Improved calculation of vibrational mode lifetimes in anharmonic solids - Part III: Extension to fourth moment

A recent scheme for calculating approximate vibrational mode lifetimes in solids (Dickel and Daw, 2010) [1,2] is extended to the next level (fourth-moment). The extension is tested in two cases: (1) simple, low-dimensional anharmonic systems, and (2) on a simple lattice model of vibrations. We show that, for systems where the mode-resolved density of states is well-approximated by a single broadened peak, the fourth-moment approximation works well over a wide range of temperatures.