Anderson transition of three dimensional phonon modes

TL;DR

This paper investigates the Anderson transition in three-dimensional phonon modes through numerical analysis, estimating critical exponents and comparing mode statistics with electron systems, revealing universality class similarities.

Contribution

It provides the first numerical estimation of the critical exponent for phonon mode localization and links phonon mode statistics to electron system universality classes.

Findings

Critical exponent estimated for phonon localization length divergence.

Mode statistics match energy level statistics of disordered electron systems.

Phonon Anderson transition belongs to the orthogonal universality class.

Abstract

Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is shown to be in excellent agreement with the energy level statistics of the disrodered electron system belonging to the orthogonal universality class.