Noise, Diffusion, and Hyperuniformity

Abstract

We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry -when two particles interact, we give them stochastic kicks which conserve center of mass. We find that the density fluctuations in the active phase decay in the fastest manner possible for a disordered isotropic system, and we present arguments that the large scale fluctuations are determined by a competition between a noise term which generates fluctuations, and a deterministic term which reduces them. Our results may be relevant to shear experiments and may further the understanding of hyperuniformity which occurs at the critical point.

Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated dynamics

“…Moreover, we measure an exponent γ=2=d+1 corresponding to the fastest decay possible [18,20,22] (see figure 5). This is in agreement with recent studies [16] as the conservation laws (conservation of particles and conservation of center of mass) introduced in our model have been shown to lead in other models to hyperuniform behavior at long times.…”

“…The dynamics of this system is entirely controlled by the reaction kinetics governing the active repulsion between particles; in turn, our model exhibits subdiffusive behavior and aging. Finally, in its nonequilibrium steady state, this model displays hyperuniformity, which we also predict quantitatively using our macroscale stochastic differential equation ; this allows to reinterpret hyperuniformity in this system as originating from correlations in particles displacements induced by conservation of the center of mass, in agreement with [16].…”

“…This is in contrast with classical equilibrium models in which fluctuations are enhanced at the critical point (γ<d) [18]. Further, it was found in [16] that enforcing conservation of the particles center of mass during pairwise interactions in models of the Manna class, while preserving the transition to an absorbing state, leads to hyperuniformity in the active phase, even far from the critical point. Interestingly, the density fluctuations were shown to scale with exponent γ=d+1, which can be shown to be the largest possible exponent value [22].…”

“…In what follows, we will only study the resulting dynamics at high density, deep in the active phase away from the critical density where N x ?1 in steady state. As defined here, while our model is similar to the socalled COMCon model introduced in [16], it differs in the definition of the kinetic rules, which has striking consequences for the dynamics. In particular, we show in what follows that the dynamics of our system is governed by a nonlinear diffusion equation of porous medium type leading to anomalous spreading dynamics.…”

“…In dense regions (typically defined as more than 2 particles in a given neighborhood), particles are active and follow a prescribed dynamics (typically perform jumps); otherwise particles are said to be passive and remain at rest. Several microscopic models in this class have been proposed, including the Manna model, the random organization (RandOrg) model or the conserved lattice gas model and their generalizations; these are either on or off lattice, and involve different choices of kinetic rules [5,7,10,[14][15][16][17]. Recently, a renewed interest in this class of models was triggered by [15,16], where it was found that the fluctuations in density in models belonging to the Manna class scale differently than usual random systems.…”