Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects

TL;DR

This paper derives an exact microscopic expression for sound attenuation in low-temperature amorphous solids, emphasizing the role of non-affine displacements and enabling damping predictions from static configurations.

Contribution

It introduces a novel microscopic formula for sound damping that aligns with simulations and highlights the significance of non-affine effects in disordered solids.

Findings

Derived an exact expression for zero-temperature sound damping.

Validated the expression against independent simulations.

Showed non-affine displacements dominate sound attenuation at low temperatures.

Abstract

Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. The small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-affine displacements' contribution to the sound wave propagation coefficient coming from the frequency shell of the sound wave. Our expression involves only quantities that pertain to solids' static configurations. It can be used to evaluate the low temperature sound damping coefficients without directly simulating sound attenuation.