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Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring
Phys. Rev. E 93, 042113 – Published 14 April, 2016
DOI: https://doi.org/10.1103/PhysRevE.93.042113
Abstract
We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no particle in the system. The exact stationary state of this model has been known for the totally asymmetric case. We propose a basis transformation which simplifies the proof of the stationarity of this state and enables the generalization to the partially asymmetric case. Moreover, we construct low-energy excitations and obtain the exact relaxation time.
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References (21)
- C. T. MacDonald, J. H. Gibbs, and A. C. Pipkin, Biopolymers 6, 1 (1968).
- B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, J. Phys. A: Math. Gen. 26, 1493 (1993).
- A. B. Kolomeisky, G. M. Schütz, E. B. Kolomeisky, and J. P. Straley, J. Phys. A: Math. Gen. 31, 6911 (1998).
- T. Sasamoto, J. Phys. A: Math. Gen. 32, 7109 (1999).
- A. Schadschneider, Phys. A (Amsterdam, Neth.) 285, 101 (2000).
- A. Schadschneider, D. Chowdhury, and K. Nishinari, Stochastic Transport in Complex Systems: From Molecules to Vehicles (Elsevier Science, New York, 2010).
- R. A. Blythe and M. R. Evans, J. Phys. A: Math. Theor. 40, R333 (2007).
- O. Golinelli and K. Mallick, J. Phys. A: Math. Gen. 37, 3321 (2004); 38, 1419 (2005); 39, 12679 (2006).
- R. A. Blythe, M. R. Evans, F. Colaiori, and F. H. L. Essler, J. Phys. A 33, 2313 (2000).
- J. Krug, Phys. Rev. Lett. 67, 1882 (1991).
- D. Dhar, Phase Trans. 9, 51 (1987).
- L.-H. Gwa and H. Spohn, Phys. Rev. A 46, 844 (1992).
- D. Kim, Phys. Rev. E 52, 3512 (1995).
- J. de Gier and F. H. L. Essler, Phys. Rev. Lett. 95, 240601 (2005); J. Stat. Mech. (2006) P12011; Phys. Rev. Lett. 107, 010602 (2011).
- C. Arita, A. Kuniba, K. Sakai, and T. Sawabe, J. Phys. A 42, 345002 (2009).
- K. Motegi, K. Sakai, and J. Sato, J. Phys. A: Math. Theor. 45, 465004 (2012); Phys. Rev. E 85, 042105 (2012).
- A. Parmeggiani, T. Franosch, and E. Frey, Phys. Rev. Lett. 90, 086601 (2003); Phys. Rev. E 70, 046101 (2004).
- M. R. Evans, R. Juhász, and L. Santen, Phys. Rev. E 68, 026117 (2003).
- T. Mitsudo and H. Hayakawa, J. Phys. A: Math. Gen. 39, 15073 (2006).
- T. Ezaki and K. Nishinari, J. Phys. A: Math. Theor. 45, 185002 (2012).
- R. H. Fowler, Statistical Mechanics (Cambridge University Press, Cambridge, UK, 1936).