Athermal fluctuations in disordered crystals

TL;DR

This paper investigates athermal disordered crystals, revealing unique force fluctuation behaviors due to local force balance, and develops a perturbation theory to predict their properties, validated by simulations.

Contribution

It introduces a disorder perturbation expansion for athermal disordered crystals, deriving exact results for force fluctuations and coordination scaling.

Findings

Force fluctuations are constrained and non-Gaussian.

Derived exact distributions for force fluctuations.

Predicted and verified scaling of coordination with polydispersity.

Abstract

We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.