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Relaxation Dynamics of Non-Brownian Spheres Below Jamming

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Abstract

We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless soft spheres below jamming in spatial dimensions \(d=2\), 3, 4, and 8, and in the mean-field Mari–Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite d logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all d in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.

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Acknowledgements

We are grateful to M. Cates, H. Ikeda, P Olsson, M. Wyart, and F. Zamponi for useful discussions. This work was supported by a grant from the Simons Foundation (Grant No. 454933, L. B.) and JSPS KAKENHI grants (Nos. 18H05225, 19H01812, 20H01868, and 20H00128, A. I.).

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Authors and Affiliations

  1. Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095, Montpellier, France

    Yoshihiko Nishikawa & Ludovic Berthier

  2. Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo, 153-8902, Japan

    Atsushi Ikeda

  3. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK

    Ludovic Berthier

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  1. Yoshihiko Nishikawa
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Correspondence to Yoshihiko Nishikawa.

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Communicated by Andrea Liu.

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Nishikawa, Y., Ikeda, A. & Berthier, L. Relaxation Dynamics of Non-Brownian Spheres Below Jamming. J Stat Phys 182, 37 (2021). https://doi.org/10.1007/s10955-021-02710-8

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