Pinching a glass reveals key properties of its soft spots

Abstract

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.

Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p -Spin Model

“…A widely used statistical characterization of the energy landscape sampled by the glassy dynamics is the numerical study of the inherent structures (ISs), defined as the local minima of the energy potential reached by a steepest descent procedure starting from well-thermalized initial conditions at temperature T [25,[29][30][31][32]. The thermalization temperature of the initial configuration is sometimes called the parent temperature, but here, when there is no ambiguity, we simply call it temperature.…”

Mean-field model of interacting quasilocalized excitations in glasses

“…1a) emerge from self-organized glassy frustration [8], which is generic to structural glasses quenched from a melt [9]. Their associated frequencies ω have been shown [10][11][12] to follow a universal nonphononic (non-Debye) density of states D(ω)∼ω 4 as ω→0, independently of microscopic details [13,14], spatial dimension [15,16] and formation history [17,18]. Some examples for D(ω), obtained in computer glasses, are shown in Fig.…”

“…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. the dependence of the amplitude A g of the ω 4 universal law on the state of glassy disorder (cf.…”

“…Data are shifted vertically for visual clarity. (inset) The prefactor A g of the nonphononic ω 4 spectrum vs. the inverse of the parent equilibrium temperature T p from which glasses were instantaneously quenched, calculated for the soft-sphere computer glass model investigated in [17].…”

Spatial structure of unstable normal modes in a glass-forming liquid

“…The vibrational amplitudes decay with a distinct power law r −(d−1) , where r is the distance from the core and d is the spatial dimension, unless hybridization with acoustic modes occurs [29,33,39]. Moreover, the QLVs spatial structure brings useful insight into several local phenomena in low temperature glasses, such as the response to a local dipolar force or plastic events associated to shear-transformation zones [40][41][42][43][44][45].…”