Generating dense packings of hard spheres by soft interaction design

TL;DR

This paper introduces a method to generate dense disordered sphere packings in high dimensions by designing isotropic interaction potentials, achieving densities close to theoretical bounds through inverse optimization of glass transition properties.

Contribution

It presents a novel approach to optimize sphere packings in high dimensions by tuning interaction potentials based on thermodynamic and dynamical insights.

Findings

Achieves packing densities near $7 d 2^{-d}$ in high dimensions.

Demonstrates that many disordered packings can be constructed via potential design.

Utilizes recent exact formulations of liquid thermodynamics in infinite dimensions.

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.