Level statistics and Anderson delocalization in two-dimensional granular materials
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.
Cite
@article{arxiv.2008.07155,
title = {Level statistics and Anderson delocalization in two-dimensional granular materials},
author = {Ling Zhang and Yinqiao Wang and Jie Zheng and Aile Sun and Xulai Sun and Yujie Wang and Walter Schirmacher and Jie Zhang},
journal= {arXiv preprint arXiv:2008.07155},
year = {2021}
}
Comments
6 pages, 4figures