Abstract

Inter-particle forces in amorphous solids such as glasses, colloids and granular material can be used to study jamming, force-chains¹ and other non-equilibrium phenomena. In thermal materials where nevertheless the mean positions are well defined on a given time-scale, effective inter-particle forces keep the particles “in place”. If one could deduce the related effective force-laws and therefore the potential and Hessian, the analysis of these material would be greatly simplified by the usage of tools hitherto reserved for a-thermal systems. Initial characterization of the effective forces was recently performed in simulation². Quite remarkably an emergence of effective many-body interactions is observed, even when the bare interactions are purely 2-body. The many-body nature of the effective force-laws also resolves the puzzle posed by recent studies³ that showed a quantitative match between 2D/3D measurements and the infinite dimension hard spheres mean-field prediction⁴.

[1] See cover of Phys. Rev. Lett. 116 Issue 7. [2] O. Gendelman, E. Lerner, Y.G. Pollack, I. Procaccia, C. Rainone and B. Riechers, Phys. Rev. E 94 , 051001® (2016). [3] For example: P. Charbonneau, J. Kurchan , G. Parisi, P. Urbani and F. Zamponi, Ann. Rev. Cond. Matt. Phys. 8 265-288 (2017). [4] G. Parisi, Y.G. Pollack, I. Procaccia, C. Rainone and M. Singh, In preparation.