Kinetic equation taking into account the finite nature of the lifetime of thermal phonons and the thermal conductivity of dielectrics

A theory is developed for the low-temperature thermal conductivity of dielectrics, in which the relaxation of longitudinal longwave phonons is determined by Simons' mechanism. A kinetic equation is obtained which takes into account the broadening of the energy spectrum associated both with collisions between thermal phonons and with their scattering by local defects of the crystal lattice. It is shown that longitudinal longwave phonons make a considerable contribution to heat transfer in bulk dielectric specimens. This leads to a change in the value of the coefficient of thermal conductivity and its dependence on temperature, impurity concentration, and other characteristic parameters of the problem.

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