Exclusion process for particles of arbitrary extension: hydrodynamic limit and algebraic properties

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called l-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length l. Stationary and dynamical properties of the l-ASEP with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many-body system. In particular, the hydrodynamic equation for the local density evolution and the time-dependent diffusion constant of a tracer particle are calculated. As a fundamental algebraic property of the symmetric exclusion process the SU(2) symmetry is generalized to the case of extended particles.

[1]  A. Pipkin,et al.  Kinetics of biopolymerization on nucleic acid templates , 1968, Biopolymers.

[2]  Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics , 2003, cond-mat/0305340.

[3]  Wall-Induced Density Profiles and Density Correlations in Confined Takahashi Lattice Gases , 1999, cond-mat/9911081.

[4]  Exact solution of the asymmetric exclusion model with particles of arbitrary size. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  J. H. Gibbs,et al.  Concerning the kinetics of polypeptide synthesis on polyribosomes , 1969 .

[6]  T. Liggett.  Interacting Particle Systems , 1985 .

[7]  Anatoly B. Kolomeisky,et al.  Local inhomogeneity in asymmetric simple exclusion processes with extended objects , 2004 .

[8]  Schütz,et al.  Non-Abelian symmetries of stochastic processes: Derivation of correlation functions for random-vertex models and disordered-interacting-particle systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Anderson A Ferreira,et al.  Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  R. Arratia.  The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$ , 1983 .

[11]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

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

[13]  R. Kutner,et al.  Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice , 1983 .

[14]  S. Alexander,et al.  Diffusion of labeled particles on one-dimensional chains , 1978 .

[15]  M. R. Evans.  Phase transitions in one-dimensional nonequilibrium systems , 2000 .

[16]  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.

[17]  C. Landim,et al.  Scaling Limits of Interacting Particle Systems , 1998 .

[18]  M. Wadati,et al.  Exact results for one-dimensional totally asymmetric diffusion models , 1998 .