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Register a new userGrowing timescales and lengthscales characterizing vibrations of amorphous solids
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Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debyes 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 Debyes 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, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time and length scales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.
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The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the non-linear elastic exponent, the yielding strain/stress and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path towards understanding complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.
It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to the glass transition. The zero temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.
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, $overline{Deltagamma}$, scaling like $N^alpha$ with $alpha$ 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.
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 systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.
Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The lengthscale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characterisitic timescale is several times larger than the alpha relaxation time. A second crossover lengthscale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back in the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.
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