Interaction-driven relaxation of two-level systems in glasses

We study how the elastic interaction of two-level systems contributes to their relaxational motion. Evaluating the Mori-Zwanzig memory function in terms of a perturbation series in powers of the couplings J(ij), we find a null result at second order, which means that interacting pairs of two-level systems do not give rise to relaxation, yet a finite relaxation rate does occur in fourth order; i.e., a diffusive band is formed by resonant triples. Our results provide a simple explanation for several puzzling experimental observations. Regarding the temperature dependence of the sound velocity delta v similar to lnT in the kHz range, we find that its slope below and above the maximum takes opposite signs but the same absolute value, in agreement with the measured ratio 1: - 1. Below the relaxation plateau, the internal friction is shown to vary linearly with T, in agreement with experiment.