Improved calculation of vibrational mode lifetimes in anharmonic solids – Part II: Numerical results

In a two-part publication, we propose and analyze a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. In the first part, we derived the lifetime of vibrational modes in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. In this second part, we present a numerical analysis of a simple anharmonic model of lattice vibrations which exhibits two regimes of behavior, at low temperature and at high temperature. Our results show that, for this simple model, the mode lifetime as a function of temperature and wavevector can be simply approximated as a function of the shift in frequency from the harmonic limit. We next compare these calculations, obtained using both Monte Carlo and computationally intensive molecular dynamics, with those using the lowest order moment formalism from the Part I. We show that, in the high temperature regime, the lowest order approximation gives a reliable approximation to the calculated lifetimes. The results also show that extension to at least fourth moment is required to obtain reliable results over a full range of temperatures.