Athermal fluctuations in disordered crystals

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.

arXiv comment5 pages, 4 figures, +Supplemental Material

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Cited by in corpus (8)

• Emergent Elasticity in Amorphous Solids
• Contact network changes in ordered and disordered disk packings
• Jamming and replica symmetry breaking of weakly disordered crystals
• Disorder Perturbation Expansion for Athermal Crystals
• Long-range correlations in pinned athermal networks
• Displacement correlations in disordered athermal networks
• Athermal fluctuations in three dimensional disordered crystals
• First contact breaking distributions in strained disordered crystals