Abstract
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.
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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).
J. Krug, Phys. Rev. Lett. 67, 1882 (1991).
I.T. Georgiev, B. Schmittmann, R.K.P. Zia, Phys. Rev. Lett. 94, 115701 (2005).
C.T. MacDonald, J.H. Gibbs, A.C. Pipkin, Biopolymers 6, 1 (1968).
N. Hirokawa, Science 279, 519 (1998).
J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Press, Sunderland, Massachusetts, 2001).
R. Lipowsky, S. Klumpp, T.M. Nieuwenhuizen, Phys. Rev. Lett. 87, 108101 (2001).
K. Kruse, K. Sekimoto, Phys. Rev. E 66, 031904 (2002).
S. Klumpp, R. Lipowsky, J. Stat. Phys. 113, 233 (2003).
G.A. Klein, K. Kruse, G. Cuniberti, F. Juelicher, Phys. Rev. Lett. 94, 108102 (2005).
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).
I. Žutić, J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76, 323 (2004).
T. Reichenbach, T. Franosch, E. Frey, Phys. Rev. Lett. 97, 050603 (2006).
D. Helbing, Rev. Mod. Phys. 73, 1067 (2001).
D. Chowdhury, L. Santen, A. Schadschneider, Phys. Rep. 329, 199 (2000).
B. Derrida, Phys. Rep. 301, 65 (1998).
G. Schütz, in Phase Transitions and Critical Phenomena, edited by C. Domb, J. Lebowitz, Vol. 19 (Academic Press, San Diego, 2001) pp. 3–251.
B. Derrida, E. Domany, D. Mukamel, J. Stat. Phys. 69, 667 (1992).
G. Schütz, E. Domany, J. Stat. Phys. 72, 277 (1993).
B. Derrida, M. Evans, V. Hakim, V. Paquier, J. Phys. A: Math. Gen. 26, 1493 (1993).
E.K.A. Kolomeisky, G. Schütz, J. Straley, J. Phys. A: Math. Gen. 31, 6911 (1998).
L. Santen, C. Appert, J. Stat. Phys. 106, 187 (2002).
T. Reichenbach, E. Frey, T. Franosch, New J. Phys. 9, 159 (2007) doi:10.1088/1367-2630/9/6/159.
D. Mukamel, in Soft and Fragile Matter, edited by M. Cates, M. Evans (Institute of Physics Publishing, Bristol, 2000) pp. 237–258.
M.R. Evans, R. Juhász, L. Santen, Phys. Rev. E 68, 026117 (2003).
R. Juhász, L. Santen, J. Phys. A: Math. Gen. 37, 3933 (2004).
A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. Lett. 90, 086601 (2003).
A. Parmeggiani, T. Franosch, E. Frey, Phys. Rev. E 70, 046101 (2004).
V. Popkov, A. Rákos, R.D. Willmann, A.B. Kolomeisky, G.M. Schütz, Phys. Rev. E 67, 066117 (2003).
B. Schmittmann, J. Krometis, R.K.P. Zia, Europhys. Lett. 70, 299 (2005).
E. Pronina, A.B. Kolomeisky, J. Phys. A: Math. Gen. 37, 9907 (2004).
E. Pronina, A.B. Kolomeisky, Physica A 372, 12 (2006).
D.T. Gillespie, J. Comput. Phys. 22, 403 (1976).
D.T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
P. Pierobon, A. Parmeggiani, F. von Oppen, E. Frey, Phys. Rev. E 72, 036123 (2005).
U. Täuber, lecture note, http://www.phys.vt.edu/~tauber/chapI2.ps
N. van Kampen, Stochastic Processes in Physics and Chemistry, 1st edition (North Holland Publishing Company, 1981).
R. Juhász, Phys. Rev. E 76, 021117 (2007).
A. Basu, D. Chowdhury, Phys. Rev. E 75, 021902 (2007).
D. Chowdhury, A. Garai, J.S. Wang, Traffic of singleheaded motor proteins KIF1A: effects of lane changing (2007) http://www.citebase.org/abstract?id=oai: arXiv.org:0712.4304.
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Reichenbach, T., Franosch, T. & Frey, E. Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states. Eur. Phys. J. E 27, 47–56 (2008). https://doi.org/10.1140/epje/i2008-10350-3
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DOI: https://doi.org/10.1140/epje/i2008-10350-3