The Asymmetric Exclusion Process and Brownian Excursions

We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.

[1]  Fabian H.L. Essler,et al.  Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries , 1995 .

[2]  R. A. Blythe,et al.  Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra , 2000 .

[3]  Modeling, simulations, and analyses of protein synthesis: Driven lattice gas with extended objects , 2003 .

[4]  B. Derrida,et al.  Large Deviation Functional of the Weakly Asymmetric Exclusion Process , 2003 .

[5]  Tomohiro Sasamoto.  One-dimensional partially asymmetric simple exclusion process with open boundaries: Orthogonal polynomials approach , 2001 .

[6]  E. Domany,et al.  Phase transitions in an exactly soluble one-dimensional exclusion process , 1993, cond-mat/9303038.

[7]  Eytan Domany,et al.  An exact solution of a one-dimensional asymmetric exclusion model with open boundaries , 1992 .

[8]  K. Mallick,et al.  Shocks in the asymmetry exclusion model with an impurity , 1996 .

[9]  S. Sandow,et al.  Partially asymmetric exclusion process with open boundaries. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  H. Spohn.  Large Scale Dynamics of Interacting Particles , 1991 .

[11]  B. Derrida,et al.  Exact solution of a 1d asymmetric exclusion model using a matrix formulation , 1993 .

[12]  V. Popkov,et al.  Steady-state selection in driven diffusive systems with open boundaries , 1999, cond-mat/0002242.

[13]  Herbert Spohn,et al.  Long range correlations for stochastic lattice gases in a non-equilibrium steady state , 1983 .

[14]  B Derrida,et al.  Exact free energy functional for a driven diffusive open stationary nonequilibrium system. , 2002, Physical review letters.

[15]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[16]  T. D. Lee,et al.  Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .

[17]  Kelvin H. Lee,et al.  Totally asymmetric exclusion process with extended objects: a model for protein synthesis. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Krug,et al.  Boundary-induced phase transitions in driven diffusive systems. , 1991, Physical review letters.

[19]  Tom Chou,et al.  Totally asymmetric exclusion processes with particles of arbitrary size , 2003 .

[20]  Sven Sandow,et al.  Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process , 1997 .

[21]  C. Landim,et al.  Fluctuations in stationary nonequilibrium states of irreversible processes. , 2001, Physical review letters.

[22]  C. Landim,et al.  Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States , 2001, cond-mat/0108040.

[23]  E. R. Speer,et al.  Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process , 2002 .

[24]  Bernard Derrida,et al.  Exact correlation functions in an asymmetric exclusion model with open boundaries , 1993 .

[25]  B. Derrida,et al.  Free energy functional for nonequilibrium systems: an exactly solvable case. , 2001, Physical review letters.

[26]  Bernard Derrida,et al.  Exact diffusion constant for one-dimensional asymmetric exclusion models , 1993 .

[27]  Beate Schmittmann,et al.  Statistical mechanics of driven diffusive systems , 1995 .