2020/08/17 by Ling Zhang, Yinqiao Wang, Jie Zheng +5
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Anderson impurity model #Condensed matter physics #Delocalized electron #Electron #Exponent #Gaussian #Mathematics #Nonlinear Photonic Systems #Physics #Poisson distribution #Quantum mechanics #Random lasers and scattering media #Scaling #Seismic Waves and Analysis #Statistical physics #Statistics #Tsallis statistics #cond-mat.soft
paper · pdf · doi:10.1103/physrevb.103.104201
published as Phys. Rev. B 103, 104201 (2021) · 6 pages, 4figures
arxiv created 2020/08/17 · openalex created_date 2020/08/21 · openalex publication_date 2021/03/02 · arxiv updated 2021/03/10 · openalex updated_date 2026/08/05
Contrary to the theoretical predictions of one-parameter scaling theory 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 find that the level-distance distribution obeys Gaussian-orthogonal-ensemble (GOE) statistics of the Wigner-Dyson classification in the low-frequency (boson-peak) and intermediate-frequency regimes, whereas in the high-frequency regime Poisson statistics are observed. This means that at low and intermediate frequencies we have delocalized modes, and only at very high frequencies do localized modes exist. Evaluating the system-size dependence of the delocalization-localization crossover frequency, we obtain evidence of a true transition with a mobility edge at 80% of the Debye frequency and a value of the critical correlation-length exponent \ensuremathν\ensuremath∼ 1.66 that is similar to that of the three-dimensional electronic Anderson model. We argue that for force-constant disorder one-parameter scaling might not be applicable.