Athermal fluctuations in disordered crystals

• Published in: arXiv.org
• Main Authors: Acharya, Pappu, Sengupta, Surajit, Chakraborty, Bulbul, Kabir Ramola
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.07.2020
• Subjects: Computer simulation; Disks; Perturbation; Physics - Soft Condensed Matter; Physics - Statistical Mechanics; Polydispersity; Variation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1910.06352

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.