Microscopic theory of sound attenuation in amorphous solids from nonaffine motions
Abstract
We present a microscopic derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory, which is entirely microscopic and takes into account the nonaffine displacements in transverse waves, is able to predict both the ubiquitous lowenergy diffusive damping $\sim k^{2}$, as well as the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevintype) damping in particle motion (which arises from anharmonicity), and to the nonaffine correction to the static shear modulus, whereas the Rayleigh damping emerges in the limit of low anharmonicity, consistent with previous observations and macroscopic models. The calculation is demonstrated on the important example of transverse waves, although it is straightforward to generalize the results to longitudinal waves.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.13446
 Bibcode:
 2021arXiv211013446B
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Materials Science;
 Condensed Matter  Statistical Mechanics
 EPrint:
 v1: 7 pages, 2 figures