Bulk diffusion in a kinetically constrained lattice gas

Abstract

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas, viz. to the Kob-Andersen model on the square lattice.

29 pages, 12 figures. v2: minor changes

References in corpus (10)

• Glassy dynamics of kinetically constrained models
• Monte Carlo simulations of 2d hard core lattice gases
• Generalized Exclusion Processes: Transport Coefficients
• Variational calculation of transport coefficients in diffusive lattice gases
• Equation of state for hard square lattice gases
• Hydrodynamics in kinetically-constrained lattice-gas models
• Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems
• Exclusion Processes with Avalanches
• Thermal conductivity for stochastic energy exchange models
• Kinetically constrained lattice gases: tagged particle diffusion

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• Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores
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• Cooperative transport with selective kinetic constraints
• Tracer and current fluctuations in driven diffusive systems
• Kinetically constrained model for gravity-driven granular flow and clogging
• Casimir-like forces in cooperative exclusion processes
• Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system
• Four state deterministic cellular automaton rule emulating random diffusion
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Constraint relaxation leads to jamming
• Macroscopic fluctuation theory of interacting Brownian particles