Light scattering in a non-equilibrium phonon gas

Light scattering spectrum from phonon-density fluctuations has been studied by extended thermodynamics of phonon gas. For hydrodynamic phonon regime, it has been found that the scattering spectrum essentially consists of two parts, one of which arises from equilibrated collective excitation of phonons, and the other of which arises from non-equilibrium, fast fluctuations due to collisions between individual phonons. At low temperature, where collisions between phonons are infrequent and local thermal equilibrium cannot be established within a length scale defined by the reciprocal of a scattering wave-vector, the spectrum cannot be separated into two components, and only one component due to unequilibrated fluctuations in phonon density persists. The theoretical spectral line shapes are in good agreement with the experimental light scattering spectra observed in many dielectric materials. Fits of the obtained expression to the experimental spectra that were observed in SrTiO(3) imply a possibility of second sound in this material.