Hyperuniformity of Critical Absorbing States

Abstract

The properties of the absorbing states of non-equilibrium models belonging to the conserved directed percolation universality class are studied. We find that at the critical point the absorbing states are hyperuniform, exhibiting anomolously small density fluctuations. The exponent characterizing the fluctuations is measured numerically, a scaling relation to other known exponents is suggested, and a new correlation length relating to this ordering is proposed. These results may have relevance to photonic band-gap materials.PACS numbers: 05.65.+b, 47.57.E-, 05.20.-y Dynamical systems with absorbing states [1][2][3] are intrinsically out of equilibrium, as they necessarily violate detailed balance -by definition, once they arrive at an absorbing state, they can never get out. There are many such systems, and they have an extensive literature [3]. Recently [4,5], an experimental system of non-Brownian colloids displaying a transition to an absorbing state has been studied, and a model, called "random organization" [5], has been proposed as a description of the experimental phenomena.Absorbing states satisfy some model-dependent condition, the specifics of which do not appear to change the behavior qualitatively. The control-parameter space is divided into two regions -one where absorbing states are achieved for any typical initial state, the other where absorbing states, although possible, are not attained, resulting in a non-equilibrium steady state with a non-zero average number of "active" particles which violate the stipulated condition. These regions are separated by a critical line, and the transition between the two phases displays characteristics of a continuous phase transition, with a diverging correlation length. This phenomenology is common to all absorbing state models.In this Letter we shall study the "order" that develops in several absorbing state models as the system approaches the critical point from within the absorbing phase. Remarkably, even though the initial states are random, the dynamics are random, and there is an enormous number of random absorbing states, those absorbing states actually attained by the system are special, with greatly diminshed density fluctuations. As we approach criticality, these fluctuations scale differently from the usual random system -they are, in fact, hyperuniform [6]. Hyperuniform systems have recently attracted interest due to their relation to photonic bandgap materials [7,8]. Thus, the setup in [4,5] may provide an efficient method to create such materials in bulk.For a system in d dimensions, we characterize the density fluctuations in a region of volume d as a function of byRandom systems, such as a Poisson process, have the standard " √ N " fluctuations; this corresponds to λ = d. When λ > d, the particles are distributed more uniformly; such distributions are termed hyperuniform [6]. For example, a crystal whose atoms are displaced by small random amounts from their lattice sites will have λ = d + 1. We find that for the models we study, λ > d for c...

Ensemble Theory for Stealthy Hyperuniform Disordered Ground States

“…2 for a vivid illustration. During the last decade, a variety of disordered hyperuniform states have been identified that exist as both equilibrium and nonequilibrium phases, including maximally random jammed particle packings [33][34][35][36], jammed athermal granular media [37], jammed thermal colloidal packings [38,39], cold atoms [40], transitions in nonequilibrium systems [41,42], surfaceenhanced Raman spectroscopy [43], terahertz quantum cascade laser [44], wave dynamics in disordered potentials based on supersymmetry [45], avian photoreceptor patterns [46], and certain Coulombic systems [47]. Moreover, disordered hyperuniform materials possess novel physical properties potentially important for applications in photonics [25][26][27]48,49] and electronics [50][51][52].…”

Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated 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.…”

“…In [15], a variety of models belonging to the Manna class were shown to display hyperuniformity (γ>d) at the critical point. This is in contrast with classical equilibrium models in which fluctuations are enhanced at the critical point (γ<d) [18].…”

Hyperuniformity disorder length spectroscopy for extended particles

“…We start with a one dimensional rectangular particle of length p, that covers p/p o pixels and has volume V P = I o p. The sums in Eqs. (16)(17)(18)(19) with I(i) = I o are readily evaluated. Dividing V R V Q 2 by V P V Ω 2 = I o pL 2 then gives the predicted relative variance for random particle placements as…”

“…Examples include jamming in amorphous materials [4,5,[7][8][9][10], complete optical band gaps in disordered photonics materials [11][12][13][14][15], and reversibility/irreversibility in periodically driven systems [16][17][18]. Hyperunformity is also important in the arrangement of photoreceptors in the retina [19], and in the large-scale structure of the universe [2].…”