Exclusion Processes with Avalanches

Abstract

In an exclusion process with avalanches, when a particle hops to a neighboring empty site which is adjacent to an island the particle on the other end of the island immediately hops and if it joins another island this triggers another hop. There are no restrictions on the length of islands and the duration of the avalanche. This process is well-defined in the low-density region, ρ<1/2. We describe the nature of steady states (on a ring) and determine all correlation functions. For the asymmetric version of the process, we compute the steady state current, and we describe shock and rarefaction waves which arise in the evolution of the step-function initial profile. For the symmetric version, we determine the diffusion coefficient and examine the evolution of a tagged particle.

9 pages, 3 figures; v2: minor clarifications, references added

References in corpus (9)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Glassy dynamics of kinetically constrained models
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models
• Facilitated Asymmetric Exclusion
• Asymmetric exclusion processes with constrained dynamics
• Entrainment and unit velocity: Surprises in an accelerated exclusion process
• Dynamic Singularities in Cooperative Exclusion
• Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases