Bulk diffusion in a kinetically constrained lattice gas. (21st February 2018)

• Record Type: Journal Article
• Authors: Arita, Chikashi; Krapivsky, P L; Mallick, Kirone
• Is Part Of: Journal of physics. Volume 51:Number 12(2018)
• Publication Date: 2018-02-21
• Subjects: lattice gas -- kinetically constrained model -- diffusion coefficient -- variational method; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaac89
• Languages: English
• ISSNs: 1751-8113

Abstract

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