Bulk diffusion in a kinetically constrained lattice gas

Chikashi Arita (1) , P. L. Krapivsky (2, 3) , Kirone Mallick (3)

1 Universität des Saarlandes [Saarbrücken]
2 Department of Physics [Boston]
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 in two dimensions, viz. to the Kob-Andersen model on the square lattice.

Mots clés: lattice gas; kinetically constrained model; diffusion coefficient; variational method

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Automates cellulaires et gaz sur réseau [nlin.CG]

Chikashi Arita, P. L. Krapivsky, Kirone Mallick. Bulk diffusion in a kinetically constrained lattice gas. Journal of Physics A: Mathematical and Theoretical, 2018, 51 (12), pp.125002. ⟨10.1088/1751-8121/aaac89⟩. ⟨cea-02923442⟩