Level statistics and Anderson delocalization in two-dimensional granular materials

TL;DR

This study experimentally investigates wave localization in two-dimensional granular materials, revealing a frequency-dependent transition from delocalized to localized modes, challenging the notion that all waves are localized in such systems.

Contribution

It provides the first experimental evidence of a crossover from delocalized to localized vibrational modes in 2D granular packings, with detailed level statistics analysis.

Findings

Delocalized modes in low-frequency regime with GOE statistics.

Localized modes in high-frequency regime with Poisson statistics.

Crossover frequency just below the Debye frequency.

Abstract

Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered granular packing of photoelastic disks. More specifically, we have performed an experiment in analyzing the level statistics of normal mode vibrations. We observe delocalized modes in the low-frequency boson-peak regime and localized modes in the high frequency regime with the crossover frequency just below the Debye frequency. We find that the level-distance distribution obeys Gaussian-Orthogonal-Ensemble (GOE) statistics, i.e. Wigner-Dyson distribution, in the boson-peak regime, whereas those in the high-frequency regime Poisson statistics is observed. The scenario is found to coincide with that of harmonic vibrational excitations in three-dimensional disordered solids.