2024/05/10 by Florian Vogel, Vogel, Florian, Philipp Baumgärtel +3
Engineering · Materials Science · #FOS: Physical sciences #Metallic Glasses and Amorphous Alloys #Phase-change materials and chalcogenides #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Thin-Film Transistor Technologies
paper · pdf · doi:10.48550/arxiv.2405.06537
openalex publication_date 2024/05/10 · openalex created_date 2024/05/14 · openalex updated_date 2026/07/28
We study amorphous solids with strong elastic disorder and find an un-jamming instability that exists, inter alia, in an harmonic model built using Euclidean random matrices (ERM). Employing the Zwanzig-Mori projection operator formalism and Gaussian factorization approximations, we develop a first-principles, self-consistent theory of transverse momentum correlations in athermal disordered materials, extending beyond the standard Born approximation. The vibrational anomalies in glass at low temperatures are recovered in the stable solid limit, and floppy modes lacking restoring forces are predicted in unstable states below the jamming transition. Near the un-jamming transition, the speed of sound v0^⊥ vanishes with ∝ √ε, where ε denotes the distance from the critical point. Additionally, the density of states develops a plateau, independent of ε above a frequency ω_* which vanishes at the transition, ω_*∝ |ε|. We identify a characteristic length scale in the un-jammed phase, λ-^⊥∝1/√ε, indicating the distance over which injected momentum remains correlated. We confirm the theoretical predictions with numerical solutions of a scalar ERM model, demonstrating overall good qualitative and partly quantitative agreement.