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 ${\cal D}(ω)\!\sim\!ω^4$. 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 (BMGs). 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.
The scaling form and system-size dependence of the low-frequency wing of the nonphononic vibrational spectrum of two-dimensional structural glasses have been debated in recent literature. Here we provide numerical evidence that the prefactor $A_{\rm g}$ of the low-frequency nonphononic vibrational spectrum -- the latter grows from zero frequency ($ω\!=\!0$) as $A_{\rm g}ω^β$ -- is system-size dependent, and that the exponent $β$ exhibits a similar glass-formation-protocol and system-size dependence as seen in three-dimensional structural glasses.
The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency $ω$ in structural glasses, ${\cal D}(ω)$, was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, ${\cal D}(ω)$ increases from zero frequency as $ω^4$, independent of spatial dimension and of microscopic details. However, in [E. Lerner, and E. Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)] it was shown that the preparation protocol employed to create glassy samples may affect the…
It is now well established that glasses feature quasilocalized nonphononic excitations --- coined "soft spots"---, which follow a universal $ω^4$ density of states in the limit of low frequencies $ω$. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the non-universal prefactor of the universal $ω^4$ law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show th…
Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies $ω$ follow a universal $\sim\!ω^4$ distribution as $ω\!\to\!0$, independently of the glass formation history, the interparticle interaction potential or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structu…
Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e. feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes e…
Low-frequency vibrational modes play a central role in determining various basic properties of glasses, yet their statistical and mechanical properties are not fully understood. Using extensive numerical simulations of several model glasses in three dimensions, we show that in systems of linear size $L$ sufficiently smaller than a crossover size $L_{D}$, the low-frequency tail of the density of states follows $D(ω)\!\sim\!ω^4$ up to the vicinity of the lowest Goldstone mode frequency. We find that the sample-to-sample statistics of the minimal vibrational frequency in systems of size $L\!<\!L_…
We find that the density dependence of the glass transition temperature of Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) systems can be predicted from properties of the zero-temperature ($T=0$) glasses. Below a crossover density $ρ_s$, LJ and WCA glasses show different structures, leading to different vibrational properties and consequently making LJ glasses more stable with higher glass transition temperatures than WCA ones. Above $ρ_s$, structural and vibrational quantities of the $T=0$ glasses show scaling collapse. From scaling relations and dimensional analysis, we predict a densit…
The excess low-frequency normal modes for two widely-used models of glasses were studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is based on analyzing the vibrational energy originating from the excess contacts per particle over the minimum number needed for mechanical stability. Even though both glasses studied have a high coordination number, most of the additional contacts can be considered to be weak.
We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles which readily permit variation of sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in packing fraction. The experimental res…
Glasses show vibrational properties that are markedly different to those of crystals which are known as phonons. For example, excess low-frequency modes (the so-called boson peak), vibrational localization, and strong scattering of phonons have been the most discussed topics, and a theoretical understanding of these phenomena is challenging. To address this problem, computational simulations are a powerful tool, which have been employed by many previous works. In this chapter, we describe simulation methods for studying the vibrational properties of glasses (and any solid-state materials). We …
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s' at least, it is a well established experimental fact that the specific heat of glasses is instead just linear in $T$ at $T \sim 1K$, and presents a pronounced peak when normalized by $T^{3}$, known as the boson peak. Here we present a new approach which sugge…
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 non-phononic soft excitations may assume the form of quasilocalized, harmonic vibrational modes whose frequency follows a universal density of states $D(ω)\!\sim\!ω^4$, independently of microscopic details, and for a broad range of glass preparation protocols. Here we further establish the universality of the non-phononic density of vibrat…
Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency $ω_\text{BP}$, and their vibrational densities of state follow $g(ω) \propto ω^4$ ($ω$ is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of app…
We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, giving thus rise to a non-trivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamic…
Computational studies of supercooled liquids often focus on various analyses of their "underlying inherent states" --- the glassy configurations at zero temperature obtained by an infinitely-fast (instantaneous) quench from equilibrium supercooled states. Similar protocols are also regularly employed in investigations of the unjamming transition at which the rigidity of decompressed soft-sphere packings is lost. Here we investigate the statistics and localization properties of low-frequency vibrational modes of glassy configurations obtained by such instantaneous quenches. We show that the den…
We numerically study the evolution of the vibrational density of states $D(ω)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(ω) \sim ω^2$) at low-frequency, with a…
We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibr…
