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A canonical quantization procedure is applied to the interaction of elasticwaves --phonons-- with infinitely long dislocations that can oscillate about anequilibrium, straight line, configuration. The interaction is implementedthrough the well-known Peach-Koehler force. For small dislocation excursionsaway from the equilibrium position, the quantum theory can be solved to allorders in the coupling constant. We study in detail the quantum excitations ofthe dislocation line, and its interactions with phonons. The consequences forthe drag on a dislocation caused by the phonon wind are pointed out. We computethe cross-section for phonons incident on the dislocation lines for anarbitrary angle of incidence. The consequences for thermal transport areexplored, and we compare our results, involving a dynamic dislocation, withthose of Klemens and Carruthers, involving a static dislocation. In our case,the relaxation time is inversely proportional to frequency, rather thandirectly proportional to frequency. As a consequence, the thermal transportanisotropy generated on a material by the presence of a highly-oriented arrayof dislocations is considerably more sensitive to the frequency of eachpropagating mode, and therefore, to the temperature of the material.

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The scattering of phonons by infinitely long quantum dislocations  segments and the generation of thermal transport anisotropy in a solid  threaded by many parallel dislocations