Emergent Many-body Interactions Suggest Inapplicability in Practice of Hard Sphere Theory

Inter-particle forces in amorphous solids such as glasses, colloids and granular material can be used to study phenomena such as jamming and force-chains. So far, no generally applicable methods exist for measuring the forces between each and every particle in the system. Our recently developed methods aim to x this unfortunate situation in both a-thermal and thermal systems, and produce some interesting insights as to the nature of these forces. In the a-thermal case all that is required for nding the force-law are the xed particle positions and the pressure. The method is shown to accurately recover the force-law in simulation. In the thermal case, we are developing a method to extract an eective potential, using the mean positions. This will allow for analysis of thermal systems using tools hitherto reserved for a-thermal ones, and thereby prediction of thermodynamic properties, study of stability, etc. Quite remarkably we observe the emergence of eective many-body interactions, even when the bare interactions are purely 2-body. This resolves the puzzle posed by recent studies that showed a quantitative match between 2D/3D measurements and the innite dimension mean-eld prediction.