Detecting low-energy quasilocalized excitations in computer glasses.

Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow one to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies, and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input and outputs a library of QLEs embedded in that sample. We demonstrate the power of the algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon hybridizations. Future applications are discussed.

Unified quantifier of mechanical disorder in solids.

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase in the activation barrier ΔE(T) with decreasing temperature T. A class of theoretical frameworks-known as elastic models-attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus G∞(T). While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose and test the possibility that viscous slowing down is controlled by a mesoscopic elastic stiffness κ(T), defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent structures. First, we show that κ(T)-which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses-increases more strongly with decreasing T than the macroscopic inherent structure shear modulus G(T) [the glass counterpart of liquids' G∞(T)] in several computer liquids. Second, we show that the simple relation ΔE(T) ∝ κ(T) holds remarkably well for some computer liquids, suggesting a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the ΔE(T) ∝ κ(T) relation holds from those in which it does not is that the latter feature highly fragmented/granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. Under such conditions, it appears that the sub-basins do not properly represent the landscape properties relevant for structural relaxation.

Elastic moduli fluctuations predict wave attenuation rates in glasses.

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate Γ(ω) in the low-frequency limit (ω → 0) and its dependence on glass history and properties. A theoretical framework-termed Fluctuating Elasticity Theory (FET)-predicts low-frequency Rayleigh scattering scaling in -d spatial dimensions, Γ(ω) ∼ γ ω -d+1, where γ = γ(Vc) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume Vc that remains debated. Here, using extensive computer simulations, we show that Γ(ω) ∼ γω3 is asymptotically satisfied in two dimensions ( -d = 2) once γ is interpreted in terms of ensemble-rather than spatial-averages, where Vc is replaced by the system size. In doing so, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal ω4 density of states of soft quasilocalized modes. These results not only strongly support FET but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.

Simple and Broadly Applicable Definition of Shear Transformation Zones.

Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements-the so-called shear transformation zones (STZs)-is still ongoing. Here we present a simple definition of STZs-based solely on the harmonic approximation of a glass's energy. We explain why and demonstrate directly that our proposed definition of plasticity carriers in amorphous solids is more broadly applicable compared to anharmonic definitions put forward previously. Finally, we offer an open-source library that analyzes low-lying STZs in computer glasses and in laboratory materials such as dense colloidal suspensions for which the harmonic approximation is accessible. Our results constitute a physically motivated methodological advancement towards characterizing mechanical disorder in glasses, and understanding how they yield.

Universality of the Nonphononic Vibrational Spectrum across Different Classes of Computer Glasses.

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies ω follow a gapless, universal distribution D(ω)∼ω^{4}. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here, we demonstrate the emergence of the universal ω^{4} nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses. Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal ω^{4} law, independently of the nature of its microscopic interactions.

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots.

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations-often called "soft spots"-that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes-coined here nonlinear quasilocalized excitations (NQEs)-that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling.

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k†, where phonons are no longer quantized into bands. For k < k†, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k†, we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼k¯d+1 (¯d is the spatial dimension) and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼k¯d+1 log(k0/k) emerges (k0 > k† is a characteristic wavenumber). Our results suggest that macroscopic glasses-and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations-exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.

Fast generation of ultrastable computer glasses by minimization of an augmented potential energy.

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional degrees of freedom. We demonstrate how our glasses' mechanical stability, which is readily tunable in our approach, is reflected in both microscopic and macroscopic observables. Our observations indicate that the stability of our computer glasses is at least comparable to that of computer glasses generated by the celebrated Swap Monte Carlo algorithm. Strikingly, some key properties support even qualitatively enhanced stability in our scheme: the density of quasilocalized excitations displays a gap in our most stable computer glasses, whose magnitude scales with the polydispersity of the particles. We explain this observation, which is consistent with the lack of plasticity we observe at small stress. It also suggests that these glasses are depleted from two-level systems, similarly to experimental vapor-deposited ultrastable glasses.

Universal Nonphononic Density of States in 2D, 3D, and 4D Glasses.

It is now well established that structural glasses possess disorder- and frustration-induced soft quasilocalized excitations, which play key roles in various glassy phenomena. Recent work has established that in model glass formers in three dimensions, these nonphononic soft excitations may assume the form of quasilocalized, harmonic vibrational modes whose frequency follows a universal density of states D(ω)∼ω^{4}, independently of microscopic details, and for a broad range of glass preparation protocols. Here, we further establish the universality of the nonphononic density of vibrational modes by direct measurements in model structural glasses in two dimensions and four dimensions. We also investigate their degree of localization, which is generally weaker in lower spatial dimensions, giving rise to a pronounced system-size dependence of the nonphononic density of states in two dimensions, but not in higher dimensions. Finally, we identify a fundamental glassy frequency scale ω_{c} above which the universal ω^{4} law breaks down.