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

Abstract

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length $\ell$. Stationary and dynamical properties of the $\ell$-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 (SEP) the SU(2)-symmetry is generalized to the case of extended particles.

References in corpus (4)

• The totally asymmetric exclusion process with extended objects, a model for protein synthesis
• Local Inhomogeneity in Asymmetric Simple Exclusion Processes with Extended Objects
• Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes
• Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics

Cited by in corpus (30)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Inhomogeneous exclusion processes with extended objects: The effect of defect locations
• Interacting RNA polymerase motors on DNA track: effects of traffic congestion and intrinsic noise on RNA synthesis
• Traffic of interacting ribosomes on mRNA during protein synthesis: effects of chemo-mechanics of individual ribosomes
• Traffic of interacting ribosomes: effects of single-machine mechano-chemistry on protein synthesis
• The key parameters that govern translation efficiency
• Effects of multiple occupancy and inter-particle interactions on selective transport through narrow channels: theory versus experiment
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
• Driven lattice gas of dimers coupled to a bulk reservoir
• Fluctuations in protein synthesis from a single RNA template: stochastic kinetics of ribosomes
• Single-file transport in periodic potentials: The Brownian asymmetric exclusion process
• Particle Ordering in Zero Range Process : Exact spatial correlations of the corresponding exclusion models
• Random walk models in the life sciences: including births, deaths and local interactions
• Diffusion of tagged particles in a crowded medium
• Duality relations in single-file diffusion
• Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models
• Directed diffusion of reconstituting dimers
• Driven k-mers: Correlations in space and time
• RNA polymerase motors: dwell time distribution, velocity and dynamical phases
• Brownian walkers within subdiffusing territorial boundaries
• Collective transport of weakly interacting molecular motors with Langmuir kinetics
• Persistent random walk with exclusion
• Exactly solvable interacting vertex models
• Gradient structure and transport coefficients for strong particles
• Phase separation transition of reconstituting k-mers in one dimension
• A Multispecies Exclusion Process with Fusion and Fission of Rods: a model inspired by Intraflagellar Transport
• Phase coexistence and spatial correlations in reconstituting k-mer models
• Simulations of driven and reconstituting lattice gases
• Resource Letter: Bio-molecular Nano-machines: where Physics, Chemistry, Biology and Technology meet
• A deterministic model for non-monotone relationship between translation of upstream and downstream open reading frames