Lattice gases with a point source

Abstract

We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion process and random walkers. The interplay between the injection events and the positions of the particles already present implies an effective collective interaction even for the ostensibly non-interacting random walkers. We determine the average total number of particles entering into the initially empty system. We also compute the average total number of distinct sites visited by all particles, and discuss the shape of the visited domain and the statistics of visits.

References in corpus (17)

• 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
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Does a Single Zealot Affect an Infinite Group of Voters ?
• Exact Results for Kinetics of Catalytic Reactions
• Precursor films in wetting phenomena
• Universal cumulants of the current in diffusive systems on a ring
• Observation of a Narrow Meson Decaying to Ds pi0 gamma at a Mass of 2.458 GeV/c^2
• Exact distributions of the number of distinct and common sites visited by N independent random walkers
• Molecular Spiders with Memory
• Superdiffusive transport by multivalent molecular walkers moving under load
• Exact time-dependent correlation functions for the symmetric exclusion process with open boundary
• Number of distinct sites visited by N random walkers on a Euclidean lattice
• Number of Common Sites Visited by N Random Walkers
• Symmetric Exclusion Process with a Localized Source
• First Passage Properties of Molecular Spiders
• Universal fluctuations in the support of the random walk

Cited by in corpus (5)

• Free Fermions with a Localized Source
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Random walk through a fertile site