Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?

G. Zhang; F. H. Stillinger; S. Torquato

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arXiv · 1705.04415

Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?

G. Zhang·F. H. Stillinger·S. Torquato

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Abstract

The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-size limit (e.g., equilibrium liquid states) is non-zero. Such "hole" statistics are intimately linked to the physical properties of the system. Disordered "stealthy' many-particle configurations in $d$-dimensional Euclidean space $\mathbb{R}^d$ are exotic amorphous states of matter that lie between a liquid and crystal that prohibit single-scattering events for a range of wave vectors and possess no Bragg peaks [Torquato et al., Phys. Rev. X, 2015, 5, 021020]. In this paper, we provide strong numerical evidence that disordered stealthy configurations across the first three space dimensions cannot tolerate arbitrarily large holes in the infinite-system-size limit, i.e., the hole probability has compact support. This structural "rigidity" property apparently endows disordered stealthy systems with novel thermodynamic and physical properties, including desirable band-gap, optical and transport characteristics. We also determine the maximum hole size that any stealthy system can possess across the first three space dimensions.

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G. Zhang, F. H. Stillinger, S. Torquato. 2017-05-12. Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?. https://arxiv.org/abs/1705.04415

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