Instability transitions and ensemble equivalence in diffusive flow

Meesoon Ha
  • 1 Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea
  • 2 School of Physics, Korea Institute for Advanced Study, Seoul, 130-722, Korea

Abstract

We investigate the critical behavior of one-dimensional (1D) stochastic flow with competing nonlocal and local hopping events, in context of the totally asymmetric simple exclusion process (TASEP) with a defect site in a 1D closed chain. The defect site can effectively generate various boundary conditions, controlling the total number of particles in the system. Both open and periodic-like setups exhibit dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. In the stationary populated phase, strong clustering promoted by nonlocal skids drives such transitions and determines their scaling properties. By static and dynamic simulations, we locate such transition points, and discuss their nature and scaling properties. In the open TASEP variant, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current, while it is first order in the regime where the bulk controls the current. Since it is well known that such transitions are absent in the periodic TASEP variant, we compare our results in the open setup with those in the periodic-like setup, and discuss the issue of the ensemble equivalence. Finally, the same discussion is extended to the symmetric cases.

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  • [1] B. Schmittmann, R. K. P. Zia, In: C. Domb, J. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, Vol. 17. (Academic, London, 1995)

  • [2] M. Schrenckenberg, D. E. Wolf (Eds.), Traffic and Granular Flow’97 (Springer-Verlag, Singapore, 1998)

  • [3] P. Biswas, A. Majumdar, A. Mehta, J. K. Bhattacharjee, Phys. Rev. E 58, 1266 (1998) http://dx.doi.org/10.1103/PhysRevE.58.1266

  • [4] R. Lahir, S. Ramaswamy, Phys. Rev. Lett. 79, 1150 (1997) http://dx.doi.org/10.1103/PhysRevLett.79.1150

  • [5] M. A. Rutgers, J.-Z. Xue, E. Herbolzheimer, W. B. Russel, P.M. Chaikin, Phys. Rev. E 51, 4674 (1995) http://dx.doi.org/10.1103/PhysRevE.51.4674

  • [6] S. E. Paulin, B. J. Ackerson, Phys. Rev. Lett 64, 2663 (1990) http://dx.doi.org/10.1103/PhysRevLett.64.2663

  • [7] M. E. Fisher, A.B. Kolomeisky, Physica A, 274, 241 (1999) http://dx.doi.org/10.1016/S0378-4371(99)00389-1

  • [8] T. Harms, R. Lipowsky, Phys. Rev. Lett. 79, 2895 (1997) http://dx.doi.org/10.1103/PhysRevLett.79.2895

  • [9] F. Jülicher, J. Prost, Phys. Rev. Lett. 78, 4510 (1997) http://dx.doi.org/10.1103/PhysRevLett.78.4510

  • [10] M. Ha, M. den Nijs, Phys. Rev. E 66, 036118 (2002) http://dx.doi.org/10.1103/PhysRevE.66.036118

  • [11] B. Derrida, M. R. Evans, V. Hakim, V. Pasquier, J. Phys. A 26, 1493 (1993) http://dx.doi.org/10.1088/0305-4470/26/7/011

  • [12] B. Derrida, E. Domany, D. Mukamel, J. Stat. Phys. 69, 667 (1992) http://dx.doi.org/10.1007/BF01050430

  • [13] B. Derrida, B. Doucot, P.-E. Rohche, J. Stat. Phys. 115, 17 (2004)

  • [14] B. Derrida, J. L. Lebowitz, E. R. Speer, J. Stat. Phys. 107, 599 (2002) http://dx.doi.org/10.1023/A:1014555927320

  • [15] F. Spitzer, Adv. Math. 5, 246 (1970) http://dx.doi.org/10.1016/0001-8708(70)90034-4

  • [16] O. J. O’Loan, M. R. Evans, M. E. Cates, Phys. Rev. E 58, 1404 (1998) http://dx.doi.org/10.1103/PhysRevE.58.1404

  • [17] M. R. Evans, Braz. J. Phys. 30, 43 (2000) http://dx.doi.org/10.1590/S0103-97332000000100005

  • [18] K. Jain, M. Barma, Phys. Rev. E 64, 016107 (2001) http://dx.doi.org/10.1103/PhysRevE.64.016107

  • [19] M. Ha, H. Park, M. den Nijs, J. Phys. A 32, L495 (1999) http://dx.doi.org/10.1088/0305-4470/32/47/101

  • [20] R. Rajesh, S. N. Majumdar, Phys. Rev. E 63, 036114 (2001) http://dx.doi.org/10.1103/PhysRevE.63.036114

  • [21] S. N. Majumdar, S. Krishnamurthy, M. Barma, J. Stat. Phys. 99, 1 (2000) http://dx.doi.org/10.1023/A:1018632005018

  • [22] S. N. Majumdar, S. Krishnamurthy, M. Barma, Phys. Rev. Lett. 81, 3691 (1998) http://dx.doi.org/10.1103/PhysRevLett.81.3691

  • [23] R. Rajesh, S. Krishnamurthy, Phys. Rev. E 66, 046132 (2002) http://dx.doi.org/10.1103/PhysRevE.66.046132

  • [24] M. Plischke, Z. Rácz, D. Liu, Phys. Rev. B 35, 3485 (1987) http://dx.doi.org/10.1103/PhysRevB.35.3485

  • [25] D. Dhar, Phase Transitions 9, 51 (1987) http://dx.doi.org/10.1080/01411598708241334

  • [26] L.-H. Gwa, H. Spohn, Phys. Rev. Lett. 68, 725 (1992) http://dx.doi.org/10.1103/PhysRevLett.68.725

  • [27] L.-H. Gwa, H. Spohn, Phys. Rev. A 46, 844 (1992) http://dx.doi.org/10.1103/PhysRevA.46.844

  • [28] P. Meakin, P. Ramanlal, L. M. Sander, R. C. Ball, Phys. Rev. A 34, 5091 (1986) http://dx.doi.org/10.1103/PhysRevA.34.5091

  • [29] H. Park, M. Ha, I.-M. Kim, Phys. Rev. E 51, 1047 (1995) http://dx.doi.org/10.1103/PhysRevE.51.1047

  • [30] B. Derrida, J. L. Lebowitz, E. R. Speer, H. Spohn, Phys. Rev. Lett. 67, 165 (1991) http://dx.doi.org/10.1103/PhysRevLett.67.165

  • [31] B. Derrida, J. L. Lebowitz, E. R. Speer, H. Spohn, J. Phys. A 24, 4805 (1991) http://dx.doi.org/10.1088/0305-4470/24/20/015

  • [32] M. Ha, H. Park, M. den Nijs, Phys. Rev. E 75, 061131 (2007) http://dx.doi.org/10.1103/PhysRevE.75.061131

  • [33] A. Nagar, M. Ha, H. Park, Phys. Rev. E 77, 061118 (2008) http://dx.doi.org/10.1103/PhysRevE.77.061118

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