Kruse, G. Cuniberti, F. Juelicher, Phys. Rev. Lett. 94, 108102 (2005).CrossRefADSGoogle Scholar
  11. 11.
    H. Hinsch, R. Kouyos, E. Frey, in Traffic and Granular Flow’ 05, edited by A. Schadschneider, T. Pöschel, R. Kühne, M. Schreckenberg, D.E. Wolf (Springer, 2006).Google Scholar
  12. 12.
    I. Žutić, J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76, 323 (2004).ADSCrossRefGoogle Scholar
  13. 13.
    T. Reichenbach, T. Franosch, E. Frey, Phys. Rev. Lett. 97, 050603 (2006).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    D. Helbing, Rev. Mod. Phys. 73, 1067 (2001).CrossRefADSGoogle Scholar
  15. 15.
    D. Chowdhury, L. Santen, A. Schadschneider, Phys. Rep. 329, 199 (2000).CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    B. Derrida, Phys. Rep. 301, 65 (1998).CrossRefMathSciNetGoogle Scholar
  17. 17.
    G. Schütz, in Phase Transitions and Critical Phenomena, edited by C. Domb, J. Lebowitz, Vol. 19 (Academic Press, San Diego, 2001) pp. 3–251.Google Scholar
  18. 18.
    B. Derrida, E. Domany, D. Mukamel, J. Stat. Phys. 69, 667 (1992).MATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    G. Schütz, E. Domany, J. Stat. Phys. 72, 277 (1993).MATHCrossRefADSGoogle Scholar
  20. 20.
    B. Derrida, M. Evans, V. Hakim, V. Paquier, J. Phys. A: Math. Gen. 26, 1493 (1993).MATHCrossRefADSGoogle Scholar
  21. 21.
    E.K.A. Kolomeisky, G. Schütz, J. Straley, J. Phys. A: Math. Gen. 31, 6911 (1998).MATHCrossRefADSGoogle Scholar
  22. 22.
    L. Santen, C. Appert, J. Stat. Phys. 106, 187 (2002).MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    T. Reichenbach, E. Frey, T. Franosch, New J. Phys. 9, 159 (2007) doi:10.1088/1367-2630/9/6/159.CrossRefADSGoogle Scholar
  24. 24.
    D. Mukamel, in Soft and Fragile Matter, edited by M. Cates, M. Evans (Institute of Physics Publishing, Bristol, 2000) pp. 237–258.Google Scholar
  25. 25.
    M.R. Evans, R. Juhász, L. Santen, Phys. Rev. E 68, 026117 (2003).CrossRefADSGoogle Scholar
  26. 26.
    R. Juhász, L. Santen, J. Phys. A: Math. Gen. 37, 3933 (2004).CrossRefADSGoogle Scholar
  27. 27.
    A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. Lett. 90, 086601 (2003).CrossRefADSGoogle Scholar
  28. 28.
    A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. E 70, 046101 (2004).CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    V. Popkov, A. Rákos, R.D. Willmann, A.B. Kolomeisky, G.M. Schütz, Phys. Rev. E 67, 066117 (2003).CrossRefADSGoogle Scholar
  30. 30.
    B. Schmittmann, J. Krometis, R.K.P. Zia, Europhys. Lett. 70, 299 (2005).CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    E. Pronina, A.B. Kolomeisky, J. Phys. A: Math. Gen. 37, 9907 (2004).MATHCrossRefADSMathSciNetGoogle Scholar
  32. 32.
    E. Pronina, A.B. Kolomeisky, Physica A 372, 12 (2006).CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    D.T. Gillespie, J. Comput. Phys. 22, 403 (1976).CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    D.T. Gillespie, J. Phys. Chem. 81, 2340 (1977).CrossRefGoogle Scholar
  35. 35.
    P. Pierobon, A. Parmeggiani, F. von Oppen, E. Frey, Phys. Rev. E 72, 036123 (2005).CrossRefADSGoogle Scholar
  36. 36.
    U. Täuber, lecture note,
  37. 37.
    N. van Kampen, Stochastic Processes in Physics and Chemistry, 1st edition (North Holland Publishing Company, 1981).Google Scholar
  38. 38.
    R. Juhász, Phys. Rev. E 76, 021117 (2007).CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    A. Basu, D. Chowdhury, Phys. Rev. E 75, 021902 (2007).CrossRefADSGoogle Scholar
  40. 40.
    D. Chowdhury, A. Garai, J.S. Wang, Traffic of singleheaded motor proteins KIF1A: effects of lane changing (2007)

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© Springer 2008

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of PhysicsLudwig-Maximilians-Universität MünchenMünchenGermany

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