English

Self-consistent theory for sound propagation in a simple model of a disordered, harmonic solid

Disordered Systems and Neural Networks 2024-12-20 v2 Statistical Mechanics

Abstract

We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the interparticle distances, i.e the Euclidean random matrix model of Mezard et al. [Nucl. Phys. 559B, 689 (1999)]. The derivation of the theory combines two exact projection operator steps and a factorization approximation. Within our approach the square of the speed of sound is non-negative. The unjamming transition manifests itself through vanishing of the speed of sound.

Keywords

Cite

@article{arxiv.2407.13039,
  title  = {Self-consistent theory for sound propagation in a simple model of a disordered, harmonic solid},
  author = {Grzegorz Szamel},
  journal= {arXiv preprint arXiv:2407.13039},
  year   = {2024}
}

Comments

Revised version; accepted for publication in Phys. Rev. E

R2 v1 2026-06-28T17:45:15.536Z