  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.
