Yielding and memory in a driven mean-field model of glasses

Abstract

Glassy systems reveal a wide variety of generic behaviors, which lack a unified theoretical description. Here, we study a mean-field model, recently shown to reproduce the universal non-phononic vibrational spectra of glasses, under oscillatory driving forces. The driven mean-field model, featuring a disordered Hamiltonian structure, naturally predicts the salient dynamical phenomena in cyclically deformed glasses. Specifically, it features an oscillatory yielding transition, characterized by an absorbing-to-diffusive transition in the system's microscopic trajectories and large-scale hysteresis. The model also reveals dynamic slowing-down from both sides of the transition, as well as mechanical and thermal annealing effects that mirror their glass counterparts. Finally, we demonstrate a non-equilibrium ensemble equivalence between the driven post-yielding dynamics at fixed quenched disorder and quenched disorder averages of the non-driven system, along with memory formation.

v2: Expanded manuscript, improved abstract, new Appendix E & Fig. 6A (quenched disorder dependence of nonphononic modes)