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Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways., Comment: 42 pages, 9 figures

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions $d=2$-$8$., Comment: 9 pages; 6 figures

The ideal glass, a disordered system of particles with zero configurational entropy, cannot be realized through thermal processes. Nevertheless, we present a method for constructing ideal jammed packings of soft spheres, and thus the zero temperature ideal glass, in two dimensions. In line with the predicted properties, these critically jammed packings have high bulk and shear moduli as well as an anomalously high density. While the absence of pressure scaling in the shear moduli of crystalline materials is often attributed to the ordered nature of the particles, we show for the first time that disordered ideal packings also have this feature. We also find that the density of states avoids the low frequency power law scaling famously found in most amorphous materials. Finally, these configurations display hyperuniformity. In addition to resolving a long-standing mystery, this methodology represents a valuable shortcut in the generation of well-equilibrated glassy systems. The creation of such an ideal packing makes possible a complete exploration and explanation of two dimensional jammed and glassy systems., Comment: 6 pages incl. citations, 4 figures

Protocol-dependent states in structural glasses can encode a disordered, yet retrievable memory. While training such materials is typically done via a global drive, such as external shear, in dense active matter the driving is instead local and spatio-temporally correlated. Here we focus on the impact of such spatial correlation on memory formation. We investigate the mechanical response of a dense amorphous packing of athermal particles, subject to an oscillatory quasistatic driving with a tunable spatial correlation, akin to the instantaneous driving pattern in active matter. We find that the capacity to encode memory can be rendered comparable upon a proper rescaling on the spatial correlation, whereas the efficiency in memory formation increases with motion cooperativity.

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that the terminal relaxation times $\tau$ for FIRE energy minimization of soft-sphere glasses exhibit thermal onset as samples become increasingly well-equilibrated. Although $\tau(\phi)$ can decrease by orders of magnitude as equilibration proceeds and the jamming density $\phi_{\rm J}$ increases via thermal onset, it always scales as $\tau(\phi) \sim (\phi_{\rm J} - \phi)^{-2} \sim [Z_{\rm iso} - Z_{\rm ms}(\tau)]^{-2}$, where $\phi_{\rm J}$ is the jamming density and $Z_{\rm ms}(\tau)$ is the average coordination number of particles satisfying a minimal local mechanical stability criterion ($Z \geq d+1$) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse $\tau$ datasets that look very different when plotted as a function of $\phi$, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant $\phi$ and $T$?, Comment: resubmitted in response to referee comments

The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, 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-$d$ corrections 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 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 $\alpha_2$. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations in more realistic glass formers., Comment: 10 pages, 7 figures

Jamming is an emergent phenomenon wherein the local stability of individual particles percolates to form a globally rigid structure. However, the onset of rigidity does not imply that every particle becomes rigid, and indeed some remain locally unstable. These particles, if they become unmoored from their neighbors, are called \textit{rattlers}, and their identification is critical to understanding the rigid backbone of a packing, as these particles cannot bear stress. The accurate identification of rattlers, however, can be a time-consuming process, and the currently accepted method lacks a simple geometric interpretation. In this manuscript, we propose two simpler classifications of rattlers based on the convex hull of contacting neighbors and the maximum inscribed sphere of the radical Voronoi cell, each of which provides geometric insight into the source of their instability. Furthermore, the convex hull formulation can be generalized to explore stability in hyperstatic soft sphere packings, spring networks, non-spherical packings, and mean-field non-central-force potentials., Comment: 9 pages, 9 figures

Real structural glasses form through various out-of-equilibrium processes, including temperature quenches, rapid compression, shear, and aging. Each of these processes should be formally understandable within the recently formulated dynamical mean-field theory of glasses, but many of the numerical tools needed to solve the relevant equations for sufficiently long timescales do not yet exist. Numerical simulations of structureless (and therefore mean-field-like) model glass formers can nevertheless aid searching for and understanding such solutions, thanks to their ability to disentangle structural from dimensional effects. We here study the infinite-range Mari-Kurchan model under simple non-equilibrium processes and compare the results with those from the random Lorentz gas [J. Phys. A: Math. Theor. 55 334001, (2022)], which are both mean-field-like and become formally equivalent in the limit of infinite spatial dimensions. Of particular interest are jamming from crunching and under instantaneous temperature quenches. The study allows for an algorithmic understanding of the jamming density and of its approach to the infinite-dimensional limit. The results provide important insight into the eventual solution of the dynamical mean-field theory, including onsets and anomalous relaxation, as well as into the various algorithmic schemes for jamming., Comment: 13 pages, 6 figures

Hyperuniform many-particle systems are characterized by a structure factor $S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; and stealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0 < |{\mathbf{k}}| \le K$, called the "exclusion region." Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing $S(\mathbf{k})$ in the exclusion region is computationally intensive as the system size becomes large. In this Letter, we present an improved methodology to generate such states using double-double precision calculations on GPUs that reduces the deviations from zero within the exclusion region by a factor of approximately $10^{30}$ for systems sizes more than an order of magnitude larger. We further show that this ultra-high accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small., Comment: 7 pages, 3 figures

