Anderson Localization in Disordered Vibrating Rods

Abstract

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.

10 pages, 6 figures

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• Small-World Disordered Lattices: Spectral Gaps and Diffusive Transport