Nonlocal hydrodynamics of phonon gas in dielectrics

It is shown that for certain dispersion laws of transverse vibrations, realizable in dielectric crystals of high and low symmetry, the nature of hydrodynamic effects in these dielectric crystals changes considerably. Thermal phonons, as usual, are the carriers of energy and momentum, whereas “viscosity” is determined by the longitudinal, long-wave phonons, carrying energy and momentum over distances comparable with the characteristic dimension of the system. Under these conditions the hydrodynamic variables obey an integral equation, whose structure depends on the dispersion law properties of transverse vibrations. The calculated temperature dependences of the thermal conductivity and second sound attenuation coefficients are close to the experimental observations.

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