论文标题
二维颗粒材料的水平统计和安德森离域化
Level statistics and Anderson delocalization in two-dimensional granular materials
论文作者
论文摘要
与理论上的预测相反，二维无序材料中的所有波都是本地化的，仅在各向同性堵塞的二维无序无序的光弹性磁盘中，才能观察到安德森定位。更具体地说，我们已经进行了一个实验，以分析正常模式振动的水平统计数据。我们观察到低频玻色峰制度和高频制度中的本地化模式，在Debye频率低于Debye频率的情况下，将其定位模式。我们发现，在玻色子峰政权中，级别距离分布遵守高斯 - 正交 - 汇总（GOE）统计数据，即Wigner-Dyson分布，而在高频政权统计中的统计数字则观察到了。该方案与三维无序固体中的谐波振动激发相吻合。
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.
