Searcharxiv⌕ Search

arXiv subjects

Edan Lerner

Publications and source records attributed to Edan Lerner.

At least 73 records · Page 4Linked to original sources
arXiv2019

Theory for the density of interacting quasi-localised modes in amorphous solids

Quasi-localised modes appear in the vibrational spectrum of amorphous solids at low-frequency. Though never formalised, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, $D_{L}(ω)\simω^α$, that establishes this link for systems at zero temperature under quasi-static loading. It predicts two regimes depending on the density of shear transformations $P(x)\sim x^θ$ (with $x$ the additional stress needed to trigger a shear transformation). If $θ>1/4$, $α=4$ and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If $θ<1/4$, $α=3+ 4 θ$ and all quasi-localised modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically.

cond-mat.soft↗
arXiv2019

Anisotropic Structural Predictor in Glassy Materials

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial/anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal $ω^4$ density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.

cond-mat.soft↗
arXiv2019

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 both in 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.

cond-mat.soft↗
arXiv2018

On the protocol dependence of plasticity in ultra-stable amorphous solids

While perfect crystals may exhibit a purely elastic response to shear all the way to yielding, the response of amorphous solids is punctuated by plastic events. The prevalence of this plasticity depends on the number of particles $N$ of the system, with the average strain interval before the first plastic event, $\overline{Δγ}$, scaling like $N^α$ with $α$ negative: larger samples are more susceptible to plasticity due to more numerous disorder-induced soft spots. In this paper we examine this scaling relation in ultra-stable glasses prepared with the Swap Monte Carlo algorithm, with regard to the possibility of protocol-dependent scaling exponent, which would also imply a protocol dependence in the distribution of local yield stresses in the glass. We show that, while a superficial analysis seems to corroborate this hypothesis, this is only a pre-asymptotic effect and in fact our data can be well explained by a simple model wherein such protocol dependence is absent.

cond-mat.soft↗
arXiv2018

A characteristic energy scale in glasses

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 glassy dynamics, we propose that the bulk average of the glass response to a localized force dipole defines such a characteristic energy scale. We show that this characteristic glassy energy scale features remarkable properties: $(i)$ It increases dramatically with decreasing temperature of equilibrium supercooled states, significantly surpassing the corresponding increase in the shear modulus, dismissing the common view that structural variations in supercooled liquids upon vitrification are minute $(ii)$ Its variation with annealing and system size is very similar in magnitude and form to that of the energy of the softest non-phononic vibrational mode, thus establishing a very unusual relation between a rare glassy fluctuation and a bulk average $(iii)$ It exhibits striking dependence on spatial dimensionality and system size, due to the long-ranged fields associated with quasilocalization, which are speculated to be related to peculiarities of the glass transition in two dimensions. In addition, we identify a truly-static growing lengthscale associated with the characteristic glassy energy scale, and discuss possible connections between the increase of this energy scale and the slowing down of dynamics near the glass transition temperature. Open questions and future directions are discussed.

cond-mat.soft↗
arXiv2018

Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses

The translational symmetry of solids gives rise to the existence of low-frequency phonons. In ordered systems, some phonons characterized by different wavevectors are degenerate, i.e. they share the same frequency $ω$; in finite-size systems, phonons form a discrete set of bands with $n_q(ω)$-fold degeneracy. Here we focus on understanding how this degeneracy is lifted in the presence of disorder, and its physical implications. Using standard degenerate perturbation theory and simple statistical considerations, we predict the dependence of the disorder-induced frequency width of phonon bands to be $Δω\!\sim\!σ\,ω\sqrt{n_q}/\sqrt{N}$, where $σ$ is the strength of disorder and $N$ is the total number of particles. This theoretical prediction is supported by extensive numerical calculations for disordered lattices characterized by topological, mass, stiffness and positional disorder, and for computer glasses, where disorder is self-generated, thus establishing its universal nature. The predicted scaling leads to the identification of a crossover frequency $ω_\dagger\!\sim\!L^{-2/(d+2)}$ in systems of linear size $L$ in $d\!>\!2$ dimensions, where the disorder-induced width of phonon bands becomes comparable to the frequency gap between neighboring bands. Consequently, phonons continuously cover the frequency range $ω\!>\!ω_\dagger$, where the notion of discrete phonon bands becomes ill-defined. Two basic applications of the theory are presented; first, we show that the phonon scattering lifetime is proportional to $(Δω)^{-1}$ for $ω\!<\!ω_\dagger$. Second, the theory is applied to the basic physics of glasses, allowing to determine the range of frequencies in which the recently established universal density of states of non-phononic excitations can be directly probed for different system sizes.

