During the project, substantial progress has been achieved.
First of all, a rather complete understanding of the Gardner transition was obtained. We now understand that, while the transition is common to all amorphous solids in the abstract limit of infinite spatial dimensions, in physical three-dimensional systems it is only observed in the vicinity of the “jamming” transition, which is characteristics of soft emulsions, colloids and grains. As a consequence, the vibrations of these systems are strongly anomalous: all atoms vibrate together in a “collective” way, but strongly different from the plane waves that characterize crystals. On the contrary, structural glasses (such as window glasses) do not show the transition. Their vibrations are mostly plane waves as in crystals, but occasionally, rare “localized” defects constituted by a few atoms can scatter these waves and induce anomalies. The distinction between “collective” and “localized” excitations is a crucial property of glasses, and the interplay of these two kinds of excitations can lead to a very rich phenomenology, as we discussed in Nature Communications 10, 5102 (2019).
Additional progress has been made by developing a theory for the vibration of non-spherical particles (such as M&M’s candies) around their jammed state, published in PNAS 115, 11736 (2018). This problem, which might look very academic, is actually very important because most granular systems are composed of non-spherical particles. Furthermore, friction originates from rough surface interactions between particles, and is potentially described by the same non-spherical framework, as we discuss in Physical Review Letters 124, 208001 (2020).
We also investigated quantum effects in very low-temperature glasses, which are dominated by localized defects that tunnel between two locally stable states because of quantum mechanical dynamics. We have presented, for the first time, a direct observation of tunnelling defects in a model for structural glass simulated in the computer, in Physical Review Letters 124, 225901 (2020). We confirmed that such defects are strongly suppressed in ultra-stable glasses prepared by slow annealing or vapor deposition, in quantitative agreement with experiment. This work opens the way for a more direct investigation of such defects, which are very important for quantum decoherence in glasses and thus relevant for applications, e.g. in quantum computing.
Finally, we worked on understanding the failure of glasses subjected to external loads, which happens at the so-called “yielding transition”. We extended mean field theory to describe a characteristic two-step yielding process observed in attractive colloids. We made progress in understand the universality class of yielding, by investigating variants of the random field Ising model that should belong to that class, which should provide important insight on the basic mechanisms for glass failure, again with important potential applications, see Physical Review Letters 129, 228002 (2022).
