Marginally jammed states of hard disks in a one-dimensional channel

Abstract

We have studied a class of marginally jammed states in a system of hard disks confined in a narrow channel---a quasi-one-dimensional system---whose exponents are not those predicted by theories valid in the infinite dimensional limit. The exponent $\gamma$ which describes the distribution of small gaps takes the value $1$ rather than the infinite dimensional value $0.41269\dots$. Our work shows that there exist jammed states not found within the tiling approach of Ashwin and Bowles. The most dense of these marginal states is an unusual state of matter that is asymptotically crystalline.

arXiv comment8 pages, 8 figures; Fig. 3 updated; new discussion of polydispersity

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• A renewal approach to configurational entropy in one dimension
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• On the structure factor of jammed particle configurations on the one-dimensional lattice