Probing Gardner Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles

Dynamics and fluctuations of minimally structured glass formers

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α_{2}. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.

Shear-induced criticality in glasses shares qualitative similarities with the Gardner phase

Although glass phases are ubiquitously found in various soft matter systems, we are still far from a complete understanding of them. The concept of marginal stability predicted by infinite-dimensional mean-field theories is drawing attention as a candidate for a universal and distinguishing unique feature of glasses. While among theoretical predictions, the non-Debye scaling has indeed been observed universally over various classes of glasses, the Gardner phase is found only in a limited portion of them. In this work, we numerically demonstrate that plastic events observed in two-dimensional Lennard-Jones glasses under quasistatic shear exhibit statistical properties that are qualitatively consistent with the picture of an infinitely hierarchical energy landscape associated with the Gardner phase.

Dynamic Gardner cross-over in a simple glass

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.

How to count in hierarchical landscapes: A full solution to mean-field complexity

We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multistep replica symmetry breaking and one with full replica symmetry breaking.

Gardner-like crossover from variable to persistent force contacts in granular crystals

We report experimental evidence of a Gardner-like crossover from variable to persistent force contacts in a two-dimensional bidisperse granular crystal by analyzing the variability of both particle positions and force networks formed under uniaxial compression. Starting from densities just above the freezing transition and for variable amounts of additional compression, we compare configurations to both their own initial state and to an ensemble of equivalent reinitialized states. This protocol shows that force contacts are largely undetermined when the density is below a Gardner-like crossover, after which they gradually transition to being persistent, being fully so only above the jamming point. We associate the disorder that underlies this effect with the size of the microscopic asperities of the photoelastic disks used, by analogy to other mechanisms that have been previously predicted theoretically.

High-energy velocity tails in uniformly heated granular materials

We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of β=1.50±0.03 for volume fractions of 0.111≤ϕ≤0.832, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of ϕ=0.832 where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of β=1.50 are a characteristic of uniformly heated granular matter.