Generating dense packings of hard spheres by soft interaction design

Thibaud Maimbourg, Mauro Sellitto, Guilhem Semerjian, Francesco Zamponi

SciPost Phys. 4, 039 (2018) · published 26 June 2018

Abstract

Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.

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Glasses Hard spheres Infinite dimension Liquids Packing

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