Carolina Brito, Giorgio Parisi, Francesco Zamponi
We consider a system of hard spheres close to jamming, where translation invariance is broken by pinning a randomly chosen set of particles. We show that the jamming transition is not affected by random pinning: the jamming density is only slightly reduced, a generalized isostaticity condition holds, and the typical structural signatures of jamming are unchanged. However, random pinning has a dramatic effect on the low-frequency vibrational spectrum of the packings: the softest modes are stabilized by pinning, in such a way that their typical frequency does not vanish anymore at the jamming transition. In this way we unveil the typical length scale of the soft modes of the unpinned system, and we show that their physics must be intimately related with the translational symmetry.
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http://arxiv.org/abs/1205.6007
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