This paper discusses the possibility of weak localization of the phonon modes in a nonideal harmonic crystal lattice whose separate layers are weakly coupled to each other. An expression is obtained for the diffusivity tensor. The role of inverse coherent scattering processes is studied. It is established that, when such processes occur under conditions of strong diagonal disorder in the region of relatively low frequencies, where the dispersion law of the phonon modes exhibits two-dimensional properties, substantial renormalization of the diffusivity can take place. The paper analyzes the situation that occurs under conditions of off-diagonal disorder when resonant-scattering impurity centers are present in the lattice. The question of the possible nature of the low-temperature plateau in the thermal conductivity of the complex crystals BSCCO and BSYCO is discussed.
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