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On the rigidity of a hard sphere glass near random close packing

Carolina Brito·Matthieu Wyart
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Abstract

We study theoretically and numerically the microscopic cause of the mechanical stability of hard sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard sphere interaction can be described by an effective potential which is exactly logarithmic at the random close packing $ϕ_c$. This allows to define normal modes, and to apply recent results valid for elastic networks: mechanical stability is a non-local property of the packing geometry, and is characterized by some length scale $l^*$ which diverges at $ϕ_c$ [1, 2]. We compute the scaling of the bulk and shear moduli near $ϕ_c$, and speculate on the possible implications of these results for the glass transition.

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Carolina Brito, Matthieu Wyart. 2006-10-27. On the rigidity of a hard sphere glass near random close packing. https://doi.org/10.1209/epl%2Fi2006-10238-x

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