The low-temperature thermal properties of glasses are anomalous with respect to those of crystals. These thermal anomalies indicate that the low-frequency vibrational properties of glasses differ from those of crystals. Recent studies revealed that, in the simplest model of glasses, i.e., the harmonic potential system, phonon modes coexist with soft localized modes in the low-frequency (continuum) limit. However, the nature of low-frequency vibrational modes of more realistic models is still controversial. In the present work, we study the Lennard-Jones (LJ) system using large-scale molecular-…
We applied an efficient methodology to separate vibrational and configurational entropies in bulk metallic glasses by means of molecular dynamics simulation based on a combination of non-equilibrium adiabatic switching and reversible scaling methods. This approach involves calculating the vibrational free energy using the Einstein crystal as a reference for the solid phase and the recently proposed Uhlenbeck-Ford model for the fluid phase. This methodology has the advantage that it does not require a crystalline solid phase for separating the entropies. Therefore, in principle, it is applicabl…
We show that quasi localized low-frequency modes in the vibrational spectrum can be used to construct soft spots, or regions vulnerable to rearrangement, which serve as a universal tool for the identification of flow defects in solids. We show that soft spots not only encode spatial information, via their location, but also directional information, via directors for particles within each soft spot. Single crystals with isolated dislocations exhibit low-frequency phonon modes that localize at the core, and their polarization pattern predicts the motion of atoms during elementary dislocation gli…
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $ω$ as $ω^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_\text{exc}(ω)\sim ω^2 $ …
To better understand the surprising low-frequency vibrational modes in structural glasses, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination. We find $D(ω)$ has three regimes: a very-low-frequency regime that can be predicted analytically using extremal statistics, an intermediate regime with quasi-localized modes, and a plateau with $D(ω) \sim ω^0$. In the special case of uniform bond weights, the intermediate regime displays $D(ω) \sim ω^4$, independent of network coordination and syste…
We present theoretical investigation on the high-frequency collective dynamics in liquids and glasses at microscopic length scales and terahertz frequency region based on the mode-coupling theory for ideal liquid-glass transition. We focus on recently investigated issues from inelastic-X-ray-scattering and computer-simulation studies for dynamic structure factors and longitudinal and transversal current spectra: the anomalous dispersion of the high-frequency sound velocity and the nature of the low-frequency excitation called the boson peak. It will be discussed how the sound mode interferes w…
We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glass…
Implications of reduction procedures applied to the low energy part of the vibrational density of states in glasses and supercooled liquids are considered by advancing a detailed comparison between the excess - over the Debye limit - vibrational density of states g(w) and the frequency-reduced representation g(w)/w^2 usually referred to as the Boson peak. Analyzing representative experimental data from inelastic neutron and Raman scattering we show that reduction procedures distort to a great extent the otherwise symmetric excess density of states. The frequency of the maximum and the intensit…
The boson peak (BP) is a universal feature in the Raman and inelastic scattering spectra of both disordered and crystalline materials. The current paradigm presents the boson peak as the result of a Ioffe-Regel crossover between ballistic (phonon) and diffusive-type excitations, where the loss of coherence of phonons is described as a purely harmonic process due to structural disorder. This "harmonic disorder" paradigm for the BP has never been challenged or tested at the atomistic level. Here, through a set of atomistically-resolved characterizations of amorphous metallic alloys, we uncover a…
Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensiv…
The unconventional thermal properties of jammed amorphous solids are directly related to their density of vibrational states. While the vibrational spectrum of jammed soft sphere solids has been fully described, the vibrational spectrum of hard spheres, a model for colloidal glasses, is still unknown due to the difficulty of treating the non-analytic interaction potential. We bypass this difficulty using the recently described effective interaction potential for the free energy of thermal hard spheres. By minimizing this effective free energy we mimic a quench and produce typical configuration…
The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decreas…
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests…
It was recently shown that different simple models of glass formers with binary interactions define a universality class in terms of the density of states of their quasi-localized low-frequency modes. Explicitly, once the hybridization with standard Debye (extended) modes is avoided, a number of such models exhibit a universal density of state, depending on the mode frequencies as $D(ω) \sim ω^4$. It is unknown however how wide is this universality class, and whether it also pertains to more realistic models of glass formers. To address this issue we present analysis of the quasi-localized mod…
The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxatio…
We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{θ_e}$ the force distribution of such pairs and $ϕ_c$ the packing fraction at which pressure diverges, we predict that (i…
The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity etc. The old Debye model of vibrational spectra at low energy gives the vibrational density of states (VDOS) as proportional to the frequency squared, but in many materials the spectrum departs from this law which results in a peak upon normalizing the VDOS by frequency squared, which is known as the "boson peak". A description of the VDOS of solids (bo…
