Absence of Hyperuniformity in Amorphous Hard-Sphere Packings of Nonvanishing Complexity

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    Abstract

    We relate the structure factor
    S
    (
    k

    0
    )
    in a system of jammed hard spheres of number density
    ρ
    to its complexity per particle
    Σ
    (
    ρ
    )
    by the formula
    S
    (
    k

    0
    )
    =

    1
    /
    [
    ρ
    2
    Σ
    ′′
    (
    ρ
    )
    +
    2
    ρ
    Σ

    (
    ρ
    )
    ]
    . We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find
    Σ
    (
    ρ
    )
    and
    S
    (
    k
    )
    analytically. Hyperuniformity, which is the vanishing of
    S
    (
    k

    0
    )
    , will therefore not occur if the complexity is nonzero. An example is given of a jammed state of hard disks in a narrow channel which is hyperuniform when generated by dynamical rules that produce a nonextensive complexity.
    Original languageEnglish
    Article number075503
    JournalPhysical Review Letters
    Volume121
    Issue number7
    Early online date17 Aug 2018
    DOIs
    Publication statusPublished - 17 Aug 2018

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