Driven k-mers: Correlations in space and time

Abstract

Steady state properties of hard objects with exclusion interaction and a driven motion along a one-dimensional periodic lattice are investigated. The process is a generalization of the asymmetric simple exclusion process (ASEP) to particles of length k, and is called the k-ASEP. Here, we analyze both static and dynamic properties of the k-ASEP. Density correlations are found to display interesting features, such as pronounced oscillations in both space and time, as a consequence of the extended length of the particles. At long times, the density autocorrelation decays exponentially in time, except at a special k-dependent density when it decays as a power law. In the limit of large k at a finite density of occupied sites, the appropriately scaled system reduces to a nonequilibrium generalization of the Tonks gas describing the motion of hard rods along a continuous line. This allows us to obtain in a simple way the known two-particle distribution for the Tonks gas. For large but finite k, we also obtain the leading-order correction to the Tonks result.

11 pages, 9 figures. Version 2: restructuring with small changes in content, published version

References in corpus (5)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Inhomogeneous exclusion processes with extended objects: The effect of defect locations
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• Stretched exponential to power-law: crossover of relaxation in a kinetically constrained model
• Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions
• Roughening of $k$-mer growing interfaces in stationary regimes
• Particle hopping on a ladder: exact solution using multibalance