Improved Calculation of Vibrational Mode Lifetimes in Anharmonic Solids - Part I: Theory

TL;DR

This paper introduces a theoretical framework for calculating vibrational mode lifetimes in anharmonic solids using a recursion method and Monte Carlo, aiming for more efficient and practical computations.

Contribution

It develops a formal foundation based on the Liouvillian and moments analysis, enabling shorter and more practical lifetime calculations for vibrational modes.

Findings

Framework based on moments of the power spectrum

Monte Carlo evaluation of ensemble averages

Potential for significantly shorter calculations

Abstract

We propose here a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. From this we derive the lifetime of a vibrational mode 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. These insights should lead to significantly shorter calculations compared to current methods. A companion piece presents numerical results.