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We derive Quantum kinetic equationKinetic equationquantum kinetic equation for phonons and reveal the important role of the Umklapp processesUmklappUmklapp process. We solve the kinetic equation by Chapman–Enskog methodChapman-EnskogChapman-Enskog methodMethodChapman-Enskog method and calculate the phonon relaxation timeTimerelaxation time in \(\tau \)-approximation. We establish different temperature regimes for the phonon thermal conductivityThermo-conductivityphonon thermo-conductivity coefficientCoefficientthermo-conductivity coefficientThermo-conductivity coefficient in the dielectric crystalDielectricdielectric crystal including diffusive and ballistic (Knudsen) regime.

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Lecture 13. Phonon Thermal Conductivity in Crystals

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  • 发表日期：

    2026年

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  • Maxim Kagan

摘要

We derive Quantum kinetic equationKinetic equationquantum kinetic equation for phonons and reveal the important role of the Umklapp processesUmklappUmklapp process. We solve the kinetic equation by Chapman–Enskog methodChapman-EnskogChapman-Enskog methodMethodChapman-Enskog method and calculate the phonon relaxation timeTimerelaxation time in \(\tau \)-approximation. We establish different temperature regimes for the phonon thermal conductivityThermo-conductivityphonon thermo-conductivity coefficientCoefficientthermo-conductivity coefficientThermo-conductivity coefficient in the dielectric crystalDielectricdielectric crystal including diffusive and ballistic (Knudsen) regime.