Generalized Exclusion Processes: Transport Coefficients

Abstract

A class of generalized exclusion processes parametrized by the maximal occupancy, $k\ge 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\le k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.

v1: 9 pages, 6 figures. v2: + 2 references. v3: 10 pages, 7 figures, published version

References in corpus (20)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Macroscopic fluctuation theory for stationary non equilibrium states
• Large Deviations in Single File Diffusion
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Stationary distributions of multi-type totally asymmetric exclusion processes
• Cumulants and large deviations of the current through non-equilibrium steady states
• Matrix representation of the stationary measure for the multispecies TASEP
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Exact solution of an exclusion process with three classes of particles and vacancies
• Shocks in the asymmetric exclusion process with internal degree of freedom
• Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion
• Diffusion of interacting particles in discrete geometries
• Dynamics of Repulsion Processes
• TASEP on a ring with internal degrees of freedom
• Zero-range process with finite compartments: Gentile's statistics and glassiness
• Exclusion Processes with Avalanches

Cited by in corpus (27)

• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• Variational calculation of transport coefficients in diffusive lattice gases
• Bulk diffusion in a kinetically constrained lattice gas
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• Motion of active tracer in a lattice gas with cross-shaped particles
• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Hydrodynamics in kinetically-constrained lattice-gas models
• Mean field approach for diffusion of interacting particles
• Transport in exclusion processes with one-step memory: density dependence and optimal acceleration
• Exact hydrodynamics and onset of phase separation for an active exclusion process
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Nonlocal birth-death competitive dynamics with volume exclusion
• Transport and fluctuations in mass aggregation processes: mobility driven clustering
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Symmetric exclusion processes on a ring with moving defects
• Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores
• Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores
• Reply to "Comment on Generalized Exclusion Processes: Transport Coefficients"
• Correlations and transport in exclusion processes with general finite memory
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• Jamming of active particles in narrow pores: Implications for ratchet effect and diffusion coefficient
• Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries
• Density-dependent transport coefficients in two-dimensional cellular aggregates
• On Interactions for Large Scale Interacting Systems
• Anomalous current fluctuations and mobility-driven clustering