Stability and Degrees of Freedom

Recent advances in both the jamming and glass communities have led to the development of new protocols that can create particularly stable solids. Such systems, whether they be physical systems created using vapor-deposition or numerical systems created using the SWAP or breathing algorithms, exist in exceptionally deep energy minima that are marked by the absence of low-frequency modes. We introduce new protocols for creating stable jammed packings that work by first introducing and then subsequently removing degrees of freedom such as particle size or interparticle stiffness. We find that different choices for the degrees of freedom can lead to very different gains in the stability of the packing. At least in one case, those degrees of freedom that can push a system to much deeper energy minima are also the ones responsible for the rigidity transition itself.