Dynamics of a first-order transition to an absorbing state

Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks

Non-equilibrium phase coexistence is commonly observed in both biological and artificial systems, yet understanding it remains a significant challenge. Unlike equilibrium systems, where free energy provides a unifying framework, the absence of such a quantity in non-equilibrium settings complicates their theoretical understanding. Granular materials, driven out of equilibrium by energy dissipation during collisions, serve as an ideal platform to investigate these systems, offering insights into the parallels and distinctions between equilibrium and non-equilibrium phase behavior. For example, the coexisting dense phase is typically colder than the dilute phase, a result usually attributed to greater dissipation in denser regions. In this article, we demonstrate that this is not always the case. Using a simple numerical granular model, we show that a hot solid and a cold liquid can coexist in granular systems. This counterintuitive phenomenon arises because the collision frequency can be lower in the solid phase than in the liquid phase, consistent with equilibrium results for hard-disk systems. We further demonstrate that kinetic theory can be extended to accurately predict phase temperatures even at very high packing fractions, including within the solid phase. Our results highlight the importance of collisional dynamics and energy exchange in determining phase behavior in granular materials, offering new insights into non-equilibrium phase coexistence and the complex physics underlying granular systems.

Enhancing (quasi-)long-range order in a two-dimensional driven crystal

It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg-Mermin-Wagner (HMW) theorem, which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons, which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.

Anomalous flocking in nonpolar granular Brownian vibrators

Using Brownian vibrators, we investigated the structures and dynamics of quasi-2d granular materials, with packing fractions (ϕ) ranging from 0.111 to 0.832. Our observations revealed a remarkable large-scale flocking behavior in hard granular disk systems, encompassing four distinct phases: granular fluid, flocking fluid, poly-crystal, and crystal. Anomalous flocking emerges at ϕ = 0.317, coinciding with a peak in local density fluctuations, and ceased at ϕ = 0.713 as the system transitioned into a poly-crystal state. The poly-crystal and crystal phases resembled equilibrium hard disks, while the granular and flocking fluids differed significantly from equilibrium systems and previous experiments involving uniformly driven spheres. This disparity suggests that collective motion arises from a competition controlled by volume fraction, involving an active force and an effective attractive interaction resulting from inelastic particle collisions. Remarkably, these findings align with recent theoretical research on the flocking motion of spherical active particles without alignment mechanisms.

Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.

Pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres

We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted so that the particles do not levitate over the grid, resulting in quasi-two-dimensional dynamics. We show that the behavior of diffusion and correlations in this system is particularly rich. Noticeably as well (and related to the complex dynamical behavior), a variety of phases appear, with important peculiarities with respect to analogous setups. We observe gas, liquid, glass, and hexagonal crystal phases. Most notably, we show that the melting of the hexagonal crystal occurs in coexistence with a liquid phase. This strikingly differs from the corresponding transition in a purely two-dimensional systems of air-fluidized disks, for which no phase coexistence has been reported in the literature.

Finite-size scaling for discontinuous nonequilibrium phase transitions

A finite-size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E 92, 062126 (2015)PLEEE81539-375510.1103/PhysRevE.92.062126], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities such as response functions, reduced cumulants, and equal area probability distributions are derived from phenomenological arguments. Irrespective of system details, all these quantities scale with the volume, establishing the dependence on size. The approach generality is illustrated through the analysis of different models. The present results are a relevant step in trying to unify the scaling behavior description of nonequilibrium transition processes.

Critical phenomena in quasi-two-dimensional vibrated granular systems

The critical phenomena associated to the liquid-to-solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are associated to the fourfold bond-orientational order parameter χ_{4}, which measures the level of square crystallization of the system. Previous experimental results have shown that the transition of χ_{4}, when varying the vibration amplitude, can be either discontinuous or continuous, for two different values of the height of the box. Exploring the amplitude-height phase space, a transition line is found, which can be either discontinuous or continuous, merging at a tricritical point and the continuous branch ends in an upper critical point. In the continuous transition branch, the critical properties are studied. The exponent associated to the amplitude of the order parameter is β=1/2, for various system sizes, in complete agreement with the experimental results. However, the fluctuations of χ_{4} do not show any critical behavior, probably due to crossover effects by the close presence of the tricritical point. Finally, in quasi-one-dimensional systems, the transition is only discontinuous, limited by one critical point, indicating that two is the lower dimension for having a tricritical point.

Noise induces rare events in granular media

The granular Leidenfrost effect [B. Meerson, et al., Phys. Rev. Lett. 91, 024301 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.024301; P. Eshuis et al., Phys. Rev. Lett. 95, 258001 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.258001] is the levitation of a mass of granular matter when a wall below the grains is vibrated, giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.

Attractor nonequilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one-dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSSs we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique nonequilibrium stationary state, completely different from its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g., spatial density or velocity distribution) of the system itself.

Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

Based on quasistationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as response functions, cumulants, and equal area probability distributions all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions-to single and infinitely many absorbing states-are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasistationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to a unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.