Theory for the density of interacting quasilocalized modes in amorphous solids

Ji, Wencheng; Popović, Marko; Geus, Tom W. J. de; Lerner, Edan; Wyart, Matthieu

doi:10.1103/physreve.99.023003

Cited by 40 publications

(56 citation statements)

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“…At finite γ the relation τ 3 ∼ ω 3 must break down, because destabilizing cubic modes' thirdorder coefficients τ 3 were shown to remain constant upon approaching the instability strain [24], whereas their frequency vanishes. Moreover, it was recently shown that under shear, D(ω) ∼ ω 4 does not always hold, but instead an exponent smaller than 4 is observed for well-annealed glasses [63]. This is consistent with recent numerical investigations which have highlighted a non-monotonic behavior of θ as a function of γ.…”

Section: Discussion and Outlooksupporting

confidence: 87%

“…This is consistent with recent numerical investigations which have highlighted a non-monotonic behavior of θ as a function of γ. In particular, it was shown that θ first decreases as a function of γ, before increasing again upon approaching the yielding transition, and finally reaching a plateau value θ ≈ 1/2 in the steady state regime [55,58,63]. Furthermore, it was reported that the decrease of θ at intermediate strain is protocol-dependent and is significantly stronger for better-annealed glasses [58,62].…”

Section: Discussion and Outlookmentioning

confidence: 99%

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Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

2020

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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 multi-dimensional 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 re-introduce 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 first 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, non-hybridized 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. arXiv:1912.10930v1 [cond-mat.soft]

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Section: Discussion and Outlooksupporting

confidence: 87%

Section: Discussion and Outlookmentioning

confidence: 99%

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

2020

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“…It is interesting to note that the range of variability observed in Fig. 4, Right appears to be consistent with a very recent study (61) of the depletion of tunneling two-level systems in stable computer glasses, possibly indicating that a subset of the QLMs is associated with tunneling two-level systems (1,2,36,62).…”

Section: Estimating Qlms' Frequency Scale By Pinching a Glasssupporting

confidence: 88%

Pinching a glass reveals key properties of its soft spots

Rainone

Bouchbinder

Lerner

2020

Proc. Natl. Acad. Sci. U.S.A.

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It is now well established that glasses feature quasilocalized nonphononic excitations—coined “soft spots”—, which follow a universal ω4 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 nonuniversal prefactor of the universal ω4 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 that by pinching a glass—i.e., by probing its response to force dipoles—one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in nonequilibrium thermodynamic approaches to the relaxation, flow, and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass.

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“…Several other non-mean-field models [22,23] and phenomenological theories [1,[24][25][26] were previously put forward to the same aim; most of them, however, require parameter fine-tuning [22][23][24]26] or some rather strong a priori assumptions [1]. In addition, several other mean-field models, introduced in order to explain the low-frequency spectra of structural glasses, predict D(ω) ∼ ω 2 , independently of spatial dimension [16,[39][40][41].…”

Section: Discussionmentioning

confidence: 99%

“…Yet, despite previous efforts [1,[22][23][24][25][26], we currently lack insight into the origin of QLMs' statistical-mechanical properties. Moreover, recent progress in studying computer glass-formers revealed intriguing properties of QLMs [17,18,27], e.g.…”

Section: Introductionmentioning

confidence: 99%

Mean-field model of interacting quasilocalized excitations in glasses

et al. 2021

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Structural glasses feature quasilocalized excitations whose frequencies \omegaω follow a universal density of states {D}(\omega)\!\sim\!\omega^4D(ω)∼ω4. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff \kappa_0κ0) in the absence of interactions, interact among themselves through random couplings (characterized by a strength JJ) and with the surrounding elastic medium (an interaction characterized by a constant force hh). We first show that the model gives rise to a gapless density of states {D}(\omega)\!=\!A_{g}\,\omega^4D(ω)=Agω4 for a broad range of model parameters, expressed in terms of the strength of the oscillators’ stabilizing anharmonicity, which plays a decisive role in the model. Then — using scaling theory and numerical simulations — we provide a complete understanding of the non-universal prefactor A_{g}(h,J,\kappa_0)Ag(h,J,κ0), of the oscillators’ interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that A_{g}(h,J,\kappa_0)Ag(h,J,κ0) is a non-monotonic function of JJ for a fixed hh, varying predominantly exponentially with -(\kappa_0 h^{2/3}\!/J^2)−(κ0h2/3/J2) in the weak interactions (small JJ) regime — reminiscent of recent observations in computer glasses — and predominantly decays as a power-law for larger JJ, in a regime where hh plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

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Theory for the density of interacting quasilocalized modes in amorphous solids

Cited by 40 publications

References 45 publications

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

Pinching a glass reveals key properties of its soft spots

Mean-field model of interacting quasilocalized excitations in glasses

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