Nichtlineare Phonon-Phonon-Wechselwirkung in elastischen Nichtleitern

Abstract

For a simplified model we investigate the influence of anharmonicity of the lattice potential on the propagation of sound. In the low temperature region it is possible to describe the lattice dynamics by means of the theory of nonlinear elastic media. It is shown that three-phonon processes are possible even if the colliding phonons have the same polarization. At low temperature the lifetime of a single lattice oscillation is decisively influenced by the processL+L⇄L, whereL stands for longitudinal polarization. By means of temperature dependent doubletime Green functions we investigate energy shift and damping rate of impressed phonons. The temperature dependent frequency shift is interpreted as a temperature dependence of the elasticity modulus. Comparison yields satisfactory agreement between theory and experiment.