Abstract
The time evolution of the atomic displacement field in a dielectric crystal subjected to an external force is studied in the domain of linear response by means of imaginary time Green's functions. For slowly varying disturbances two coupled equations have to be solved: a differential equation for the amplitude of an acoustic wave and a linearized Boltzmann equation. The latter results from the integral equation for the vertex part and includes an additional integral operator. The collision equation is solved for different relative magnitudes of the sound frequency and the frequencies for normal and Umklapp processes using the method developed by Weiss. Some of the expressions showing up in the velocity and damping of the sound wave are estimated numerically for rare gases with two-body forces in the form of the Morse potential.
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