Jamming transition of randomly pinned systems

TL;DR

This paper investigates how random pinning affects the jamming transition in hard sphere systems, revealing that isostatic packings remain largely unaffected while hyperstatic packings are significantly altered.

Contribution

It introduces two protocols for generating jammed packings with random pinning and compares their effects on isostatic and hyperstatic systems, highlighting the role of constraints.

Findings

Isostatic jamming density slightly reduced by pinning

Vibrational modes remain unchanged in isostatic packings

Hyperstatic packings show increased stability and shifted vibrational modes

Abstract

We consider a system of hard spheres close to jamming, where translation invariance is broken by pinning a randomly chosen set of particles. Using two different protocols, we generate two kinds of packings at the jamming point, isostatic and hyperstatic packings. In the case where the packings are isostatic, jamming transition is not affected by random pinning: the jamming density is only slightly reduced, a generalized isostaticity condition holds, the system is marginally rigid over the entire glass phase, and the typical structural signatures of jamming are unchanged. Besides, random pinning does not have effect on the vibrational modes of the amorphous system, at least on the time and length scale that we are able to probe. For packings that are hyperstatic at jamming, the microscopic properties of the system are strongly affected by the random pinning: the frozen degrees of freedom introduce an excess of constraints that drives the system far from the mechanical marginality conditions and stabilize the low frequency modes of the system, shifting them to higher frequencies. The distance from the isostatic point seems to be the only relevant parameter in the system in both cases. These two cases are in contrast with the behavior of the plane waves of a crystal: the whole spectrum in this case is shifted to higher frequencies as soon as some particles are pinned.