- Access by Xinjiang University
Current fluctuations in the weakly asymmetric exclusion process with open boundaries
Phys. Rev. E 86, 051114 – Published 15 November, 2012
DOI: https://doi.org/10.1103/PhysRevE.86.051114
Abstract
The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. We apply this principle to the weakly asymmetric exclusion process (WASEP). We also calculate the cumulant generating function of the current and the density profiles associated with rare currents in finite systems using a numerical approach based on the density matrix renormalization group. Comparison of the two approaches allows us to verify the validity of the additivity principle and to get insight into the finite size scaling theory for current fluctuations in the WASEP. No evidence for a dynamical phase transition is found.
Article Text
References (32)
- G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995).
- J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
- T. Bodineau and B. Derrida, Phys. Rev. Lett. 92, 180601 (2004).
- B. Derrida, J. Stat. Mech.: Theor. Exp. (2007) P07023.
- P. I. Hurtado and P. L. Garrido, Phys. Rev. Lett. 102, 250601 (2009); Phys. Rev. E 81, 041102 (2010).
- K. Saito and A. Dhar, Phys. Rev. Lett. 107, 250601 (2011).
- L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Phys. Rev. Lett. 87, 040601 (2001).
- L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Phys. Rev. Lett. 94, 030601 (2005).
- T. Bodineau and B. Derrida, Phys. Rev. E 72, 066110 (2005).
- P. I. Hurtado and P. L. Garrido, Phys. Rev. Lett. 107, 180601 (2011).
- G. Jona-Lasinio, Prog. Theor. Phys. 124, 731 (2010).
- T. Bodineau and B. Derrida, J. Stat. Phys. 123, 277 (2006).
- S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
- M. Gorissen, J. Hooyberghs, and C. Vanderzande, Phys. Rev. E 79, 020101(R) (2009); M. Gorissen and C. Vanderzande, J. Phys. A 44, 115005 (2011).
- A. Imparato, V. Lecomte, and F. van Wijland, Phys. Rev. E 80, 011131 (2009).
- H. Spohn, Large Scale Dynamics of Interacting Particles (Springer, Berlin, 1991).
- H. Touchette, Phys. Rep. 478, 1 (2009).
- C. Giardinà, J. Kurchan, and L. Peliti, Phys. Rev. Lett. 96, 120603 (2006).
- V. Lecomte and J. Tailleur, J. Stat. Mech.: Theory Exp. (2007) P03004.
- M. Gorissen, Ph.D. thesis, Hasselt University, Diepenbeek, 2011.
- J. P. Garrahan, R. L. Jack, V. Lecomte, E. Pitard, K. van Duijvendijk, and F. van Wijland, J. Phys. A 42, 075007 (2009).
- U. Schollwöck, Ann. Phys. 326, 96 (2011).
- Y. Hieida, J. Phys. Soc. Jpn. 67, 369 (1998).
- E. Carlon, M. Henkel, and U. Schollwöck, Eur. Phys. J. B 12, 99 (1999).
- B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, J. Phys. A 26, 1493 (1993).
- J. de Gier and F. H. L. Essler, J. Stat. Mech. (2006) P12011.
- P. I. Hurtado, C. Pérez-Espigares, J. J. del Pozo, and P. L. Garrido, Proc. Natl. Acad. Sci. USA 108, 7704 (2011).
- B. Derrida (private communication).
- B. Derrida, B. Douçot, and P.-E. Roche, J. Stat. Phys. 115, 717 (2004).
- In the present paper we counted the number of particles flowing through one bond of the lattice. In Ref. [14] the current was counted through all bonds. In that case the argument of the scaling function in Eq. (21) becomes .
- B. Derrida and J. L. Lebowitz, Phys. Rev. Lett. 80, 209 (1998); B. Derrida and C. Appert, J. Stat. Phys. 94, 1 (1999).
- M. Gorissen, A. Lazarescu, K. Mallick, and C. Vanderzande, Phys. Rev. Lett. 109, 170601 (2012).