A recent letter titled "Explicit Analytical Solution for Random Close Packing in d=2 and d=3" published in Physical Review Letters proposes a first-principle computation of the random close packing (RCP) density in spatial dimensions d=2 and d=3. This problem has a long history of such proposals, but none capture the full picture. This paper, in particular, once generalized to all d fails to describe the known behavior of jammed systems in d>4, thus suggesting that the low-dimensional agreement is largely fortuitous., Comment: 2 pages, 1 figure

The formulation of the mean-field, infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension $d$ increases. A careful numerical assessment of the matter has long been hindered by the exponential increase of computational costs with $d$. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on $D_d$ lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to $d=13$. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite $d$ by leveraging standard liquid-state theory, and thus help bridge the gap from the other direction. The relatively smooth evolution of both structure and dynamics across the $d$ gap allows us to relate the two approaches, and to identify some of the missing features that a finite-$d$ theory of glasses might hope to include to achieve near quantitative agreement., Comment: 11 pages, 8 figures

Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: (A) crystallization is impeded and the glass phase constitutes the densest packing, (B) crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible, or (C) crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings in dimension $d=3$-$10$ using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close-packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free volume expansion and that a meaningful polynomial correction can be formulated., Comment: 17 pages, 9 figures. Edits coincide with the published version

Although much is known about the metastable liquid branch of hard spheres--from low dimension $d$ up to ${d\to\infty}$--its crystal counterpart remains largely unexplored for $d>3$. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to $d=10$, and the dimensional trends suggest that crystal stability likely persists well beyond that point., Comment: 12 pages, 7 figures. Edits are reflective of the published version and thus include results for d=10

The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior should be equivalent in infinite dimensions, up to a rescaling factor that depends on the correlation length of the applied field. We test these predictions in 2d using a new numerical protocol, termed `athermal quasi-static random displacement', and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolate between the uncorrelated localized forces that occur in the high-persistence limit of dense active matter, and system-spanning correlated displacements that occur under applied shear. These results suggest a universal framework for predicting flow, deformation, and failure in active and sheared disordered materials.

Liquids equilibrated below an onset density share similar inherent states, while above that density their inherent states markedly differ. Although this phenomenon was first reported in simulations over 20 years ago, the physical origin of this memory remains controversial. Its absence from mean-field descriptions, in particular, has long cast doubt on its thermodynamic relevance. Motivated by a recent theoretical proposal, we reassess the onset phenomenology in simulations using a fast hard sphere jamming algorithm and find it both thermodynamically and dimensionally robust. Remarkably, we also uncover a second type of memory associated with a Gardner-like change in behavior along the jamming algorithm.

Under shear, a system of particles changes its contact network and becomes unstable as it transitions between mechanically stable states. For hard spheres at zero pressure, contact breaking events necessarily generate an instability, but this is not the case at finite pressure, where we identify two types of contact changes: network events that do not correspond to instabilities and rearrangement events that do. The relative fraction of such events is constant as a function of system size, pressure and interaction potential, consistent with our observation that both nonlinearities obey the same finite-size scaling. Thus, the zero-pressure limit of the nonlinear response is highly singular.

Recent theoretical advances have led to the creation of a unified phase diagram for the thermal glass and athermal jamming transitions. This diagram makes clear that, while related, the mode-coupling---or dynamic---glass transition is distinct from the jamming transition, occurring at a finite temperature and significantly lower density than the jamming transition. Nonetheless, we demonstrate a pre-jamming transition in athermal frictionless spheres which occurs at the same density as the mode-coupling transition and is marked by percolating clusters of locally rigid particles. At this density in both the thermal and athermal systems, individual motions of an extensive number of particles become constrained, such that only collective motion is possible. This transition, which is well below jamming, exactly matches the definition of collective behavior at the dynamical transition of glasses. Thus, we reveal that the genesis of rigidity in both thermal and athermal systems is governed by the same underlying topological transition in their shared configuration space.

There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.

A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponents. Furthermore, we define a real space geometric correlation function which also displays a signature of jamming. Taken together, these results demonstrate the validity and usefulness of a purely geometric approach to jamming.

A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding adsorption on nanotubes and other graphitic materials is key to many sensing and storage applications. Here we show that nanotube resonators offer a powerful new means of investigating fundamental aspects of adsorption on carbon, including the collective behaviour of adsorbed matter and its coupling to the substrate electrons. By monitoring the vibrational resonance frequency in the presence of noble gases, we observe the formation of monolayers on the cylindrical surface and phase transitions within these monolayers, and simultaneous modification of the electrical conductance. The monolayer observations also demonstrate the possibility of studying the fundamental behaviour of matter in cylindrical geometry., Comment: Unpublished; 7 pages with 4 figures plus 3 pages of supplementary material