Statistical mechanics of local force dipole responses in computer glasses

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are involved in several glassy anomalies such as the low-temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances; however, direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g., phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we, therefore, study here the statistical-mechanical properties of these responses in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs’ frequencies. We find that as opposed to the spatial-dimension-independent universal distribution of QLMs’ frequencies ω (and, consequently, also of their stiffness κ = ω²), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs—associated with dimension-dependent long-range elastic fields—and the universal statistical properties of their frequencies. Based on our findings, we propose a conjecture about the form of the full distribution of QLMs’ frequencies and its protocol-dependence. Finally, we discuss possible connections of our findings to basic aspects of glass formation and deformation.