We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(ω_{\min}) \sim ω^{5}_{\min}$ regime, as opposed to the $ω^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $γ$ near the plastic event occurring at $γ_{P}$, displays a collapse when scaled by $\sqrt{γ_P - γ}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(ω_{\min}) \sim ω^{6}_{\min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event.
We perform an extensive numerical study of avalanche behavior in a 2D LJ glass at T=0, sheared at finite strain rates $\dotγ$. From the finite size analysis of stress fluctuations and of transverse diffusion we show that flip-flip correlations remain relevant at all realistic strain rates. We predict that the avalanche size scales as $\dotγ^{-1/d}$, with $d$ the space dimension.
At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher densities remains, however, unclear. One might expect to find simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field solutions, however, these solutions are only strictly applicable to the limit of infinite spatial dimension, and it is unclear what value they have for finite-dim…
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots -- locations where particles rearrange under stress and that resemble two-level sy…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the form of collective avalanches. We investigate their characterization through energy vs. stress drops and at multiple stages of deformation, thus revealing a change of spatial extent of the avalanches and degree of stress correlations as deformation progresses. We show that the statistics of stress and energy drops only become comparable for large events in …
We have studied the statistics of plastic rearrangement events in a simulated amorphous solid at T=0. Events are characterized by the energy release and the ``slip volume'', the product of plastic strain and system volume. Their distributions for a given system size $L$ appear to be exponential, but a characteristic event size cannot be inferred, because the mean values of these quantities increase as $L^α$ with $α\sim 3/2$. In contrast to results obtained in 2D models, we do not see simply connected avalanches. The exponent suggests a fractal shape of the avalanches, which is also evidenced b…
The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counter-intuitive because any solid material is expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons following the Debye law. A number of phenomenological explanations have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Recently, the microscopic mean-field theories have been developed to predict the universal non-Debye scaling law.…
We construct a quantum mechanical model of perfectly isotropic amorphous solids as fuzzy crystals and establish an analytical theory of vibrations for glasses at low temperature. Our theoretical framework relies on the basic principle that the disorder in a glass is similar to the disorder in a classical fluid, while the latter is mathematically encoded by noncommutative coordinates in the Lagrange formulation of fluid mechanics. We find that the density of states in the acoustic branches flattens significantly, leading naturally to a boson peak in the specific heat as a manifestation of a van…
Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a Boson Peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here,…
High-resolution neutron backscattering techniques are exploited to study the elastic and quasi-elastic response of the high-density amorphous (HDA), the low-density amorphous (LDA) and the crystalline ice Ic upon temperature changes. Within the temperature ranges of their structural stability (HDA at T > 80 K, LDA at T > 135 K, ice Ic at T < 200 K) the Debye-Waller factors and mean-square displacements characterise all states as harmonic solids. During the transformations HDA->LDA (T ~ 100 K), LDA->Ic (T ~ 150K) and the supposed glass transition with Tg ~ 135 K no relaxation processes can be d…
We have investigated the response of amorphous silicon (a-Si), in particular crystallization, to external mechanical shear deformations using classical molecular dynamics (MD) simulations and the empirical Environment Dependent Inter-atomic Potential (EDIP) [Phys. Rev. B 56, 8542 (1997)]. In agreement with previous results we find that, at low shear velocity and low temperature, shear deformations increase disorder and defect density. At high temperatures, however, the deformations are found to induce crystallization, demonstrating a dynamical transition associated with both shear rate and tem…
Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit-cycles in which plastic events repeat indefinitely under the oscillatory drive. Reaching reversible limit-cycles, can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again a…
Amorphous solids have excess soft modes in addition to the phonon modes described by the Debye theory. Recent numerical results show that if the phonon modes are carefully removed, the density of state of the excess soft modes exhibit universal quartic scaling, independent of the interaction potential, preparation protocol, and spatial dimensions. We hereby provide a theoretical framework to describe this universal scaling behavior. For this purpose, we extend the mean-field theory to include the effects of finite dimensional fluctuation. Based on a semi-phenomenological argument, we show that…
Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states $g(ω)$ obeys a characteristic power law, $g(ω)\simω^2$, called the non-Debye scaling in the low-frequency region. Numerical studies have however reported that this scaling breaks down at low frequencies, due to finite dimensional effects. In this study, we prepare amorphous packings of up to $128000$ particles in spatial dimensions from $d=3$ to $d=9$ to characterise the ra…
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…
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…
Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses $x$. We find that in this distribution, the most unstable sites are located in a system size dependent plateau. While the entrance into the plateau is set by the lower cutoff o…
Thermal activation drives a finite-size crossover from scale-free to runaway avalanches in amorphous solids
Instituto de Física del Sur (IFISUR), Universidad Nacional del Sur (UNS), CONICET（南方物理研究所，南国立大学，阿根廷国家科学研究委员会）；Instituto de Nanociencia y Nanotecnología, CNEA–CONICET, Centro Atómico Bariloche（纳米科学与技术研究所，巴里洛切原子能委员会-阿根廷国家科学研究委员会，巴里洛切原子中心）
Self-organization, Memory and Learning: From Driven Disordered Systems to Living Matter
Institute for Biological Physics, University of Cologne（科隆大学生物物理研究所）；Institute of Theoretical Physics II, Heinrich-Heine University（杜塞尔多夫海因里希·海涅大学理论物理二系）；Institut Universitaire de France (IUF)（法国高等研究院）；PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité（巴黎机械与材料物理中心，法国国家科学研究中心，巴黎国立高等物理化工学院，巴黎文理研究大学，索邦大学，巴黎西岱大学）；Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心）
In this work we study morphological characteristics of the critically-sized crystalline nuclei at initial stage of the shear-induced crystallization of a model single-component amorphous (glassy) system. These characteristics are estimated quantitatively through statistical treatment of the non-equilibrium molecular dynamics simulation results for the system under steady shear at various (fixed) values of the shear rate $\dotγ$ and at different temperatures. It is found that the sheared glassy system is crystallized through nucleation mechanism. From analysis of a time-dependent trajectories o…
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…
Rayleigh anomalies and disorder-induced mixing of polarizations at nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride glass
Universitá degli studi di Roma ”La Sapienza”（罗马第一大学）；Istituto Italiano di Tecnologia - Center for Life Nanoscience（意大利理工大学-生命纳米科学中心）；University of Geneva（日内瓦大学）；Chalmers University of Technology（查尔姆斯理工大学）；Sincrotrone Trieste S.C.p.A.（的里雅斯特同步辐射中心）
The boson peak (BP) is an excess of vibrational states over the Debye law appearing at terahertz frequencies. It is found in all glasses and marks the crossover between the long-wavelength behavior, where the solid can be considered as an isotropic continuum, and the region where the wavelength of the sound wave starts to experience the microscopic details of the structure. This chapter is devoted to a review of the main experimental observations regarding the vibrational dynamics of amorphous solids, as detected by neutron and X-ray scattering techniques. A first part of the chapter is devote…
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…
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…
