Calculation of mode lifetimes in weakly anharmonic solids using self-consistent ensemble eigenstates of the Liouvillian

Journal Article · 02 August 2020 · Computational Materials Science

DOI: https://doi.org/10.1016/j.commatsci.2020.109918 · OSTI ID:1851081

Dickel, D. ^[1]; Daw, M. S. ^[2]

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1. Mississippi State Univ., Starkville, MS (United States). Center for Advanced Vehicular Systems; Mississippi State Univ., Starkville, MS (United States)
2. Clemson Univ., SC (United States). Dept. of Physics and Astronomy

Recent schemes for the efficient calculation of vibrational mode frequencies and lifetimes in weakly anharmonic systems such as solid crystal structures have shown promise, with simple relationships being observed between low order moments of the Liouvillian and the observed lifetime. While only shown empirically, two parameters seemed sufficient to determine the lifetime to high accuracy over a large range of temperatures for a few simple low degree of freedom models and a Lennard–Jones solid. In this paper we analytically reproduce the numerically observed relationship using a few generally applicable assumptions about the density of states. This advance is made by studying the autocorrelation based on an “ensemble eigenstate” of the Liouvillian. We propose the use of this ensemble eigenstate as the basis for autocorrelations to simplify calculations in richer systems. Finally, an analysis is also performed of the relationship between canonical and microcanonical autocorrelation functions and a long standing error in the long time behavior of such functions originally presented by Sen, Sinkovits, and Chakravarti is corrected.

• Research Organization: Clemson Univ., SC (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: SC0008487
• OSTI ID: 1851081
• Journal Information: Computational Materials Science, Journal Name: Computational Materials Science Journal Issue: C Vol. 185; ISSN 0927-0256
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English