Hydrodynamics of amorphous solids with application to the light-scattering spectrum

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Abstract
The set of hydrodynamic equations for a pure one-component amorphous solid is considered here on the basis of the formalism introduced earlier. The solution to the linearized equations can be represented in terms of eight hydrodynamic modes. These modes consist of two longitudinal diffusion modes, two longitudinal sound modes, and two twofold degenerate transverse sound modes. The two diffusive modes are interpretated as heat flow and "configurational rearrangement." The two are coupled, however, via a thermal diffusion of the configurational rearrangement. The spectrum of light scattered from such a system is calculated from these equations. The polarized Rayleigh peak consists of two Lorentzian lines similar to that observed in a binary mixture. The configurational rearrangement in the glass plays the role of concentration diffusion in the binary mixture. The Brillouin peak has the usual interpretation of a sound-propagation mode with an additional attenuation due to the coupling to configurational rearrangement. The transverse sound modes contribute to the depolarized spectrum.