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Abstract
摘要
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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[1]distance distribution obeys Gaussian-Orthogonal-Ensemble (GOE) statistics of the Wigner-Dyson classification, in the low-frequency (boson-peak) and intermediate frequency regime, whereas in the high-frequency regime Poisson statistics are observed. This means that at the low and intermediate frequencies we have delocalized modes, and only at the very high frequencies localized modes exist. Evaluating the system-size dependence of the delocalization-localization crossover frequency we obtain evidence for a true transition with a mobility edge at 80% of the Debye frequency and a value of the critical correlation-length exponent ν ~1.66 being similar to that of the three-dimensional electronic Anderson model. We argue that for force-constant disorder one-parameter scaling might not be applicable.
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