Diffusive description of lattice gas models

T. Fiig, H.J. Jensen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We have investigated a lattice gas model consisting of repulsive particles following deterministic dynamics. Two versions of the model are studied. In one case we consider a Finite open system in which particles can leave and enter the lattice over the edge. In the other case we use periodic boundary conditions. In both cases the density fluctuations exhibit a 1/f power spectrum. The individual particles behave asymptotically like ordinary random walkers. The collective behavior of these particles shows that due to the deterministic dynamics the particles behave as if they are correlated in time. We have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. We discuss the appropriate Langevin-like diffusion equation which can reproduce our numerical findings. Our conclusion is that the deterministic lattice gases are described by a diffusion equation without any bulk noise. The open lattice gas exhibits a crossover behavior as the probability for introducing particles at the edge of the system becomes small. The power spectrum changes from a 1/f to a 1/f2 spectrum. The diffusive description, proven to be valid for a moderate boundary drive, fails altogether when the drive goes to zero.
    Original languageEnglish
    JournalJournal of Statistical Physics
    Volume71
    Issue number3-4
    Pages (from-to)653-682
    ISSN0022-4715
    DOIs
    Publication statusPublished - May 1993

    Keywords

    • DIFFUSION EQUATION
    • POWER SPECTRA
    • LATTICE GAS
    • EXACT SOLUTIONS
    • CORRELATION FUNCTIONS
    • LIFETIME DISTRIBUTION
    • SINGLE PARTICLE PROPERTIES
    • COLLECTIVE PROPERTIES
    • DYNAMIC CROSSOVER

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