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In a two-part publication, we propose and analyze a formal foundation forpractical calculations of vibrational mode lifetimes in solids. The approach isbased on a recursion method analysis of the Liouvillian. In the first part, wederived the lifetime of vibrational modes in terms of moments of the powerspectrum of the Liouvillian as projected onto the relevant subspace of phasespace. In practical terms, the moments are evaluated as ensemble averages ofwell-defined operators, meaning that the entire calculation is to be done withMonte Carlo. In this second part, we present a numerical analysis of a simpleanharmonic model of lattice vibrations which exhibits two regimes of behavior,at low temperature and at high temperature. Our results show that, for thissimple model, the mode lifetime as a function of temperature and wavevector canbe simply approximated as a function of the shift in frequency from theharmonic limit. We next compare these calculations, obtained using both MonteCarlo and computationally intensive molecular dynamics, with those using thelowest order moment formalism from the Part I. We show that, in thehigh-temperature regime, the lowest order approximation gives a reliableapproximation to the calculated lifetimes. The results also show that extensionto at least fourth moment is required to obtain reliable results over a fullrange of temperatures.

Improved Calculation of Vibrational Mode Lifetimes in Anharmonic Solids - Part II: Numerical Results