Correlations in optical phonon spectra of complex solids

TL;DR

This paper investigates spectral correlations in optical phonon spectra of complex solids using Wigner-Dyson statistics, revealing predominantly GUE-type behavior influenced by crystal symmetry and Brillouin zone location.

Contribution

It introduces an analysis of spectral correlations in complex solid phonons using random matrix theory, highlighting the GUE dominance despite real force constants.

Findings

Spectral correlations follow GUE statistics depending on zone location.

Analytic and numerical results show crossover from GOE to GUE.

Force constants being real does not prevent GUE-like spectral behavior.

Abstract

Spectral correlations in the optical phonon spectrum of a solid with a complex unit cell are analysed using the Wigner-Dyson statistical approach. Despite the fact that all force constants are real, we find that the statistics are predominantly of the GUE type depending on the location within the Brillouin zone of a crystal and the unit cell symmetry. Analytic and numerical results for the crossover from GOE to GUE statistics are presented.