Memory Formation in Jammed Hard Spheres

Patrick Charbonneau and Peter K. Morse

Phys. Rev. Lett. 126, 088001 – Published 22 February 2021

Abstract

Liquids equilibrated below an onset condition share similar inherent states, while those above that onset have inherent states that markedly differ. Although this type of materials memory was first reported in simulations over 20 years ago, its physical origin remains controversial. Its absence from mean-field descriptions, in particular, has long cast doubt on its thermodynamic relevance. Motivated by a recent theoretical proposal, we reassess the onset phenomenology in simulations using a fast hard sphere jamming algorithm and find it to be both thermodynamically and dimensionally robust. Remarkably, we also uncover a second type of memory associated with a Gardner-like regime of the jamming algorithm.

Received 3 September 2020
Accepted 13 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.088001

Physics Subject Headings (PhySH)

Dynamical phase transitions Glass transition Jamming Phase transitions

Glasses Liquids

Replica methods

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Patrick Charbonneau ^1,2 and Peter K. Morse ^1,*

¹Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
²Department of Physics, Duke University, Durham, North Carolina 27708, USA

^*Corresponding author. peter.k.morse@gmail.com

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Issue

Vol. 126, Iss. 8 — 26 February 2021

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Images

Figure 1
(a) Schematic of the two-substep iterative jamming algorithm. (i) Inflation: particles (black disks) separated by minimum gap $h_{n}$ expand uniformly (red disks) until $h_{n}^{'}$ . (ii) Repulsion: an effective free energy is minimized until the minimum gap reaches $h_{n + 1} = h_{n}$ . The cycle is repeated until density converges at jamming. (b) The onset is clearly visible in $d = 3$ for all system sizes considered. Lines are fits to the phenomenological crossover form, Eq. (2). The thermodynamic $N \to \infty$ limit of the fit parameters (black line) shows that the onset appears well before the dynamical (mode-coupling) crossover (dashed black line). (c) Finite-size scaling of the jamming transition $ϕ_{J 0}$ below the onset (top), and finite-size scaling of the onset (below). Lines are fits to Eq. (1) and curves are vertically oset by a factor of $d^{2}$ for visual clarity.
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Figure 2
Infinite-system size onset curves for different dimensions can be collapsed, suggesting that the inherent structure onset exists in both the thermodynamic and the infinite-dimensional limits. Shaded regions give the standard error of Eq. (2) with 95% confidence intervals on parameters, and dashed lines denote $ϕ_{d}$ from Ref. [55]. The steady increase of $ϕ_{d}$ with dimension on this scale shows that $ϕ_{co} < ϕ_{d}$ . The collapse further supports the identification $ϕ_{on} \sim 0.9 ϕ_{co}$ . Inset: Scaling of $ϕ_{J 0}$ and $ϕ_{on}$ with $d$ , compared with those for the avoided dynamical transition $ϕ_{d}$ and the onset of non-Fickian diffusion $ϕ_{nf}$ from Ref. [55] reveals that both $ϕ_{nf}$ and $ϕ_{on}$ exhibit a trivial mean-field-like dimensional scaling down to physical dimensions, unlike $ϕ_{d}$ and $ϕ_{J 0}$ .
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Figure 3
The onset of the algorithmic slowdown at $ϕ_{G}$ is simultaneously characterized by three observables, which robustly identify a change in the crunching process. The results shown here for $d = 4$ with $ϕ_{eq} = 0.2$ are typical of other $d$ and $ϕ_{eq}$ . (a) At $ϕ_{G}$ , the distribution of gaps narrows significantly, such that the minimum gap most closely approaches the average gap. (b) The number of minimization loops necessary to complete the repulsion substep of the jamming algorithm grows precipitously, and is manually cut off at $τ = 2$ . (c) The correlation between contact networks $c_{i}$ for an unperturbed system at jamming and $c_{j}$ for a replica perturbed at $ϕ_{break}$ shows that systems perturbed before $ϕ_{G}$ (gray zone) end up with markedly different contact networks compared to systems perturbed beyond $ϕ_{G}$ (white zone). Increasing system size makes the effect more prominent and shifts the process to higher densities but nonetheless remain distinct from $ϕ_{J}$ [30]. (d) Taken together, these observations suggest that saddles start to dominate the landscape of the crunch algorithm around $ϕ_{G}$ , thus resulting in sluggish dynamics and a large contact network response to small perturbations in particle positions. In other words, a slightly perturbed system (i) jams as (iii), whereas the original system jams as (ii). This series of observations for an out-of-equilibrium algorithm is reminiscent of the Gardner-like behavior of quasistatic state followings in ultrastable glasses [59].
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Figure 4
(a) The algorithmic $ϕ_{G}$ in $d = 3$ , identified as in Fig. 3, shifts with system size. Inset: The low-density slope of $ϕ_{G}$ tends to a finite value as $N$ increases in all dimensions (dashed lines). Because the density dependence of $ϕ < ϕ_{on}$ seemingly persists in the thermodynamic limit, memory of the initial state appears upon crunching.
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