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.
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