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

TL;DR

This paper tests a new method for calculating vibrational mode lifetimes using low moments of the Liouvillian, demonstrating effectiveness in simple models with single-peaked vibrational densities across temperatures.

Contribution

It introduces and validates a Liouvillian moment-based approximation scheme for vibrational mode lifetime calculations in low-dimensional anharmonic systems.

Findings

Fourth-moment approximation performs well for single-peaked vibrational densities.

Method is effective across a range of temperatures.

Approximations based on ensemble averages are practical for simple models.

Abstract

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.