Evaluation of Lattice Thermal Conductivity for a Disordered One-Dimensional Harmonic Crystal

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Abstract
Thermal conductivity has been calculated for the case of a disordered one-dimensional insulating crystal with harmonic forces. The calculation is carried through exactly, to lowest order in the concentration of impurities, using propagator formalism to evaluate the Kubo formula for transport coefficients. The contribution of "local mode" vibrations to the conductivity is also calculated. This contribution is found to be of higher order in the concentration of impurities, but to display a distinctive temperature dependence.