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Using low moments of the Liouvillian to calculate mode lifetimes in low dimensional models

A recent proposal for practical calculation of vibrational mode lifetimes is tested on simple, low-dimensional anharmonic models. The proposed scheme approximates the mode lifetime in terms of ensemble averages of specific functions in phase-space; various levels of approximation correspond to ensemble moments of the Liouvillian. It is shown that, for systems where the vibrational density of states is well-approximated by a single broadened peak, the fourth-moment approximation works well over the full range of temperature.