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arXiv · 2008.07155

Level statistics and Anderson delocalization in two-dimensional granular materials

Ling Zhang·Yinqiao Wang·Jie Zheng·Aile Sun·Xulai Sun·Yujie Wang·Walter Schirmacher·Jie Zhang
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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.

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Ling Zhang, Yinqiao Wang, Jie Zheng, Aile Sun, Xulai Sun, Yujie Wang, Walter Schirmacher, Jie Zhang. 2020-08-17. Level statistics and Anderson delocalization in two-dimensional granular materials. https://doi.org/10.1103/physrevb.103.104201

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