# Simulation of the Phonon Drag of Point Defects in a Harmonic Crystal

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## Abstract

In the framework of quantum physical kinetics methods, an expression is formulated for the force acting on a point defect from the side of the nonequilibrium phonon subsystem under the conditions of phonon heat transfer. Based on the solution of the problem of phonon scattering by a mass defect of a harmonic crystal, the expression for the transition t-matrix is written in the framework of the Lifshitz method in the continuum approximation. Using the representation of the t-matrix in terms of the Green’s function of an ideal crystal, expressions for the partial coefficients of phonon drag in a cubic crystal are obtained. Based on the pole representation of the Green’s function, an expression is obtained for the partial coefficients in terms of the phonon dispersion law in the crystal. To execute a computational experiment, the Born–Karman phonon spectrum model was used, modified taking into account the conditions for the phonon spectrum at the boundary of the Brillouin cubic zone and the presence of sections of the “negative” dispersion. The size of these sections is characterized by the parameter *ε*. A method is proposed for calculating surface integrals over isofrequency surfaces based on the Samarsky method. For various values of the parameter, the integrals are calculated and the partial drag coefficients are calculated. An analysis of the drag coefficient of point defects by the flow of thermal phonons showed that, with the parameter values \( \varepsilon > 0.27 \), the drag force is directed against the heat flux. The asymmetry of the drag coefficient with respect to the sign of the defect power due to the effect of resonant phonon scattering is established.

## Keywords

Point defects Phonon drag Scattering matrix Harmonic crystal Resonant scattering## References

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