cond-mat.stat-mech↗
arXiv2018

Universal non-phononic 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 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 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 non-phononic 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.

cond-mat.soft↗
arXiv2018

Theory for Swap Acceleration near the Glass and Jamming Transitions

Swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamic is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. \maa{ The magnitude of this effect is proportional to the width of the radii distribution, and decreases with compression for finite-range purely repulsive interaction potentials.} We test these predictions numerically and discuss the implications of these findings for the glass transition.We extend these results to the case of hard spheres where swap is argued to destroy meta-stable states of the free energy coarse-grained on vibrational time scales. Our analysis unravels the soft elastic modes responsible for the speed up swap induces, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular for continuously poly-disperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is new algorithm that generates ultra-stable glasses by simple descent in an appropriate effective potential.

cond-mat.soft↗
arXiv2018

Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses

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 emerge from a balance between a local elasticity term and an internal stress term in the dynamical matrix, where the difference between them is orders of magnitude smaller than their typical magnitude. By artificially reducing the magnitude of internal stresses in a computer glass former in three dimensions, we show that a gap is formed in the density of states below which no vibrational modes exist, thus demonstrating the crucial importance of internal stresses. Finally, we show that while better annealing the glass upon cooling from the liquid state significantly reduces its internal stresses, the self-organizational processes during cooling render the gapless $D(ω)\!\sim\!ω^4$ density of state unaffected.

cond-mat.soft↗
arXiv2017

Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses

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 density of vibrational modes grows as $ω^β$ with $β$ depending on the parent temperature $T_{0}$ from which the glassy configurations were instantaneously quenched. For quenches from high temperature liquid states we find $β\!\approx\!3$, whereas $β$ appears to approach the previously-observed value $β\!=\!4$ as $T_0$ approaches the glass transition temperature. We discuss the consistency of our findings with the theoretical framework of the Soft Potential Model, and contrast them with similar measurements performed on configurations obtained by continuous quenches at finite cooling rates. Our results suggest that any physical quench at rates sufficiently slower than the inverse vibrational timescale --- including all physically-realistic quenching rates of molecular or atomistic glasses --- would result in a glass whose density of vibrational modes is universally characterized by $β\!=\!4$.

cond-mat.soft↗
arXiv2017

Statistics and properties of low-frequency vibrational modes in structural glasses

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 $L\!<\!L_D$ is Weibullian, with scaling exponents in excellent agreement with the $ω^4$ law. We further show that the lowest frequency modes are spatially quasi-localized, and that their localization and associated quartic anharmonicity are largely frequency-independent. The effect of preparation protocols on the low-frequency modes is elucidated and a number of glassy lengthscales are briefly discussed.

cond-mat.soft↗
arXiv2017

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change due to thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses --- an intrinsic signature of glassy frustration ---, anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal $ω^4$ density of states of quasi-localized low-frequency vibrational modes. When the spatial thermal energy field --- a `softness field' --- is considered, this power-law tail manifests itself by highly localized spots which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal-modes-based approach. These results offer a general, system/model-independent, physical-observable-based approach to identify structural properties of quiescent glasses and to relate them to glassy dynamics.

