Sound attenuation in low temperature amorphous solids is primarily determined by non-affine displacements

We analyze sound attenuation in low temperature classical amorphous solids. Starting from the microscopic equations of motion we derive an exact expression for the zero-temperature sound damping coefficient. We use computer simulations of glasses of widely varying stability to verify that the sound damping coefficients calculated from our expression agree with results from direct simulations of sound damping. To get some physical understanding of the content and the meaning of our expression we analyze it in the limit of small wavevectors. We find 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 approach can be used to evaluate the low temperature sound damping coefficients without directly simulating sound attenuation.