{
  "id": "2407.13039",
  "version": "v1",
  "published": "2024-07-17T22:11:34.000Z",
  "updated": "2024-07-17T22:11:34.000Z",
  "title": "Self-consistent theory for sound propagation in a simple model of a disordered, harmonic solid",
  "authors": [
    "Grzegorz Szamel"
  ],
  "comment": "13 pages",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-17T22:11:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-consistent theory",
      "sound propagation",
      "simple model",
      "harmonic solid",
      "exact projection operator steps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}