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

TYPEStatistical & Bio Seminar
Speaker:Yoav G. Pollack
Affiliation:Weizmann Institute
Organizer:Yariv Kafri
Time:14:30 - 15:30
Location:Lidow Nathan Rosen (300)



A large effort has been devoted in the last decade to the development of an infinite-dimensional mean-field theory for the jamming transition of hard spheres[1]. The lastest studies on this topic indicate that the predictions of this theory (e.g. scaling exponents) match simulation measurements in 2D/3D suprisingly well[2], seemingly suggesting that the infinite-dimensional theory is relevant for realistic systems. Our current work addresses the puzzle of this lack of strong dimensional dependence usually observed in critical phenomena.

We use effective inter-particle forces to study the jamming transition. In thermal materials where nevertheless the mean positions are well defined on a given time-scale, these effective forces are what keeps the particles ”in place”. In continuation to a recent study in which emergence of effective many-body forces was observed[3], our current work quantifies the amount of non-binary effective interactions as a function of the closeness of jamming. We conclude that for hard spheres the effective forces are binary only at jamming, similarly to the infinite-dimensional theory and propose that this explains the match of theory and measurements. Further study of the effective forces implies that the predictions of the infinite-dimensional theory of hard spheres should be inapplicable to more realistic particles which are never absolutely hard[4].


    1. [1]  For example: A. Altieri , S. Franz, G. Parisi, Journal of Statistical Mechanics: Theory and Experiment, 2016 093301 (2016).

    1. [2]  For example: P. Charbonneau, J. Kurchan , G. Parisi, P. Urbani and F. Zamponi, Ann. Rev. Cond. Matt. Phys. 8 265-288


    1. [3]  O. Gendelman, E. Lerner, Y.G. Pollack, I. Procaccia, C. Rainone and B. Riechers, Phys. Rev. E 94, 051001(R) (2016).

    1. [4]  G. Parisi, Y.G. Pollack, I. Procaccia, C. Rainone and M. Singh, Submitted for publication (arXiv:1709.01607).