An out-of-equilibrium Gardner-like transition in compressed hard sphere liquids

Hard sphere liquids, when compressed, form jammed structures whose properties depend both on the density of the original liquid and on the compression scheme. Liquids prepared below an onset density jam at the same density, while those prepared above that onset jam at a density that increases with the initial density. This process, whereby the solid remembers its liquid state, is called inherent state memory. We have recently shown that during the compression, the dynamics become markedly sluggish beyond a certain point. This slowdown coincides with the contact network beginning to form, suggesting a first appearance of saddles in the effective compression (optimization) landscape. This transition appears related to the Gardner transition seen in both quasi-equilibrium hard spheres and in mean-field models, albeit out-of-equilibrium. In this talk, we will explore the properties of this dynamical Gardner-like transition--itself is a second form of memory--and its relationship to the aforementioned onset. We also consider its robustness to changes of the model. Such characterization gives hope for understanding Gardner-like phenomena in experimental systems and paves the way for their theoretical understanding.