It is a persistent problem in condensed matter physics that glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses at the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. It is well known that phonons in crystals couple through phonon-phonon interactions, an extremely efficient mechanism for anharmonic decay that is also important in glasses. Here, however, we show that an additional anharmonic …
The effects of particle shape on the vibrational properties of colloidal glasses are studied experimentally. 'Ellipsoidal glasses' are created by stretching polystyrene spheres to different aspect ratios and then suspending the resulting ellipsoidal particles in water at high packing fraction. By measuring displacement correlations between particles, we extract vibrational properties of the corresponding "shadow" ellipsoidal glass with the same geometric configuration and interactions as the 'source' suspension but without damping. Low frequency modes in glasses composed of ellipsoidal particl…
Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are supposedly involved in a number of glassy anomalies such as the low temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances, however direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.~phonons). Previous studies to overcome this issue …
It has been recently shown [E. Lerner, G. Düring, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)] that the non-phononic vibrational modes of structural glasses at low-frequencies $ω$ are quasi-localized and follow a universal density of states $D(ω)\!\sim\!ω^4$. Here we show that the gapless nature of the observed density of states depends on the existence of internal stresses which generically emerge in glasses due to frustration, thus elucidating a basic element underlying this universal behavior. Similarly to jammed particulate packings, low-frequency modes in structural glasses em…
Some aspects of how sound waves travel through disordered solids are still unclear. Recent work has characterized a feature of disordered solids which seems to influence vibrational excitations at the mesoscales, local elastic heterogeneity. Sound waves propagation has been demonstrated to be strongly affected by inhomogeneous mechanical features of the materials which add to the standard anharmonic couplings, amounting to extremely complex transport properties at finite temperatures. Here, we address these issues for the case of a simple atomic glass former, by Molecular Dynamics computer sim…
Using the inherent structure formalism originally proposed by Stillinger and Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an energy landscape that has an ideal glass transition and derive the consequences for its equation of state. In doing so, we identify a separation of configurational and vibrational contributions to the pressure that corresponds with simulation studies performed in the inherent structure formalism. We develop an elementary model of landscapes appropriate to simple liquids which is based on the scaling properties of the soft-sphere potential comp…
Fossil amber offers the unique opportunity of investigating an amorphous material which has been exploring its energy landscape for more than 110 Myears of natural aging. By applying different x-ray scattering methods to amber before and after annealing the sample to erase its thermal history, we identify a link between the potential energy landscape and the structural and vibrational properties of glasses. We find that hyperaging induces a depletion of the vibrational density of states in the THz region, also ruling the sound dispersion and attenuation properties of the corresponding acoustic…
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a funct…
Glasses display a wide array of nonlinear acoustic phenomena at temperatures $T\lesssim 1$ K. This behavior has traditionally been explained by an ensemble of weakly-coupled, two-level tunneling states, a theory that is also used to describe the thermodynamic properties of glasses at low temperatures. One of the most striking acoustic signatures in this regime is the existence of phonon echoes, a feature that has been associated with two-level systems with the same formalism as spin echoes in NMR. Here we report the existence of distinctly different type of acoustic echo in classical models of…
Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic…
Glasses feature a broad distribution of relaxation times and activation energies without an obvious characteristic scale. At the same time, macroscopic quantities such as Newtonian viscosity and nonlinear plastic deformation, are interpreted in terms of a characteristic energy scale, e.g. an effective temperature-dependent activation energy in Arrhenius relations. Nevertheless, despite its fundamental importance, such a characteristic energy scale has not been robustly identified. Inspired by the accumulated evidence regarding the crucial role played by soft quasilocalized excitations in glass…
The Boson peak is believed to be the key to the fundamental understanding of the anomalous thermodynamic properties of glasses, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe the Boson peak as a strong enhancement of low frequency modes. Using…
Results on the dynamics of silica are presented: vibrations and relaxations. Using molecular dynamics, glass structures are generated by rapidly quenching melts below the glass transition. For the local minima of the structures the vibrational density of states is determined, the structures of the eigenmodes are analyzed, and the influence of the single components is discussed. Relaxations are studied in both amorphous SiO$_2$ and silica melts. Our main focus is on the type of relaxation, i.e., whether the main contributions are caused by small atomic displacements, or by bond-breaking process…
Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states of a recently simulated system, comprised of weakly compressed spheres at zero temperature. We account for the observed a) constancy of the density of modes with frequency, b) appearance of a low-frequency cutoff, and c) power-law increase of this cutoff with compression. We predict a length scale below which vibrations are very different fr…