cond-mat.soft↗
arXiv2017

Quasilocalized states of self stress in packing-derived networks

States of self stress (SSS) are assignments of forces on the edges of a network that satisfy mechanical equilibrium in the absence of external forces. In this work we show that a particular class of quasilocalized SSS in packing-derived networks, first introduced in [D. M. Sussman, C. P. Goodrich, and A. J. Liu, Soft Matter 12, 3982 (2016)], are characterized by a lengthscale $\ell_c$ that scales as $1/\sqrt{z_c-z}$ where $z$ is the mean connectivity of the network, and $z_c\!\equiv\!4$ is the Maxwell threshold in two dimensions, at odds with previous claims. Our results verify the previously proposed analogy between quasilocalized SSS and the mechanical response to a local dipolar force in random networks of relaxed Hookean springs. We show that the normalization factor that distinguishes between quasilocalized SSS and the response to a local dipole constitutes a measure of the mechanical coupling of the forced spring to the elastic network in which it is embedded. We further demonstrate that the lengthscale that characterizes quasilocalized SSS does not depend on its associated degree of mechanical coupling, but instead only on the network connectivity.

cond-mat.soft↗
arXiv2016

Nonlinear modes disentangle glassy and Goldstone modes in structural glasses

One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a family of algebraic equations whose solutions represent collective displacement directions (modes) in the multi-dimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasi-localized low-energy excitations. We present an iterative method to solve the algebraic equations, and use it to study the energetic and structural properties of a selected subset of their solutions constructed by starting from a normal mode analysis of the potential energy of a model glass. Our key result is that the structure and energies associated with harmonic glassy vibrational modes and their nonlinear counterparts converge in the limit of very low frequencies. As nonlinear modes never suffer hybridizations, our result implies that the presented theoretical framework constitutes a robust alternative definition of `soft glassy modes' in the thermodynamic limit, in which Goldstone modes overwhelm and destroy the identity of low-frequency harmonic glassy modes.

cond-mat.soft↗
arXiv2016

Emergent Inter-particle Interactions in Thermal Amorphous Solids

Amorphous media at finite temperatures, be them liquids, colloids or glasses, are made of interacting particles that move chaotically due to thermal energy, colliding and scattering continuously off each other. When the average configuration in these systems relaxes only at long times, one can introduce {\em effective interactions} that keep the {\em mean positions} in mechanical equilibrium. We introduce a new framework to determine these effective force-laws that define an effective Hessian that can be employed to discuss stability properties and density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these feel zero forces when not in contact and infinite forces when they touch. The present approach recaptures the effective interactions which for sufficiently dense spheres at temperature $T$ depends on the gap $h$ between spheres as $T/h$ [C. Brito and M. Wyart, Europhys. Lett. 76 149 (2006)]. In systems at lower densities or with longer microscopic interaction (say like Lennard-Jones), the emergent force laws will include ternary, quaternary and generally higher order many-body terms, even if the microscopic interactions are strictly binary.

cond-mat.soft↗
arXiv2016

Unjamming in models with analytic pairwise potentials

The canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cut-off in the interaction range. The sharp cut-off renders the potential non-analytic, but makes it possible to describe many properties of the solid in terms of the coordination number $z$, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cut-off in the interaction range have not been considered in this context, but are of interest for understanding the relevance of the unjamming phenomenology to systems in which such a cut-off cannot be assumed. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power-law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear to bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the hydrostatic pressure to bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number, and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

cond-mat.soft↗
arXiv2016

The micromechanics of nonlinear plastic modes

Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. The deformation-dynamics of NPMs is compared to those of the analogous observables derived from atomistic linear elastic theory, namely destabilizing eigenmodes of the dynamical matrix and their associated eigenvalues. The key result we present and explain is that the dynamics of NPMs and of destabilizing eigenmodes under external deformations follow different scaling laws with respect to the proximity to imminent instabilities. In particular, destabilizing modes vary with a singular rate, whereas NPMs' exhibit no such singularity. As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. This dynamical difference between NPMs and linear destabilizing eigenmodes underlines the usefulness of NPMs for predicting the locus and geometry of plastic instabilities, compared to their linear-elastic counterparts.

cond-mat.soft↗