Hydrodynamics in kinetically constrained lattice-gas models

Abstract

Kinetically constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We drive such models out of equilibrium by connecting them to two reservoirs of different densities, and we measure the response of the system to this perturbation. We find that under the proper coarse-graining, the behavior of these models may be expressed by a nonlinear diffusion equation, with a model- and density-dependent diffusion coefficient. We find a simple approximation for the diffusion coefficient, and we show that the relatively mild discrepancy between the approximation and our numerical results arises due to non-negligible correlations that appear as the system is driven out of equilibrium, even when the density gradient is infinitesimally small. Similar correlations appear when such kinetically constrained models are driven out of equilibrium by applying a uniform external force. We suggest that these correlations are the reason for the same discrepancy between the approximate diffusion coefficient and the numerical results for a broader group of models-nongradient lattice-gas models-for which kinetically constrained models are arguably the simplest example thereof.

Cooperative transport with selective kinetic constraints

“…For the sake of simplicity we use the normalised density profile ρ(x) defined as: Figure 3 shows the numerical results for ρ 0 = 0.3, ρ 1 = 0.6 and ρ 0 = 0.7, ρ 1 = 0.9 for a system of linear size L = 128 (the absence of finite-size effects has been checked with L = 64 and L = 256). In contrast with the boundary-driven KA model [10,15], we observe convex profiles for large values of reservoirs density, and concave ones when ρ 0 , ρ 1 are both smaller than ρ . The comparison with analytical predictions of the diffusion equation obtained in the NC approximation (full lines in Fig.…”

“…3) shows that discrepancies are rather mild, as also observed in Ref. [15] for the KA model. (The straight dotted line is the reference SSEP profile).…”

Correlations and transport in exclusion processes with general finite memory

“…After a relatively short transient time the mean density converges to a steady state. For a known diffusion coefficient, the steady state profile is given by [58] x…”

Casimir-like forces in cooperative exclusion processes

“…In this case the cooperative exclusion process). Although improved estimations can be obtained by using more refined expression of the diffusion coefficient with the systematic approaches developed in [24,25], we expect that corrections are rather mild. In particular, the prediction of the force sign and the location of the crossover between the attractive and repulsive regime should be quite accurate, as expected from numerical simulation of convexity-change profiles in the nonequilibrium steady state [30].…”

“…In this case the dynamical contribution to the Green-Kubo formula (represented by the spatial sum of the time integral of current-current correlation) vanishes and the bulk diffusion coefficient can be computed as a static average [22,23]. For non-gradient systems, such as those considered here, there are multi-site interactions that make this task very challenging (see, however [24,25] for some progress in this direction), and therefore, identifying a class of systems for which the sign of the force can be reversed…”