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 $ω^4$ 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 non-universal prefactor of the universal $ω^4$ 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 non-equilibrium 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.